From b38d42e47fc72d09a122956da8f0ab263af98c70 Mon Sep 17 00:00:00 2001 From: kazewong Date: Mon, 5 Aug 2024 16:57:46 -0400 Subject: [PATCH 01/31] update prior system --- docs/tutorials/naming_system.md | 0 docs/tutorials/prior_system.md | 15 +++++++++++++++ 2 files changed, 15 insertions(+) delete mode 100644 docs/tutorials/naming_system.md create mode 100644 docs/tutorials/prior_system.md diff --git a/docs/tutorials/naming_system.md b/docs/tutorials/naming_system.md deleted file mode 100644 index e69de29bb..000000000 diff --git a/docs/tutorials/prior_system.md b/docs/tutorials/prior_system.md new file mode 100644 index 000000000..e644d18aa --- /dev/null +++ b/docs/tutorials/prior_system.md @@ -0,0 +1,15 @@ +# Jim's naming and transform system + +The parameterization of some fundamental quantities can have significant impacts on the performance of the sampler. For example, the masses can be parameterized in the component mass spaces $\mathcal{M}_1$-$\mathcal{M}_2$ or chirp mass-mass ratio $\mathcal{M}_c$-$q$. Because of the strong correlation in the component mass space, the geometry is much harder for a sampler to explore. This can lead to slow convergence and poor performance. The chirp mass-mass ratio space is much more isotropic and easier to explore, which is often the choice to expose to the sampler. + +On the other hand, defining a prior in the component mass space is much more intuitive. The common prior of choice is uniform in the component mass space with some maximum and minimum mass. One may want to define the prior in the component mass space then sample in the chirp mass space. To make the problem even worse, there is yet another set of paraemeters one may want to choose, which is the set of parameters the model may want to take. For example, the waveform generator in ripple takes the symmetric mass ratio $\eta$ as input instead of the mass ratio. + +So in a general setting, there could be three sets of parametrizations we can choose for our problem: a parameterization which we want to define our prior in, a parameterization which we want the sampler to see, and a parameterization which the model takes. To facilitate the transformation between these parameterizations, we introduce a naming system and a transform system to handle this. + + + +# Primatives + +# Priors + +# Transforms \ No newline at end of file From 38e817cbc56caebe6d3b4972ea948a958f8c51e9 Mon Sep 17 00:00:00 2001 From: kazewong Date: Mon, 5 Aug 2024 17:35:21 -0400 Subject: [PATCH 02/31] upload prior system sketch --- docs/tutorials/prior_system.jpg | Bin 0 -> 395819 bytes 1 file changed, 0 insertions(+), 0 deletions(-) create mode 100644 docs/tutorials/prior_system.jpg diff --git a/docs/tutorials/prior_system.jpg b/docs/tutorials/prior_system.jpg new file mode 100644 index 0000000000000000000000000000000000000000..cdeb6f8fea4c9b892020f30b306aee80477d5e2d GIT binary patch literal 395819 zcmb5VcT`i|^EY}DLWzhHqTvgOMhFBnfD#gfpa!KX1dw9rNDD21bObbD11Zua1dt|8 zM0yi3C{jc3O;AG-0Wk;&mgnaA{_eZp_n-H!b@y54oH=`T_MV(Fd*(B<|C#(}0T8~T zqpt&iKmY*ZZoogEK$H5HFWVbmGt$vF(EcAr7r-r$GXOyK4)D9CdkIOlv_kSP{Le4` z<=t@d_x<<$e<|F4cgFwi9RNlY{x5C*zpA0mF8)s32AkX+<;NYIE9?<2eT4EqwA{b6 zI&W z08l^hzw7?@J@LKacjLd^LAXb-t1AF-iUB~#5&+j;c5tuOiKXT&#K_LEfR$4|< zP91w*Lk)XQm8fS!B5GaNRy}7-HMwr@NO7ZFFuWP+>l|X^LUH=H6A(;9ludq1;Ot&&jiz5R)4>BY8#OQb|?Hd2L57T^riuJ1UKJylmR` zN-3M%{AU_C$YpSch5;9WU3UiMkX}a4?`#jxnBqB+#mAXaUhllU)K~L;U?CqQXOG!O zsLw5p*u1x>NjZ%0UES3R*18oxf)CuRa%{fQ8+dFev++w=zh3`Q0K~8pDj!|xDwRJQ zKAkMJ@ag3tSq1UN)A=JT^yT>BZiRwp9T0A~wQs-vM;ubs2)ufv1E+>@q*lfSg z3LZ0QQ>P&Q*!Wi@T*>!wcl7b>bUt=_cF7BO7FKWpBs*Sr6N@KU2&zNlqY?J^<0g_I@fAh;Z*JR!9Jsl7erf25&ay#@m?uh|HMk` zReRfDNL;<;@QB(8msrYxFKODQzDMBc&m$T2pYl7BlPaE{XHKSWTBqk?JhE%a;6Nk6 z^CMj+GCQ3)L=2k|V3yMi%HD_Nc(&f6-TvNi*>55dzrvv8f7l9{@D;T4&l)&6V~kH* z(q%JTa+OS^wRzeWru}2^@x%?WEB(X=VSt#Ijvt^nebS4zNlHm-%{D^%h)K8*$}f@V zkrnLp*XlE+IU~1oi8`L1-cU)LPH{6eL)gex&>19d(EscuY)}zYzH>kRj@jP|-s)JL zd+SN!iWZ43*H7!{dv?$mWXl0XgPDsggo?CA>MT@yb`$brG$B*WS`N?SdBPVwu@pgi zqOuC{8B`sd71~xEeO)*U5WrWGCax(sprw?%8l-JifRyubk-RDp!i(l7UlWmUoO774 zyr;N$Y@+tP-|5Qz3r2nf)M7>N(^a6=vY!hhOw0aTyd9Vd$U?h$ zt{o~SS{jZM;FIu(ffA5>TJ;bSjkP>v%*PO237y@P-!I%5GNdI0tIKg~3{iR9f{@RY z?FAu4o{ptoEP<%Q%Q1F;G;s)Z?Oe#kNn+7U*FJ$%Q zQN7twq-t^9q0rr9Dp8a1BnNn@ zuxNuXPGPX_70taI)h-`i3sy;Sv*ko-3N-`b?|Xj$8Y0I*8Vc2en|jJ}P?rg5ryGLa zl|=rOF3c?<2>65_(BFf`+!q66g zk!c{apnWPmy$kgEP$pI~btI(E0bbT_-3U~j7nyJqQSNEi@lT$t`&=mj3yXMidZ~&^ zi>JtJYPo2{qj(LS$~tJZt2JUhmpZ~C5z1K&QF9iVu0EoiQ}2H)HT!Q?!OKZD)6ogH zwQl}Q|D;~$-D)AV%R1mbS0a5?$@r4;7&W}W;!APHk#{$>$1}ZVi7*%}3uizHLsPA` z96Z$>rLgp@yt$8+7mliCea&`B5apTqD|0hvsC%m3BNh?e1;7JQV)cGkY8nd*F{`Y; z+EJ0x@&9BMG>;YCswb;6vFx; zjfNrDmO9_-F(FyMBh77Ujl#9AKDw#=$Hv@|@`mQuFIyALRqZPo^}9EJRp+d+Rx&*8 zMfR-UVeRUBe_ZV=NI9>Nwvi{+x3s&IqDqe&4=b{OK`rArq=l%RF+zufflNhJtAot9 zDfHG$@ph@Miw|zv<%vMe-;uT6Q)fQt$n?;%^5+EQFtzi2ygR1aiWVeLF6Vdb z(QZ6?<0J6A^IPg|?le7y(KV^Ts<2#mH~!kr2M}+@^!JYncjn5E7agMptC)ub=0`N! 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zuasxGJ=0#23!gIc2^Y@MnHgTupe)%4wYo~cAsYBu$|iO*opl6>yl0}?`s$muZSI@s`D^SVx;NdnVOf0%+^`86{Wd!?_Yy8#^KVsq9~@fqIN-J9~8 z-*9hOwdcx4xsfqxq>0xsBK9}UX8XzkI+K*!V=Hwd{{SFvv1`rQoi?$h;wCL{YGyXo zGVqbuiM#@kkfNm8{YWlEetCf*GDf-q1ln~YY_>N8Q$A@uH6yN|y)3bK(JpEWm68Gg zoU{DMn@{Sot&;h90yT^1zh-KTysTs)ow7IZMw*-FAV+d?&gmLt0`=JXc}|AcuoL6J zM{+a*GQ1IyATFt~u5hvWfcC$epzF41L8)<8+@0C>#q0DYE!B#+3AZ?GFGYakQ(kiYmZzkm`qB+p6i1fB10 zhMC&^4KlU50owKr?c~{Jas%4$^T5JT(?{jX3v2Y9ZFUm+KmOzs^U3ao?wa)gqFZFbs{{WiI^h?gr z1-x}k;&RG4HJ-^JkrtWHMe@E$zLx|e^H`bGwSc!&oa0rQx_8tIiOyDMDEz>MNwF6N z=ghsWo~bwI^AWDO0?$2mNwjXX#rq}iOib$_Z80;EI_s5){-lhu{KP4hz2{a|H3iad za{1a4I_PhZ5=5ECNfYg!pw<3_{z*=g+??l4K<}Y5l;2Wj`&+3!uha>&-glDu=cS9@ zV=2#QNW90oZ)n&S{Ox|NOvafrJtHHug6o{ZM`O9Q^2%%m=YsjnWJdEKcvGxsk_sfv zrcAAvE`n!yza@#jR@&eYm&=vN%6WAKo=i^a?dhjc!Di$GFaD4giY-xoabvnI>JToIrRpump!j3Yu+>Dlb-sQoxrvK z0C%CJ&Su}L#o{f0AdwM!-t(~$^5@BS&Tr8oa=q`h!FGZ-NxqXh5q#|cv7FxV^tqk# znEF`0ad Date: Mon, 5 Aug 2024 18:08:09 -0400 Subject: [PATCH 03/31] Update prior system --- docs/tutorials/prior_system.md | 12 ++++++++++-- mkdocs.yml | 4 ++++ 2 files changed, 14 insertions(+), 2 deletions(-) diff --git a/docs/tutorials/prior_system.md b/docs/tutorials/prior_system.md index e644d18aa..9af337eb0 100644 --- a/docs/tutorials/prior_system.md +++ b/docs/tutorials/prior_system.md @@ -1,15 +1,23 @@ # Jim's naming and transform system +!!! warning + **Heavy development**: This is a work in progress and is subject to change. If you have any questions, please feel free to open an issue. + The parameterization of some fundamental quantities can have significant impacts on the performance of the sampler. For example, the masses can be parameterized in the component mass spaces $\mathcal{M}_1$-$\mathcal{M}_2$ or chirp mass-mass ratio $\mathcal{M}_c$-$q$. Because of the strong correlation in the component mass space, the geometry is much harder for a sampler to explore. This can lead to slow convergence and poor performance. The chirp mass-mass ratio space is much more isotropic and easier to explore, which is often the choice to expose to the sampler. On the other hand, defining a prior in the component mass space is much more intuitive. The common prior of choice is uniform in the component mass space with some maximum and minimum mass. One may want to define the prior in the component mass space then sample in the chirp mass space. To make the problem even worse, there is yet another set of paraemeters one may want to choose, which is the set of parameters the model may want to take. For example, the waveform generator in ripple takes the symmetric mass ratio $\eta$ as input instead of the mass ratio. So in a general setting, there could be three sets of parametrizations we can choose for our problem: a parameterization which we want to define our prior in, a parameterization which we want the sampler to see, and a parameterization which the model takes. To facilitate the transformation between these parameterizations, we introduce a naming system and a transform system to handle this. +# Prior + +Fundamentally, all `jim` needs is to pass a reasonable posterior function `posterior(z) = likelihood(t_1(z)) + prior(t_2(z))` to `flowMC`, so `flowMC` can sample the function. Here, `likelihood` and `prior` are functions that one pass in a vector of numbers (and data), and it returns a scalar. `z` is the vector of variables the sampler sees, and `t_1` and `t_2` are the transforms that transform the variables between the sampler and the model. + +Since we want to sample in `z`, ultimately we want to have a prior defined in `z`, meaning we can evaluate `p_Z(z)`. However, this is could be non-trivial, such as defining a prior in the $\mathcal{M}_c$-$q$ space that is equivalent to a uniform prior in the $\mathcal{M}_1$-$\mathcal{M}_2$ space requires a very complex expression. Instead of directly writing down the prior distribution in `z`, we can start by defining the prior in a space that is more intuitive, then transform the prior to the space `z` using a transform. By carrying the Jacobian of the transform, we can define the prior in the space `z` by transforming the prior in the intuitive space, $p_Z(z) = p_X(x) \left| \frac{dx}{dz} \right|$, where $x = t_2(z)$. The tricky bit here is the user often wants to start from the prior $x$ and define the transform **to** the sample space `z`, but here the transform is defined **from** the sample space `z` to the prior space $x$. So in order to make the prior-to-sample transform work in practice, the transform has to be **bijective**, which implies they are invertible and have a well-defined determinant of the Jacobian. +On the other hand, the likelihood is often related to a model instead of coming from a distribution, meaning as long as one can transform the parameters to feed into the model, there is no limitation on the transform.. So the transform for the likelihood is strictly from the sample space `z` to the model space $y = t_1(z)$. For this reason, the transform for the likelihood does not need to be bijective, it can even by a N-to-M transform. -# Primatives +## Primatives -# Priors # Transforms \ No newline at end of file diff --git a/mkdocs.yml b/mkdocs.yml index 6ece4db8a..957c389d4 100644 --- a/mkdocs.yml +++ b/mkdocs.yml @@ -42,6 +42,10 @@ markdown_extensions: permalink: "¤" # Adds a clickable permalink to each section heading toc_depth: 4 +extra_javascript: + - javascripts/mathjax.js + - https://unpkg.com/mathjax@3/es5/tex-mml-chtml.js + plugins: - search # default search plugin; needs manually re-enabling when using any other plugins - autorefs # Cross-links to headings From d12b901e2103497a605a6e46a488458f25a36538 Mon Sep 17 00:00:00 2001 From: kazewong Date: Mon, 5 Aug 2024 18:11:32 -0400 Subject: [PATCH 04/31] Update prior system --- docs/tutorials/prior_system.md | 3 +++ 1 file changed, 3 insertions(+) diff --git a/docs/tutorials/prior_system.md b/docs/tutorials/prior_system.md index 9af337eb0..3e1fee5a4 100644 --- a/docs/tutorials/prior_system.md +++ b/docs/tutorials/prior_system.md @@ -9,6 +9,9 @@ On the other hand, defining a prior in the component mass space is much more int So in a general setting, there could be three sets of parametrizations we can choose for our problem: a parameterization which we want to define our prior in, a parameterization which we want the sampler to see, and a parameterization which the model takes. To facilitate the transformation between these parameterizations, we introduce a naming system and a transform system to handle this. +A sketch of the transform system is shown below: +![A sketch of the transform system](prior_system.jpg) + # Prior Fundamentally, all `jim` needs is to pass a reasonable posterior function `posterior(z) = likelihood(t_1(z)) + prior(t_2(z))` to `flowMC`, so `flowMC` can sample the function. Here, `likelihood` and `prior` are functions that one pass in a vector of numbers (and data), and it returns a scalar. `z` is the vector of variables the sampler sees, and `t_1` and `t_2` are the transforms that transform the variables between the sampler and the model. From a0a4a56c3df2e2bc1efead032ca23c4cd0baa397 Mon Sep 17 00:00:00 2001 From: kazewong Date: Tue, 6 Aug 2024 13:58:51 -0400 Subject: [PATCH 05/31] chore: Update prior system naming to parameter transform --- docs/tutorials/prior_system.md | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/docs/tutorials/prior_system.md b/docs/tutorials/prior_system.md index 3e1fee5a4..43a924dfb 100644 --- a/docs/tutorials/prior_system.md +++ b/docs/tutorials/prior_system.md @@ -1,4 +1,4 @@ -# Jim's naming and transform system +# Jim's parameter transform system !!! warning **Heavy development**: This is a work in progress and is subject to change. If you have any questions, please feel free to open an issue. From 54f5b07ad3ae3be315a77eb571914732c7cb322f Mon Sep 17 00:00:00 2001 From: xuyuon <116078673+xuyuon@users.noreply.github.com> Date: Thu, 22 Aug 2024 09:01:14 +0800 Subject: [PATCH 06/31] Added GW150914_PV2.ipynb --- example/notebooks/GW150914_PV2.ipynb | 183 +++++++++++++++++++++++++++ 1 file changed, 183 insertions(+) create mode 100644 example/notebooks/GW150914_PV2.ipynb diff --git a/example/notebooks/GW150914_PV2.ipynb b/example/notebooks/GW150914_PV2.ipynb new file mode 100644 index 000000000..ff27b3ead --- /dev/null +++ b/example/notebooks/GW150914_PV2.ipynb @@ -0,0 +1,183 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Import Necessary Modules" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "import time\n", + "\n", + "import jax\n", + "import jax.numpy as jnp\n", + "\n", + "from jimgw.jim import Jim\n", + "from jimgw.prior import CombinePrior, UniformPrior, CosinePrior, SinePrior, PowerLawPrior\n", + "from jimgw.single_event.detector import H1, L1\n", + "from jimgw.single_event.likelihood import TransientLikelihoodFD\n", + "from jimgw.single_event.waveform import RippleIMRPhenomPv2\n", + "from jimgw.transforms import BoundToUnbound\n", + "from jimgw.single_event.transforms import MassRatioToSymmetricMassRatioTransform, SpinToCartesianSpinTransform, ComponentMassesToChirpMassMassRatioTransform, SkyFrameToDetectorFrameSkyPositionTransform\n", + "from jimgw.single_event.utils import Mc_q_to_m1_m2\n", + "from flowMC.strategy.optimization import optimization_Adam\n", + "\n", + "jax.config.update(\"jax_enable_x64\", True)\n", + "\n", + "total_time_start = time.time()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Fetch the detector data\n", + "We first fetch the 4s segment detector data centered on GW150914. " + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "gps = 1126259462.4\n", + "duration = 4\n", + "post_trigger_duration = 2\n", + "start_pad = duration - post_trigger_duration\n", + "end_pad = post_trigger_duration\n", + "fmin = 20.0\n", + "fmax = 1024.0\n", + "\n", + "ifos = [H1, L1]\n", + "\n", + "f_ref = 20.0\n", + "\n", + "for ifo in ifos:\n", + " ifo.load_data(gps, start_pad, end_pad, fmin, fmax, psd_pad=16, tukey_alpha=0.2)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Set up Prior\n", + "Prior is the prior knowledge you have on the probability distribution of the event parameters $\\theta_{prior}$. There is a few prior classes available: UniformPrior,..." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "M_c_min, M_c_max = 10.0, 80.0\n", + "q_min, q_max = 0.125, 1.0\n", + "m_1_prior = UniformPrior(Mc_q_to_m1_m2(M_c_min, q_max)[0], Mc_q_to_m1_m2(M_c_max, q_min)[0], parameter_names=[\"m_1\"])\n", + "m_2_prior = UniformPrior(Mc_q_to_m1_m2(M_c_min, q_min)[1], Mc_q_to_m1_m2(M_c_max, q_max)[1], parameter_names=[\"m_2\"])\n", + "theta_jn_prior = SinePrior(parameter_names=[\"theta_jn\"])\n", + "phi_jl_prior = UniformPrior(0.0, 2 * jnp.pi, parameter_names=[\"phi_jl\"])\n", + "theta_1_prior = SinePrior(parameter_names=[\"theta_1\"])\n", + "theta_2_prior = SinePrior(parameter_names=[\"theta_2\"])\n", + "phi_12_prior = UniformPrior(0.0, 2 * jnp.pi, parameter_names=[\"phi_12\"])\n", + "a_1_prior = UniformPrior(0.0, 1.0, parameter_names=[\"a_1\"])\n", + "a_2_prior = UniformPrior(0.0, 1.0, parameter_names=[\"a_2\"])\n", + "dL_prior = PowerLawPrior(10.0, 2000.0, 2.0, parameter_names=[\"d_L\"])\n", + "t_c_prior = UniformPrior(-0.05, 0.05, parameter_names=[\"t_c\"])\n", + "phase_c_prior = UniformPrior(0.0, 2 * jnp.pi, parameter_names=[\"phase_c\"])\n", + "psi_prior = UniformPrior(0.0, jnp.pi, parameter_names=[\"psi\"])\n", + "ra_prior = UniformPrior(0.0, 2 * jnp.pi, parameter_names=[\"ra\"])\n", + "dec_prior = CosinePrior(parameter_names=[\"dec\"])\n", + "\n", + "prior = CombinePrior(\n", + " [\n", + " m_1_prior,\n", + " m_2_prior,\n", + " theta_jn_prior,\n", + " phi_jl_prior,\n", + " theta_1_prior,\n", + " theta_2_prior,\n", + " phi_12_prior,\n", + " a_1_prior,\n", + " a_2_prior,\n", + " dL_prior,\n", + " t_c_prior,\n", + " phase_c_prior,\n", + " psi_prior,\n", + " ra_prior,\n", + " dec_prior,\n", + " ]\n", + ")" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Set up Sample Transform\n", + "Sometimes the same event can be described by multiple different set of event parameters, and it exists some transform that transform from one set of parameters to another set of parameters. Suppose we want to define prior on one set of event parameters $\\theta_1$, but sample on another set of event parameters $\\theta_2$, sample transform becomes useful. " + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "sample_transforms = [\n", + " ComponentMassesToChirpMassMassRatioTransform(name_mapping=[[\"m_1\", \"m_2\"], [\"M_c\", \"q\"]]),\n", + " BoundToUnbound(name_mapping = [[\"M_c\"], [\"M_c_unbounded\"]], original_lower_bound=10.0, original_upper_bound=80.0),\n", + " BoundToUnbound(name_mapping = [[\"q\"], [\"q_unbounded\"]], original_lower_bound=0.125, original_upper_bound=1.),\n", + " BoundToUnbound(name_mapping = [[\"theta_jn\"], [\"theta_jn_unbounded\"]] , original_lower_bound=0.0, original_upper_bound=jnp.pi),\n", + " BoundToUnbound(name_mapping = [[\"phi_jl\"], [\"phi_jl_unbounded\"]] , original_lower_bound=0.0, original_upper_bound=2 * jnp.pi),\n", + " BoundToUnbound(name_mapping = [[\"theta_1\"], [\"theta_1_unbounded\"]] , original_lower_bound=0.0, original_upper_bound=jnp.pi),\n", + " BoundToUnbound(name_mapping = [[\"theta_2\"], [\"theta_2_unbounded\"]] , original_lower_bound=0.0, original_upper_bound=jnp.pi),\n", + " BoundToUnbound(name_mapping = [[\"phi_12\"], [\"phi_12_unbounded\"]] , original_lower_bound=0.0, original_upper_bound=2 * jnp.pi),\n", + " BoundToUnbound(name_mapping = [[\"a_1\"], [\"a_1_unbounded\"]] , original_lower_bound=0.0, original_upper_bound=1.0),\n", + " BoundToUnbound(name_mapping = [[\"a_2\"], [\"a_2_unbounded\"]] , original_lower_bound=0.0, original_upper_bound=1.0),\n", + " BoundToUnbound(name_mapping = [[\"d_L\"], [\"d_L_unbounded\"]] , original_lower_bound=10.0, original_upper_bound=2000.0),\n", + " BoundToUnbound(name_mapping = [[\"t_c\"], [\"t_c_unbounded\"]] , original_lower_bound=-0.05, original_upper_bound=0.05),\n", + " BoundToUnbound(name_mapping = [[\"phase_c\"], [\"phase_c_unbounded\"]] , original_lower_bound=0.0, original_upper_bound=2 * jnp.pi),\n", + " BoundToUnbound(name_mapping = [[\"psi\"], [\"psi_unbounded\"]], original_lower_bound=0.0, original_upper_bound=jnp.pi),\n", + " SkyFrameToDetectorFrameSkyPositionTransform(name_mapping = [[\"ra\", \"dec\"], [\"zenith\", \"azimuth\"]], gps_time=gps, ifos=ifos),\n", + " BoundToUnbound(name_mapping = [[\"zenith\"], [\"zenith_unbounded\"]], original_lower_bound=0.0, original_upper_bound=jnp.pi),\n", + " BoundToUnbound(name_mapping = [[\"azimuth\"], [\"azimuth_unbounded\"]], original_lower_bound=0.0, original_upper_bound=2 * jnp.pi),\n", + "]" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Set up Likelihood Transform\n", + "To make the issue even more complicated, sometimes the model could takes another set of parameters. Therefore, we would define likelihood transforms that transform $\\theta_2$ into $\\theta_3$." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "likelihood_transforms = [\n", + " ComponentMassesToChirpMassMassRatioTransform(name_mapping=[[\"m_1\", \"m_2\"], [\"M_c\", \"q\"]]),\n", + " SpinToCartesianSpinTransform(name_mapping=[[\"theta_jn\", \"phi_jl\", \"theta_1\", \"theta_2\", \"phi_12\", \"a_1\", \"a_2\"], [\"iota\", \"s1_x\", \"s1_y\", \"s1_z\", \"s2_x\", \"s2_y\", \"s2_z\"]], freq_ref=f_ref),\n", + " MassRatioToSymmetricMassRatioTransform(name_mapping=[[\"q\"], [\"eta\"]]),\n", + "]" + ] + } + ], + "metadata": { + "language_info": { + "name": "python" + } + }, + "nbformat": 4, + "nbformat_minor": 2 +} From d5288cace38271ca251fd95798402a57304d6f7b Mon Sep 17 00:00:00 2001 From: xuyuon <116078673+xuyuon@users.noreply.github.com> Date: Thu, 22 Aug 2024 12:30:25 +0800 Subject: [PATCH 07/31] Add files via upload --- 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Date: Thu, 22 Aug 2024 12:34:17 +0800 Subject: [PATCH 10/31] Rename page2Artboard 1.png to prior_system_diagram.png --- ...page2Artboard 1.png => prior_system_diagram.png} | Bin 1 file changed, 0 insertions(+), 0 deletions(-) rename docs/tutorials/{page2Artboard 1.png => prior_system_diagram.png} (100%) diff --git a/docs/tutorials/page2Artboard 1.png b/docs/tutorials/prior_system_diagram.png similarity index 100% rename from docs/tutorials/page2Artboard 1.png rename to docs/tutorials/prior_system_diagram.png From 0bf733bb8f7dc4556ba8c390cd1545b49e896fb6 Mon Sep 17 00:00:00 2001 From: xuyuon <116078673+xuyuon@users.noreply.github.com> Date: Thu, 22 Aug 2024 18:26:42 +0800 Subject: [PATCH 11/31] Updated jim_guide.md --- docs/tutorials/jim_guide.md | 26 ++++++++++++++++++++++++++ 1 file changed, 26 insertions(+) create mode 100644 docs/tutorials/jim_guide.md diff --git a/docs/tutorials/jim_guide.md b/docs/tutorials/jim_guide.md new file mode 100644 index 000000000..3aa10b373 --- /dev/null +++ b/docs/tutorials/jim_guide.md @@ -0,0 +1,26 @@ +# Jim's parameter transform system + +!!! warning + **Heavy development**: This is a work in progress and is subject to change. If you have any questions, please feel free to open an issue. + + + +A sketch of the transform system is shown below: +![A sketch of the transform system](prior_system_diagram.jpg) + + +## Setting up Priors +Prior is the prior knowledge we have on the probability density distribution of the event parameters. In Jim, we could set up prior based a set of event parameters $\theta_{prior}$. To define the prior, we need to call the prior class built in Jim. Suppose we want to define the prior of the parameter x to be uniform, we could call the UniformPrior class: + +``` +from jimgw.prior import UniformPrior +prior = UniformPrior(0.0, 1.0, parameter_names=["x"]) +``` + +There are a few prior classes available in Jim: ... + +## Setting up Sample Transform + + +## Setting up Likelihood Transform + From ab993bfdb55fdde84645c7be8848de083f215fe7 Mon Sep 17 00:00:00 2001 From: xuyuon <116078673+xuyuon@users.noreply.github.com> Date: Fri, 23 Aug 2024 09:48:26 +0800 Subject: [PATCH 12/31] Updated jim_guide.md --- docs/tutorials/jim_guide.md | 4 ++-- 1 file changed, 2 insertions(+), 2 deletions(-) diff --git a/docs/tutorials/jim_guide.md b/docs/tutorials/jim_guide.md index 3aa10b373..2c91a83c0 100644 --- a/docs/tutorials/jim_guide.md +++ b/docs/tutorials/jim_guide.md @@ -10,14 +10,14 @@ A sketch of the transform system is shown below: ## Setting up Priors -Prior is the prior knowledge we have on the probability density distribution of the event parameters. In Jim, we could set up prior based a set of event parameters $\theta_{prior}$. To define the prior, we need to call the prior class built in Jim. Suppose we want to define the prior of the parameter x to be uniform, we could call the UniformPrior class: +Prior is the prior knowledge we have on the probability density distribution of the event parameters. In Jim, we could set up prior based a set of event parameters $\theta_{prior}$. To define the prior, we need to call the prior class `jimgw.prior` built in Jim. Suppose we want to define the prior of the parameter x to be uniform, we could call the `UniformPrior` class: ``` from jimgw.prior import UniformPrior prior = UniformPrior(0.0, 1.0, parameter_names=["x"]) ``` -There are a few prior classes available in Jim: ... +We have implemented a few basic prior classes in Jim. ## Setting up Sample Transform From d9dd7d0275389e7d689dc8372b45e4b42ef8f57f Mon Sep 17 00:00:00 2001 From: xuyuon <116078673+xuyuon@users.noreply.github.com> Date: Fri, 23 Aug 2024 09:52:20 +0800 Subject: [PATCH 13/31] Updated jim_guide.md --- docs/tutorials/jim_guide.md | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/docs/tutorials/jim_guide.md b/docs/tutorials/jim_guide.md index 2c91a83c0..e94cbf075 100644 --- a/docs/tutorials/jim_guide.md +++ b/docs/tutorials/jim_guide.md @@ -6,7 +6,7 @@ A sketch of the transform system is shown below: -![A sketch of the transform system](prior_system_diagram.jpg) +![A sketch of the transform system](prior_system_diagram.png) ## Setting up Priors From 54da400c17534d1deb649c1c70816c214e331536 Mon Sep 17 00:00:00 2001 From: xuyuon <116078673+xuyuon@users.noreply.github.com> Date: Fri, 23 Aug 2024 10:12:04 +0800 Subject: [PATCH 14/31] Updated jim_guide.md --- docs/tutorials/jim_guide.md | 33 +++++++++++++++++++++++++++++++-- 1 file changed, 31 insertions(+), 2 deletions(-) diff --git a/docs/tutorials/jim_guide.md b/docs/tutorials/jim_guide.md index e94cbf075..9945d71e7 100644 --- a/docs/tutorials/jim_guide.md +++ b/docs/tutorials/jim_guide.md @@ -10,14 +10,43 @@ A sketch of the transform system is shown below: ## Setting up Priors -Prior is the prior knowledge we have on the probability density distribution of the event parameters. In Jim, we could set up prior based a set of event parameters $\theta_{prior}$. To define the prior, we need to call the prior class `jimgw.prior` built in Jim. Suppose we want to define the prior of the parameter x to be uniform, we could call the `UniformPrior` class: +Prior represents the prior knowledge on the probability density distribution of the event parameters $\theta$. In Jim, we could set up priors using the prior class `jimgw.prior`. Suppose we want to define a uniform prior distribution for the parameter $x$, we could call the `UniformPrior` class: ``` from jimgw.prior import UniformPrior prior = UniformPrior(0.0, 1.0, parameter_names=["x"]) ``` -We have implemented a few basic prior classes in Jim. +Jim provides a number of built-in prior classes, including: +- `UniformPrior` +- `SinePrior` +- `CosinePrior` +- `PowerLawPrior` + +A complete list of prior classes available can be found in the Jim documentation (not available yet). + +## Multi-dimensional Priors +When working with multi-dimensional parameter space, we would usually want to define priors for each individual parameter first: + +``` +from jimgw.prior import UniformPrior +prior_x = UniformPrior(0.0, 1.0, parameter_names=["x"]) +prior_y = UniformPrior(0.0, 2.0, parameter_names=["y"]) +``` + +Once we have the individual priors defined, we can call the class `CombinePrior` to combine them into one single prior object: + +``` +from jimgw.prior import CombinePrior +prior = CombinePrior( + [ + prior_x, + prior_y, + ] +) +``` + +The `CombinePrior` object can later be used as input to the Jim sampler. ## Setting up Sample Transform From 1dd8cb4d4f4cf19970ad2bf4ff6ad1520a7a49d6 Mon Sep 17 00:00:00 2001 From: xuyuon <116078673+xuyuon@users.noreply.github.com> Date: Fri, 23 Aug 2024 11:46:34 +0800 Subject: [PATCH 15/31] Updated jim_guide.md --- docs/tutorials/jim_guide.md | 30 ++++++++++++++++++++++++++---- 1 file changed, 26 insertions(+), 4 deletions(-) diff --git a/docs/tutorials/jim_guide.md b/docs/tutorials/jim_guide.md index 9945d71e7..390534218 100644 --- a/docs/tutorials/jim_guide.md +++ b/docs/tutorials/jim_guide.md @@ -3,11 +3,16 @@ !!! warning **Heavy development**: This is a work in progress and is subject to change. If you have any questions, please feel free to open an issue. +The parameterization of some fundamental quantities can have significant impacts on the performance of the sampler. For example, the masses can be parameterized in the component mass spaces $\mathcal{M}_1$-$\mathcal{M}_2$ or chirp mass-mass ratio $\mathcal{M}_c$-$q$. Because of the strong correlation in the component mass space, the geometry is much harder for a sampler to explore. This can lead to slow convergence and poor performance. The chirp mass-mass ratio space is much more isotropic and easier to explore, which is often the choice to expose to the sampler. +On the other hand, defining a prior in the component mass space is much more intuitive. The common prior of choice is uniform in the component mass space with some maximum and minimum mass. One may want to define the prior in the component mass space then sample in the chirp mass space. To make the problem even worse, there is yet another set of paraemeters one may want to choose, which is the set of parameters the model may want to take. For example, the waveform generator in ripple takes the symmetric mass ratio $\eta$ as input instead of the mass ratio. + +So in a general setting, there could be three sets of parametrizations we can choose for our problem: a parameterization which we want to define our prior in, a parameterization which we want the sampler to see, and a parameterization which the model takes. To facilitate the transformation between these parameterizations, we introduce a naming system and a transform system to handle this. A sketch of the transform system is shown below: ![A sketch of the transform system](prior_system_diagram.png) +# Prior ## Setting up Priors Prior represents the prior knowledge on the probability density distribution of the event parameters $\theta$. In Jim, we could set up priors using the prior class `jimgw.prior`. Suppose we want to define a uniform prior distribution for the parameter $x$, we could call the `UniformPrior` class: @@ -25,8 +30,8 @@ Jim provides a number of built-in prior classes, including: A complete list of prior classes available can be found in the Jim documentation (not available yet). -## Multi-dimensional Priors -When working with multi-dimensional parameter space, we would usually want to define priors for each individual parameter first: +### Multi-dimensional Priors +When working with multi-dimensional parameter space, we will usually want to define priors for each individual parameter first: ``` from jimgw.prior import UniformPrior @@ -46,9 +51,26 @@ prior = CombinePrior( ) ``` -The `CombinePrior` object can later be used as input to the Jim sampler. +The `CombinePrior` object takes a list of `jimgw.prior` objects as argument and combines them into one single prior object that can be fed to the Jim sampler as input. + +# Transforms + +## Setting up Sample Transforms +Sometimes the same event can be described by multiple different set of event parameters, and it exists some transform that transform from one set of parameters to another set of parameters. Suppose we want to define prior on one set of event parameters $\theta_{prior}$, but sample on another set of event parameters $z$, sample transform becomes useful. + +### Bound-to-unbound Transforms +To set up bound-to-unbound transform, we use the transform class `BoundToUnbound`: + +``` +from jimgw.transforms import BoundToUnbound +sample_transform = [ + BoundToUnbound(name_mapping = [["x"], ["x_unbounded"]], original_lower_bound=0.0, original_upper_bound=1.0), + BoundToUnbound(name_mapping = [["y"], ["y_unbounded"]], original_lower_bound=0.0, original_upper_bound=10.0), +] +``` + +### Other Sample Transforms -## Setting up Sample Transform ## Setting up Likelihood Transform From a7b143e68b6da633c8fa9e550de7730e80ad8796 Mon Sep 17 00:00:00 2001 From: xuyuon <116078673+xuyuon@users.noreply.github.com> Date: Fri, 23 Aug 2024 14:36:09 +0800 Subject: [PATCH 16/31] Updated jim_guide.md --- docs/tutorials/jim_guide.md | 17 +++++++++++++++-- 1 file changed, 15 insertions(+), 2 deletions(-) diff --git a/docs/tutorials/jim_guide.md b/docs/tutorials/jim_guide.md index 390534218..d2532a382 100644 --- a/docs/tutorials/jim_guide.md +++ b/docs/tutorials/jim_guide.md @@ -7,11 +7,19 @@ The parameterization of some fundamental quantities can have significant impacts On the other hand, defining a prior in the component mass space is much more intuitive. The common prior of choice is uniform in the component mass space with some maximum and minimum mass. One may want to define the prior in the component mass space then sample in the chirp mass space. To make the problem even worse, there is yet another set of paraemeters one may want to choose, which is the set of parameters the model may want to take. For example, the waveform generator in ripple takes the symmetric mass ratio $\eta$ as input instead of the mass ratio. -So in a general setting, there could be three sets of parametrizations we can choose for our problem: a parameterization which we want to define our prior in, a parameterization which we want the sampler to see, and a parameterization which the model takes. To facilitate the transformation between these parameterizations, we introduce a naming system and a transform system to handle this. +So in a general setting, there could be three sets of parametrizations we can choose for our problem: a parameterization which we want to define our prior in $\vec{\theta_{prior}}$, a parameterization which we want the sampler to see $\vec{z}$, and a parameterization which the model takes $\vec{\theta_{model}}$. To facilitate the transformation between these parameterizations, we introduce a naming system and a transform system to handle this. A sketch of the transform system is shown below: ![A sketch of the transform system](prior_system_diagram.png) +Fundamentally, all `jim` needs is to pass a reasonable posterior function `posterior(z) = likelihood(t_1(z)) + prior(t_2(z))` to `flowMC`, so `flowMC` can sample the function. Here, `likelihood` and `prior` are functions that one pass in a vector of numbers (and data), and it returns a scalar. `z` is the vector of variables the sampler sees, and `t_1` and `t_2` are the transforms that transform the variables between the sampler and the model. + +Since we want to sample in `z`, ultimately we want to have a prior defined in `z`, meaning we can evaluate `p_Z(z)`. However, this is could be non-trivial, such as defining a prior in the $\mathcal{M}_c$-$q$ space that is equivalent to a uniform prior in the $\mathcal{M}_1$-$\mathcal{M}_2$ space requires a very complex expression. Instead of directly writing down the prior distribution in `z`, we can start by defining the prior in a space that is more intuitive, then transform the prior to the space `z` using a transform. + +By carrying the Jacobian of the transform, we can define the prior in the space `z` by transforming the prior in the intuitive space, $p_Z(z) = p_X(x) \left| \frac{dx}{dz} \right|$, where $x = t_2(z)$. The tricky bit here is the user often wants to start from the prior $x$ and define the transform **to** the sample space `z`, but here the transform is defined **from** the sample space `z` to the prior space $x$. So in order to make the prior-to-sample transform work in practice, the transform has to be **bijective**, which implies they are invertible and have a well-defined determinant of the Jacobian. + +On the other hand, the likelihood is often related to a model instead of coming from a distribution, meaning as long as one can transform the parameters to feed into the model, there is no limitation on the transform.. So the transform for the likelihood is strictly from the sample space `z` to the model space $y = t_1(z)$. For this reason, the transform for the likelihood does not need to be bijective, it can even by a N-to-M transform. + # Prior ## Setting up Priors @@ -54,11 +62,16 @@ prior = CombinePrior( The `CombinePrior` object takes a list of `jimgw.prior` objects as argument and combines them into one single prior object that can be fed to the Jim sampler as input. # Transforms +In a general setting, there could be three sets of parametrizations we can choose for our problem: a parameterization which we want to define our prior in $\vec{\theta_{prior}}$, a parameterization which we want the sampler to see $\vec{z}$, and a parameterization which the model takes $\vec{\theta_{model}}$. To facilitate the transformation between these parameterizations, we introduce a naming system and a transform system to handle this. ## Setting up Sample Transforms -Sometimes the same event can be described by multiple different set of event parameters, and it exists some transform that transform from one set of parameters to another set of parameters. Suppose we want to define prior on one set of event parameters $\theta_{prior}$, but sample on another set of event parameters $z$, sample transform becomes useful. +As we could have two different sets of parameterization for defining the prior and for the sampler to see, we need to set up transformations which transform from the parameter set $\vec{\theta_{prior}}$ to $\vec{z}$. ### Bound-to-unbound Transforms +In general, we want the sampler to see a set of parametrization that does not includes any hard bounds, namely that it is well defined in the whole real space. This is to prevent the situation where the samples could walk out of the bound into the parameter space where it is not well defined. However, it is often the case that parametrization we used to define prior $\vec{\theta_{prior}}$ contains hard bound. Therefore, we need a bound-to-unbound transform to transform the parametrization into another parametrization $z$ without a hard bound. + +In a nutshell, bound-to-unbound transform utilize the logit function to map real numbers from $(0, 1)$ to real numbers in $(-\infity, +\infity)$. + To set up bound-to-unbound transform, we use the transform class `BoundToUnbound`: ``` From 15874da8e020471b98aac46ee4b97c41c08a0da9 Mon Sep 17 00:00:00 2001 From: xuyuon <116078673+xuyuon@users.noreply.github.com> Date: Fri, 23 Aug 2024 14:38:43 +0800 Subject: [PATCH 17/31] Updated jim_guide.md --- docs/tutorials/jim_guide.md | 6 +++++- 1 file changed, 5 insertions(+), 1 deletion(-) diff --git a/docs/tutorials/jim_guide.md b/docs/tutorials/jim_guide.md index d2532a382..f5de0438c 100644 --- a/docs/tutorials/jim_guide.md +++ b/docs/tutorials/jim_guide.md @@ -70,7 +70,11 @@ As we could have two different sets of parameterization for defining the prior a ### Bound-to-unbound Transforms In general, we want the sampler to see a set of parametrization that does not includes any hard bounds, namely that it is well defined in the whole real space. This is to prevent the situation where the samples could walk out of the bound into the parameter space where it is not well defined. However, it is often the case that parametrization we used to define prior $\vec{\theta_{prior}}$ contains hard bound. Therefore, we need a bound-to-unbound transform to transform the parametrization into another parametrization $z$ without a hard bound. -In a nutshell, bound-to-unbound transform utilize the logit function to map real numbers from $(0, 1)$ to real numbers in $(-\infity, +\infity)$. +In a nutshell, bound-to-unbound transform utilize the logit function to map real numbers from $(0, 1)$ to real numbers in $(-\infty, +\infty)$. The logit function is given by: + +$$ +logit(\theta) = \ln{\frac{\theta}{1-\theta}} +$$ To set up bound-to-unbound transform, we use the transform class `BoundToUnbound`: From ffed0b9e710c3c3325b7b1fa195fef0a3cf7ec98 Mon Sep 17 00:00:00 2001 From: xuyuon <116078673+xuyuon@users.noreply.github.com> Date: Fri, 23 Aug 2024 14:53:07 +0800 Subject: [PATCH 18/31] Updated jim_guide.md --- docs/tutorials/jim_guide.md | 15 ++++++++++++++- 1 file changed, 14 insertions(+), 1 deletion(-) diff --git a/docs/tutorials/jim_guide.md b/docs/tutorials/jim_guide.md index f5de0438c..0d759afdb 100644 --- a/docs/tutorials/jim_guide.md +++ b/docs/tutorials/jim_guide.md @@ -76,7 +76,7 @@ $$ logit(\theta) = \ln{\frac{\theta}{1-\theta}} $$ -To set up bound-to-unbound transform, we use the transform class `BoundToUnbound`: +To set up bound-to-unbound transform, we use the transformation class `BoundToUnbound` provided in `jimgw.transforms`: ``` from jimgw.transforms import BoundToUnbound @@ -86,8 +86,21 @@ sample_transform = [ ] ``` +Basically, we want to fit all the sample transformations from parametrization $\vec{\theta_{prior}}$ to $\vec{z}$ in a list, which will be passed into the `Jim` object later. When executing the transformation, the transformations will be performed in the sequence the same as how it is arranged in the list. + ### Other Sample Transforms +We can also find other transformation that is specifically made for parameter estimation of compact binary coalescence in `jimgw.single_event.transforms`. For example, if we have defined prior on component masses $m_1$ and $m_2$, but we wish to sample on chirp mass $M_c$ and mass ratio $q$ instead. We could contain the function `ComponentMassesToChirpMassMassRatioTransform` in the sample transform list: + +``` +from jimgw.single_event.transforms import ComponentMassesToChirpMassMassRatioTransform +sample_transforms = [ + ComponentMassesToChirpMassMassRatioTransform(name_mapping=[["m_1", "m_2"], ["M_c", "q"]]), + BoundToUnbound(name_mapping = [["M_c"], ["M_c_unbounded"]], original_lower_bound=10.0, original_upper_bound=80.0), + BoundToUnbound(name_mapping = [["q"], ["q_unbounded"]], original_lower_bound=0.125, original_upper_bound=1.), +] +``` +Again, you should always include a `boundToUnbound` transform in the end. ## Setting up Likelihood Transform From 8a2acc86c3f32350a6d74f2f3617602f2773684e Mon Sep 17 00:00:00 2001 From: xuyuon <116078673+xuyuon@users.noreply.github.com> Date: Fri, 23 Aug 2024 15:04:02 +0800 Subject: [PATCH 19/31] Updated jim_guide.md --- docs/tutorials/jim_guide.md | 8 ++++++++ 1 file changed, 8 insertions(+) diff --git a/docs/tutorials/jim_guide.md b/docs/tutorials/jim_guide.md index 0d759afdb..8a1375227 100644 --- a/docs/tutorials/jim_guide.md +++ b/docs/tutorials/jim_guide.md @@ -104,4 +104,12 @@ Again, you should always include a `boundToUnbound` transform in the end. ## Setting up Likelihood Transform +Again, as the parameterization the model takes can be different from the parameterization for defining the prior, we need to set up likelihood transformations which transform from the parameter set $\vec{\theta_{prior}}$ to $\vec{\theta_{model}}$. +Setting up likelihood transforms is similar to setting up sample transform. We need to define a list of transformation that transform from the parameter set $\vec{\theta_{prior}}$ to $\vec{\theta_{model}}$. + +``` +likelihood_transforms = [ + ComponentMassesToChirpMassMassRatioTransform(name_mapping=[["m_1", "m_2"], ["M_c", "q"]]), +] +``` From 253fb5ffc8e1275f58f3bb6f792640743be027f6 Mon Sep 17 00:00:00 2001 From: xuyuon <116078673+xuyuon@users.noreply.github.com> Date: Fri, 23 Aug 2024 16:10:34 +0800 Subject: [PATCH 20/31] Updated jim_guide.md --- docs/tutorials/jim_guide.md | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/docs/tutorials/jim_guide.md b/docs/tutorials/jim_guide.md index 8a1375227..a9f883cbf 100644 --- a/docs/tutorials/jim_guide.md +++ b/docs/tutorials/jim_guide.md @@ -96,7 +96,7 @@ from jimgw.single_event.transforms import ComponentMassesToChirpMassMassRatioTra sample_transforms = [ ComponentMassesToChirpMassMassRatioTransform(name_mapping=[["m_1", "m_2"], ["M_c", "q"]]), BoundToUnbound(name_mapping = [["M_c"], ["M_c_unbounded"]], original_lower_bound=10.0, original_upper_bound=80.0), - BoundToUnbound(name_mapping = [["q"], ["q_unbounded"]], original_lower_bound=0.125, original_upper_bound=1.), + BoundToUnbound(name_mapping = [["q"], ["q_unbounded"]], original_lower_bound=0.125, original_upper_bound=1.0), ] ``` From d53bdf97b745e36efeca98ad681f14acdf44da24 Mon Sep 17 00:00:00 2001 From: xuyuon <116078673+xuyuon@users.noreply.github.com> Date: Fri, 23 Aug 2024 17:22:04 +0800 Subject: [PATCH 21/31] Updated jim_guide.md --- docs/tutorials/jim_guide.md | 34 ++++++++++++++++++++-------------- 1 file changed, 20 insertions(+), 14 deletions(-) diff --git a/docs/tutorials/jim_guide.md b/docs/tutorials/jim_guide.md index a9f883cbf..d77b3171c 100644 --- a/docs/tutorials/jim_guide.md +++ b/docs/tutorials/jim_guide.md @@ -7,7 +7,7 @@ The parameterization of some fundamental quantities can have significant impacts On the other hand, defining a prior in the component mass space is much more intuitive. The common prior of choice is uniform in the component mass space with some maximum and minimum mass. One may want to define the prior in the component mass space then sample in the chirp mass space. To make the problem even worse, there is yet another set of paraemeters one may want to choose, which is the set of parameters the model may want to take. For example, the waveform generator in ripple takes the symmetric mass ratio $\eta$ as input instead of the mass ratio. -So in a general setting, there could be three sets of parametrizations we can choose for our problem: a parameterization which we want to define our prior in $\vec{\theta_{prior}}$, a parameterization which we want the sampler to see $\vec{z}$, and a parameterization which the model takes $\vec{\theta_{model}}$. To facilitate the transformation between these parameterizations, we introduce a naming system and a transform system to handle this. +So in a general setting, there could be three sets of parametrizations we can choose for our problem: a parameterization $\vec{\theta}_{prior}$ which we want to define our prior in, a parameterization $\vec{z}$ which we want the sampler to see, and a parameterization $\vec{\theta}_{model}$ which the model takes. To facilitate the transformation between these parameterizations, we introduce a naming system and a transform system to handle this. A sketch of the transform system is shown below: ![A sketch of the transform system](prior_system_diagram.png) @@ -62,21 +62,27 @@ prior = CombinePrior( The `CombinePrior` object takes a list of `jimgw.prior` objects as argument and combines them into one single prior object that can be fed to the Jim sampler as input. # Transforms -In a general setting, there could be three sets of parametrizations we can choose for our problem: a parameterization which we want to define our prior in $\vec{\theta_{prior}}$, a parameterization which we want the sampler to see $\vec{z}$, and a parameterization which the model takes $\vec{\theta_{model}}$. To facilitate the transformation between these parameterizations, we introduce a naming system and a transform system to handle this. +In general, there could be three sets of parametrizations we need to work with in our problem: -## Setting up Sample Transforms -As we could have two different sets of parameterization for defining the prior and for the sampler to see, we need to set up transformations which transform from the parameter set $\vec{\theta_{prior}}$ to $\vec{z}$. +1. A parameterization $\vec{\theta_{prior}}$ which we want to define our prior in +2. a parameterization $\vec{z}$ which we want the sampler to see +3. a parameterization $\vec{\theta_{model}}$ which the model takes -### Bound-to-unbound Transforms -In general, we want the sampler to see a set of parametrization that does not includes any hard bounds, namely that it is well defined in the whole real space. This is to prevent the situation where the samples could walk out of the bound into the parameter space where it is not well defined. However, it is often the case that parametrization we used to define prior $\vec{\theta_{prior}}$ contains hard bound. Therefore, we need a bound-to-unbound transform to transform the parametrization into another parametrization $z$ without a hard bound. +To handle these different parameterizations, Jim provides a naming system and a transform system to facilitate the necessary transformations between the different parameterizations. -In a nutshell, bound-to-unbound transform utilize the logit function to map real numbers from $(0, 1)$ to real numbers in $(-\infty, +\infty)$. The logit function is given by: +## Setting up Sample Transformations +As mentioned earlier, we may have different parameterizations for defining the priors (θ_prior) and for the sampler to see (z). Therefore, we have to set up sample transformations that can convert between these two parameterizations. + +### Bound-to-unbound Transformations +In general, we want the sampler to sample in an unconstrained parameter space, in which the set of parameters $z$ are well-defined over the entire real space. This prevents the samples from crossing into regions of the parameter space where the value is not well-defined. + +However, the parameterization that we use to define the priors, $θ_prior$, often contain parameters with hard bounds. Therefore, we need a bound-to-unbound transformation to map the bounded parameters into an unbounded representation. In a nutshell, bound-to-unbound transformation in Jim utilize the logit function to map real numbers from $(0, 1)$ to real numbers in $(-\infty, +\infty)$. The logit function is given by: $$ logit(\theta) = \ln{\frac{\theta}{1-\theta}} $$ -To set up bound-to-unbound transform, we use the transformation class `BoundToUnbound` provided in `jimgw.transforms`: +To set up bound-to-unbound transformation, we call the transformation class `BoundToUnbound` provided in `jimgw.transforms`: ``` from jimgw.transforms import BoundToUnbound @@ -86,10 +92,10 @@ sample_transform = [ ] ``` -Basically, we want to fit all the sample transformations from parametrization $\vec{\theta_{prior}}$ to $\vec{z}$ in a list, which will be passed into the `Jim` object later. When executing the transformation, the transformations will be performed in the sequence the same as how it is arranged in the list. +These sample transformations are now contained in the list `sample_transform`, which will be passed to the `Jim` sampler. When the transformations are executed in `Jim`, they will be applied in the order as they appear in the list. ### Other Sample Transforms -We can also find other transformation that is specifically made for parameter estimation of compact binary coalescence in `jimgw.single_event.transforms`. For example, if we have defined prior on component masses $m_1$ and $m_2$, but we wish to sample on chirp mass $M_c$ and mass ratio $q$ instead. We could contain the function `ComponentMassesToChirpMassMassRatioTransform` in the sample transform list: +Other than bound-to-unbound transformations `BoundToUnbound`, Jim also provides transformations in `jimgw.single_event.transforms` for compact binary coalescence (CBC) parameter estimation problems. In these problems, we may want to sample on different parameters than the ones we used to define the priors. For example, if we have defined prior on component masses $m_1$ and $m_2$, but wish to sample on chirp mass $M_c$ and mass ratio $q$ instead. We could contain the function `ComponentMassesToChirpMassMassRatioTransform` in the sample transform list: ``` from jimgw.single_event.transforms import ComponentMassesToChirpMassMassRatioTransform @@ -100,13 +106,13 @@ sample_transforms = [ ] ``` -Again, you should always include a `boundToUnbound` transform in the end. +Again, we should always include a `boundToUnbound` transform at the end of the list of `sample_transform`. -## Setting up Likelihood Transform -Again, as the parameterization the model takes can be different from the parameterization for defining the prior, we need to set up likelihood transformations which transform from the parameter set $\vec{\theta_{prior}}$ to $\vec{\theta_{model}}$. +## Setting up Likelihood Transformations +Again, the parameterization $\vec{\theta_{model}}$ used by the model may be different from the parameterization $\vec{\theta_{prior}}$ used to define the prior. Therefore, we need to set up likelihood transformations that map from the parameterization $\vec{\theta_{model}}$ to the parameterization $\vec{\theta_{prior}}$. -Setting up likelihood transforms is similar to setting up sample transform. We need to define a list of transformation that transform from the parameter set $\vec{\theta_{prior}}$ to $\vec{\theta_{model}}$. +Similar to the sample transformations, we need to define a list of transformations that will map from $\vec{\theta_{prior}}$ space to $\vec{\theta_{model}}$ space. ``` likelihood_transforms = [ From c1c8bfe03b691ba8a7421d38eadef5b17faaa6ed Mon Sep 17 00:00:00 2001 From: xuyuon <116078673+xuyuon@users.noreply.github.com> Date: Fri, 23 Aug 2024 18:01:42 +0800 Subject: [PATCH 22/31] Add files via upload --- docs/tutorials/likelihood_transform.png | Bin 0 -> 263876 bytes docs/tutorials/sample_transform.png | Bin 0 -> 262218 bytes 2 files changed, 0 insertions(+), 0 deletions(-) create mode 100644 docs/tutorials/likelihood_transform.png create mode 100644 docs/tutorials/sample_transform.png diff --git a/docs/tutorials/likelihood_transform.png b/docs/tutorials/likelihood_transform.png new file mode 100644 index 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From 8f0e10870991277b73281c40a03af5e3a998866a Mon Sep 17 00:00:00 2001 From: xuyuon <116078673+xuyuon@users.noreply.github.com> Date: Fri, 23 Aug 2024 18:05:07 +0800 Subject: [PATCH 24/31] Updated jim_guide.md --- docs/tutorials/jim_guide.md | 2 ++ 1 file changed, 2 insertions(+) diff --git a/docs/tutorials/jim_guide.md b/docs/tutorials/jim_guide.md index d77b3171c..71cc2f4d7 100644 --- a/docs/tutorials/jim_guide.md +++ b/docs/tutorials/jim_guide.md @@ -71,6 +71,7 @@ In general, there could be three sets of parametrizations we need to work with i To handle these different parameterizations, Jim provides a naming system and a transform system to facilitate the necessary transformations between the different parameterizations. ## Setting up Sample Transformations +![Sample Transformations](sample_transform.png) As mentioned earlier, we may have different parameterizations for defining the priors (θ_prior) and for the sampler to see (z). Therefore, we have to set up sample transformations that can convert between these two parameterizations. ### Bound-to-unbound Transformations @@ -110,6 +111,7 @@ Again, we should always include a `boundToUnbound` transform at the end of the l ## Setting up Likelihood Transformations +![Likelihood transformation](likelihood_transform.png) Again, the parameterization $\vec{\theta_{model}}$ used by the model may be different from the parameterization $\vec{\theta_{prior}}$ used to define the prior. Therefore, we need to set up likelihood transformations that map from the parameterization $\vec{\theta_{model}}$ to the parameterization $\vec{\theta_{prior}}$. Similar to the sample transformations, we need to define a list of transformations that will map from $\vec{\theta_{prior}}$ space to $\vec{\theta_{model}}$ space. From edb04050036d348ccd67e71c79afbdffb79b644a Mon Sep 17 00:00:00 2001 From: xuyuon <116078673+xuyuon@users.noreply.github.com> Date: Fri, 23 Aug 2024 18:06:47 +0800 Subject: [PATCH 25/31] Updated jim_guide.md --- docs/tutorials/jim_guide.md | 3 +++ 1 file changed, 3 insertions(+) diff --git a/docs/tutorials/jim_guide.md b/docs/tutorials/jim_guide.md index 71cc2f4d7..5717f2f34 100644 --- a/docs/tutorials/jim_guide.md +++ b/docs/tutorials/jim_guide.md @@ -119,5 +119,8 @@ Similar to the sample transformations, we need to define a list of transformatio ``` likelihood_transforms = [ ComponentMassesToChirpMassMassRatioTransform(name_mapping=[["m_1", "m_2"], ["M_c", "q"]]), + MassRatioToSymmetricMassRatioTransform(name_mapping=[["q"], ["eta"]]), ] ``` + +Again when the transformations are executed in `Jim`, they will be applied in the order as they appear in the list. From fb05218fea7bc22244cfa574ee42e050cdcadf3c Mon Sep 17 00:00:00 2001 From: xuyuon <116078673+xuyuon@users.noreply.github.com> Date: Fri, 23 Aug 2024 18:09:05 +0800 Subject: [PATCH 26/31] Move the draft into prior_system.md --- docs/tutorials/prior_system.md | 115 +++++++++++++++++++++++++++++++-- 1 file changed, 109 insertions(+), 6 deletions(-) diff --git a/docs/tutorials/prior_system.md b/docs/tutorials/prior_system.md index 43a924dfb..afc5a5ef3 100644 --- a/docs/tutorials/prior_system.md +++ b/docs/tutorials/prior_system.md @@ -7,20 +7,123 @@ The parameterization of some fundamental quantities can have significant impacts On the other hand, defining a prior in the component mass space is much more intuitive. The common prior of choice is uniform in the component mass space with some maximum and minimum mass. One may want to define the prior in the component mass space then sample in the chirp mass space. To make the problem even worse, there is yet another set of paraemeters one may want to choose, which is the set of parameters the model may want to take. For example, the waveform generator in ripple takes the symmetric mass ratio $\eta$ as input instead of the mass ratio. -So in a general setting, there could be three sets of parametrizations we can choose for our problem: a parameterization which we want to define our prior in, a parameterization which we want the sampler to see, and a parameterization which the model takes. To facilitate the transformation between these parameterizations, we introduce a naming system and a transform system to handle this. +So in a general setting, there could be three sets of parametrizations we can choose for our problem: a parameterization $\vec{\theta}_{prior}$ which we want to define our prior in, a parameterization $\vec{z}$ which we want the sampler to see, and a parameterization $\vec{\theta}_{model}$ which the model takes. To facilitate the transformation between these parameterizations, we introduce a naming system and a transform system to handle this. A sketch of the transform system is shown below: -![A sketch of the transform system](prior_system.jpg) - -# Prior +![A sketch of the transform system](prior_system_diagram.png) Fundamentally, all `jim` needs is to pass a reasonable posterior function `posterior(z) = likelihood(t_1(z)) + prior(t_2(z))` to `flowMC`, so `flowMC` can sample the function. Here, `likelihood` and `prior` are functions that one pass in a vector of numbers (and data), and it returns a scalar. `z` is the vector of variables the sampler sees, and `t_1` and `t_2` are the transforms that transform the variables between the sampler and the model. -Since we want to sample in `z`, ultimately we want to have a prior defined in `z`, meaning we can evaluate `p_Z(z)`. However, this is could be non-trivial, such as defining a prior in the $\mathcal{M}_c$-$q$ space that is equivalent to a uniform prior in the $\mathcal{M}_1$-$\mathcal{M}_2$ space requires a very complex expression. Instead of directly writing down the prior distribution in `z`, we can start by defining the prior in a space that is more intuitive, then transform the prior to the space `z` using a transform. By carrying the Jacobian of the transform, we can define the prior in the space `z` by transforming the prior in the intuitive space, $p_Z(z) = p_X(x) \left| \frac{dx}{dz} \right|$, where $x = t_2(z)$. The tricky bit here is the user often wants to start from the prior $x$ and define the transform **to** the sample space `z`, but here the transform is defined **from** the sample space `z` to the prior space $x$. So in order to make the prior-to-sample transform work in practice, the transform has to be **bijective**, which implies they are invertible and have a well-defined determinant of the Jacobian. +Since we want to sample in `z`, ultimately we want to have a prior defined in `z`, meaning we can evaluate `p_Z(z)`. However, this is could be non-trivial, such as defining a prior in the $\mathcal{M}_c$-$q$ space that is equivalent to a uniform prior in the $\mathcal{M}_1$-$\mathcal{M}_2$ space requires a very complex expression. Instead of directly writing down the prior distribution in `z`, we can start by defining the prior in a space that is more intuitive, then transform the prior to the space `z` using a transform. + +By carrying the Jacobian of the transform, we can define the prior in the space `z` by transforming the prior in the intuitive space, $p_Z(z) = p_X(x) \left| \frac{dx}{dz} \right|$, where $x = t_2(z)$. The tricky bit here is the user often wants to start from the prior $x$ and define the transform **to** the sample space `z`, but here the transform is defined **from** the sample space `z` to the prior space $x$. So in order to make the prior-to-sample transform work in practice, the transform has to be **bijective**, which implies they are invertible and have a well-defined determinant of the Jacobian. On the other hand, the likelihood is often related to a model instead of coming from a distribution, meaning as long as one can transform the parameters to feed into the model, there is no limitation on the transform.. So the transform for the likelihood is strictly from the sample space `z` to the model space $y = t_1(z)$. For this reason, the transform for the likelihood does not need to be bijective, it can even by a N-to-M transform. +# Prior + ## Primatives -# Transforms \ No newline at end of file +## Setting up Priors +Prior represents the prior knowledge on the probability density distribution of the event parameters $\theta$. In Jim, we could set up priors using the prior class `jimgw.prior`. Suppose we want to define a uniform prior distribution for the parameter $x$, we could call the `UniformPrior` class: + +``` +from jimgw.prior import UniformPrior +prior = UniformPrior(0.0, 1.0, parameter_names=["x"]) +``` + +Jim provides a number of built-in prior classes, including: +- `UniformPrior` +- `SinePrior` +- `CosinePrior` +- `PowerLawPrior` + +A complete list of prior classes available can be found in the Jim documentation (not available yet). + +### Multi-dimensional Priors +When working with multi-dimensional parameter space, we will usually want to define priors for each individual parameter first: + +``` +from jimgw.prior import UniformPrior +prior_x = UniformPrior(0.0, 1.0, parameter_names=["x"]) +prior_y = UniformPrior(0.0, 2.0, parameter_names=["y"]) +``` + +Once we have the individual priors defined, we can call the class `CombinePrior` to combine them into one single prior object: + +``` +from jimgw.prior import CombinePrior +prior = CombinePrior( + [ + prior_x, + prior_y, + ] +) +``` + +The `CombinePrior` object takes a list of `jimgw.prior` objects as argument and combines them into one single prior object that can be fed to the Jim sampler as input. + +# Transforms +In general, there could be three sets of parametrizations we need to work with in our problem: + +1. A parameterization $\vec{\theta_{prior}}$ which we want to define our prior in +2. a parameterization $\vec{z}$ which we want the sampler to see +3. a parameterization $\vec{\theta_{model}}$ which the model takes + +To handle these different parameterizations, Jim provides a naming system and a transform system to facilitate the necessary transformations between the different parameterizations. + +## Setting up Sample Transformations +![Sample Transformations](sample_transform.png) +As mentioned earlier, we may have different parameterizations for defining the priors (θ_prior) and for the sampler to see (z). Therefore, we have to set up sample transformations that can convert between these two parameterizations. + +### Bound-to-unbound Transformations +In general, we want the sampler to sample in an unconstrained parameter space, in which the set of parameters $z$ are well-defined over the entire real space. This prevents the samples from crossing into regions of the parameter space where the value is not well-defined. + +However, the parameterization that we use to define the priors, $θ_prior$, often contain parameters with hard bounds. Therefore, we need a bound-to-unbound transformation to map the bounded parameters into an unbounded representation. In a nutshell, bound-to-unbound transformation in Jim utilize the logit function to map real numbers from $(0, 1)$ to real numbers in $(-\infty, +\infty)$. The logit function is given by: + +$$ +logit(\theta) = \ln{\frac{\theta}{1-\theta}} +$$ + +To set up bound-to-unbound transformation, we call the transformation class `BoundToUnbound` provided in `jimgw.transforms`: + +``` +from jimgw.transforms import BoundToUnbound +sample_transform = [ + BoundToUnbound(name_mapping = [["x"], ["x_unbounded"]], original_lower_bound=0.0, original_upper_bound=1.0), + BoundToUnbound(name_mapping = [["y"], ["y_unbounded"]], original_lower_bound=0.0, original_upper_bound=10.0), +] +``` + +These sample transformations are now contained in the list `sample_transform`, which will be passed to the `Jim` sampler. When the transformations are executed in `Jim`, they will be applied in the order as they appear in the list. + +### Other Sample Transformations +Other than bound-to-unbound transformations `BoundToUnbound`, Jim also provides transformations in `jimgw.single_event.transforms` for compact binary coalescence (CBC) parameter estimation problems. In these problems, we may want to sample on different parameters than the ones we used to define the priors. For example, if we have defined prior on component masses $m_1$ and $m_2$, but wish to sample on chirp mass $M_c$ and mass ratio $q$ instead. We could contain the function `ComponentMassesToChirpMassMassRatioTransform` in the sample transform list: + +``` +from jimgw.single_event.transforms import ComponentMassesToChirpMassMassRatioTransform +sample_transforms = [ + ComponentMassesToChirpMassMassRatioTransform(name_mapping=[["m_1", "m_2"], ["M_c", "q"]]), + BoundToUnbound(name_mapping = [["M_c"], ["M_c_unbounded"]], original_lower_bound=10.0, original_upper_bound=80.0), + BoundToUnbound(name_mapping = [["q"], ["q_unbounded"]], original_lower_bound=0.125, original_upper_bound=1.0), +] +``` + +Again, we should always include a `boundToUnbound` transform at the end of the list of `sample_transform`. + + +## Setting up Likelihood Transformations +![Likelihood transformation](likelihood_transform.png) +Again, the parameterization $\vec{\theta_{model}}$ used by the model may be different from the parameterization $\vec{\theta_{prior}}$ used to define the prior. Therefore, we need to set up likelihood transformations that map from the parameterization $\vec{\theta_{model}}$ to the parameterization $\vec{\theta_{prior}}$. + +Similar to the sample transformations, we need to define a list of transformations that will map from $\vec{\theta_{prior}}$ space to $\vec{\theta_{model}}$ space. + +``` +likelihood_transforms = [ + ComponentMassesToChirpMassMassRatioTransform(name_mapping=[["m_1", "m_2"], ["M_c", "q"]]), + MassRatioToSymmetricMassRatioTransform(name_mapping=[["q"], ["eta"]]), +] +``` + +Again when the transformations are executed in `Jim`, they will be applied in the order as they appear in the list. \ No newline at end of file From 372411c8fd8558edb6ff97a8d54d3064a27e6aac Mon Sep 17 00:00:00 2001 From: xuyuon <116078673+xuyuon@users.noreply.github.com> Date: Fri, 23 Aug 2024 18:09:37 +0800 Subject: [PATCH 27/31] Delete docs/tutorials/jim_guide.md --- docs/tutorials/jim_guide.md | 126 ------------------------------------ 1 file changed, 126 deletions(-) delete mode 100644 docs/tutorials/jim_guide.md diff --git a/docs/tutorials/jim_guide.md b/docs/tutorials/jim_guide.md deleted file mode 100644 index 5717f2f34..000000000 --- a/docs/tutorials/jim_guide.md +++ /dev/null @@ -1,126 +0,0 @@ -# Jim's parameter transform system - -!!! warning - **Heavy development**: This is a work in progress and is subject to change. If you have any questions, please feel free to open an issue. - -The parameterization of some fundamental quantities can have significant impacts on the performance of the sampler. For example, the masses can be parameterized in the component mass spaces $\mathcal{M}_1$-$\mathcal{M}_2$ or chirp mass-mass ratio $\mathcal{M}_c$-$q$. Because of the strong correlation in the component mass space, the geometry is much harder for a sampler to explore. This can lead to slow convergence and poor performance. The chirp mass-mass ratio space is much more isotropic and easier to explore, which is often the choice to expose to the sampler. - -On the other hand, defining a prior in the component mass space is much more intuitive. The common prior of choice is uniform in the component mass space with some maximum and minimum mass. One may want to define the prior in the component mass space then sample in the chirp mass space. To make the problem even worse, there is yet another set of paraemeters one may want to choose, which is the set of parameters the model may want to take. For example, the waveform generator in ripple takes the symmetric mass ratio $\eta$ as input instead of the mass ratio. - -So in a general setting, there could be three sets of parametrizations we can choose for our problem: a parameterization $\vec{\theta}_{prior}$ which we want to define our prior in, a parameterization $\vec{z}$ which we want the sampler to see, and a parameterization $\vec{\theta}_{model}$ which the model takes. To facilitate the transformation between these parameterizations, we introduce a naming system and a transform system to handle this. - -A sketch of the transform system is shown below: -![A sketch of the transform system](prior_system_diagram.png) - -Fundamentally, all `jim` needs is to pass a reasonable posterior function `posterior(z) = likelihood(t_1(z)) + prior(t_2(z))` to `flowMC`, so `flowMC` can sample the function. Here, `likelihood` and `prior` are functions that one pass in a vector of numbers (and data), and it returns a scalar. `z` is the vector of variables the sampler sees, and `t_1` and `t_2` are the transforms that transform the variables between the sampler and the model. - -Since we want to sample in `z`, ultimately we want to have a prior defined in `z`, meaning we can evaluate `p_Z(z)`. However, this is could be non-trivial, such as defining a prior in the $\mathcal{M}_c$-$q$ space that is equivalent to a uniform prior in the $\mathcal{M}_1$-$\mathcal{M}_2$ space requires a very complex expression. Instead of directly writing down the prior distribution in `z`, we can start by defining the prior in a space that is more intuitive, then transform the prior to the space `z` using a transform. - -By carrying the Jacobian of the transform, we can define the prior in the space `z` by transforming the prior in the intuitive space, $p_Z(z) = p_X(x) \left| \frac{dx}{dz} \right|$, where $x = t_2(z)$. The tricky bit here is the user often wants to start from the prior $x$ and define the transform **to** the sample space `z`, but here the transform is defined **from** the sample space `z` to the prior space $x$. So in order to make the prior-to-sample transform work in practice, the transform has to be **bijective**, which implies they are invertible and have a well-defined determinant of the Jacobian. - -On the other hand, the likelihood is often related to a model instead of coming from a distribution, meaning as long as one can transform the parameters to feed into the model, there is no limitation on the transform.. So the transform for the likelihood is strictly from the sample space `z` to the model space $y = t_1(z)$. For this reason, the transform for the likelihood does not need to be bijective, it can even by a N-to-M transform. - -# Prior - -## Setting up Priors -Prior represents the prior knowledge on the probability density distribution of the event parameters $\theta$. In Jim, we could set up priors using the prior class `jimgw.prior`. Suppose we want to define a uniform prior distribution for the parameter $x$, we could call the `UniformPrior` class: - -``` -from jimgw.prior import UniformPrior -prior = UniformPrior(0.0, 1.0, parameter_names=["x"]) -``` - -Jim provides a number of built-in prior classes, including: -- `UniformPrior` -- `SinePrior` -- `CosinePrior` -- `PowerLawPrior` - -A complete list of prior classes available can be found in the Jim documentation (not available yet). - -### Multi-dimensional Priors -When working with multi-dimensional parameter space, we will usually want to define priors for each individual parameter first: - -``` -from jimgw.prior import UniformPrior -prior_x = UniformPrior(0.0, 1.0, parameter_names=["x"]) -prior_y = UniformPrior(0.0, 2.0, parameter_names=["y"]) -``` - -Once we have the individual priors defined, we can call the class `CombinePrior` to combine them into one single prior object: - -``` -from jimgw.prior import CombinePrior -prior = CombinePrior( - [ - prior_x, - prior_y, - ] -) -``` - -The `CombinePrior` object takes a list of `jimgw.prior` objects as argument and combines them into one single prior object that can be fed to the Jim sampler as input. - -# Transforms -In general, there could be three sets of parametrizations we need to work with in our problem: - -1. A parameterization $\vec{\theta_{prior}}$ which we want to define our prior in -2. a parameterization $\vec{z}$ which we want the sampler to see -3. a parameterization $\vec{\theta_{model}}$ which the model takes - -To handle these different parameterizations, Jim provides a naming system and a transform system to facilitate the necessary transformations between the different parameterizations. - -## Setting up Sample Transformations -![Sample Transformations](sample_transform.png) -As mentioned earlier, we may have different parameterizations for defining the priors (θ_prior) and for the sampler to see (z). Therefore, we have to set up sample transformations that can convert between these two parameterizations. - -### Bound-to-unbound Transformations -In general, we want the sampler to sample in an unconstrained parameter space, in which the set of parameters $z$ are well-defined over the entire real space. This prevents the samples from crossing into regions of the parameter space where the value is not well-defined. - -However, the parameterization that we use to define the priors, $θ_prior$, often contain parameters with hard bounds. Therefore, we need a bound-to-unbound transformation to map the bounded parameters into an unbounded representation. In a nutshell, bound-to-unbound transformation in Jim utilize the logit function to map real numbers from $(0, 1)$ to real numbers in $(-\infty, +\infty)$. The logit function is given by: - -$$ -logit(\theta) = \ln{\frac{\theta}{1-\theta}} -$$ - -To set up bound-to-unbound transformation, we call the transformation class `BoundToUnbound` provided in `jimgw.transforms`: - -``` -from jimgw.transforms import BoundToUnbound -sample_transform = [ - BoundToUnbound(name_mapping = [["x"], ["x_unbounded"]], original_lower_bound=0.0, original_upper_bound=1.0), - BoundToUnbound(name_mapping = [["y"], ["y_unbounded"]], original_lower_bound=0.0, original_upper_bound=10.0), -] -``` - -These sample transformations are now contained in the list `sample_transform`, which will be passed to the `Jim` sampler. When the transformations are executed in `Jim`, they will be applied in the order as they appear in the list. - -### Other Sample Transforms -Other than bound-to-unbound transformations `BoundToUnbound`, Jim also provides transformations in `jimgw.single_event.transforms` for compact binary coalescence (CBC) parameter estimation problems. In these problems, we may want to sample on different parameters than the ones we used to define the priors. For example, if we have defined prior on component masses $m_1$ and $m_2$, but wish to sample on chirp mass $M_c$ and mass ratio $q$ instead. We could contain the function `ComponentMassesToChirpMassMassRatioTransform` in the sample transform list: - -``` -from jimgw.single_event.transforms import ComponentMassesToChirpMassMassRatioTransform -sample_transforms = [ - ComponentMassesToChirpMassMassRatioTransform(name_mapping=[["m_1", "m_2"], ["M_c", "q"]]), - BoundToUnbound(name_mapping = [["M_c"], ["M_c_unbounded"]], original_lower_bound=10.0, original_upper_bound=80.0), - BoundToUnbound(name_mapping = [["q"], ["q_unbounded"]], original_lower_bound=0.125, original_upper_bound=1.0), -] -``` - -Again, we should always include a `boundToUnbound` transform at the end of the list of `sample_transform`. - - -## Setting up Likelihood Transformations -![Likelihood transformation](likelihood_transform.png) -Again, the parameterization $\vec{\theta_{model}}$ used by the model may be different from the parameterization $\vec{\theta_{prior}}$ used to define the prior. Therefore, we need to set up likelihood transformations that map from the parameterization $\vec{\theta_{model}}$ to the parameterization $\vec{\theta_{prior}}$. - -Similar to the sample transformations, we need to define a list of transformations that will map from $\vec{\theta_{prior}}$ space to $\vec{\theta_{model}}$ space. - -``` -likelihood_transforms = [ - ComponentMassesToChirpMassMassRatioTransform(name_mapping=[["m_1", "m_2"], ["M_c", "q"]]), - MassRatioToSymmetricMassRatioTransform(name_mapping=[["q"], ["eta"]]), -] -``` - -Again when the transformations are executed in `Jim`, they will be applied in the order as they appear in the list. From 433fa83dc3fdf88d622aa1d945ccab3e8071a9d4 Mon Sep 17 00:00:00 2001 From: xuyuon <116078673+xuyuon@users.noreply.github.com> Date: Fri, 23 Aug 2024 18:10:22 +0800 Subject: [PATCH 28/31] Delete example/notebooks/GW150914_PV2.ipynb --- example/notebooks/GW150914_PV2.ipynb | 183 --------------------------- 1 file changed, 183 deletions(-) delete mode 100644 example/notebooks/GW150914_PV2.ipynb diff --git a/example/notebooks/GW150914_PV2.ipynb b/example/notebooks/GW150914_PV2.ipynb deleted file mode 100644 index ff27b3ead..000000000 --- a/example/notebooks/GW150914_PV2.ipynb +++ /dev/null @@ -1,183 +0,0 @@ -{ - "cells": [ - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "## Import Necessary Modules" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": {}, - "outputs": [], - "source": [ - "import time\n", - "\n", - "import jax\n", - "import jax.numpy as jnp\n", - "\n", - "from jimgw.jim import Jim\n", - "from jimgw.prior import CombinePrior, UniformPrior, CosinePrior, SinePrior, PowerLawPrior\n", - "from jimgw.single_event.detector import H1, L1\n", - "from jimgw.single_event.likelihood import TransientLikelihoodFD\n", - "from jimgw.single_event.waveform import RippleIMRPhenomPv2\n", - "from jimgw.transforms import BoundToUnbound\n", - "from jimgw.single_event.transforms import MassRatioToSymmetricMassRatioTransform, SpinToCartesianSpinTransform, ComponentMassesToChirpMassMassRatioTransform, SkyFrameToDetectorFrameSkyPositionTransform\n", - "from jimgw.single_event.utils import Mc_q_to_m1_m2\n", - "from flowMC.strategy.optimization import optimization_Adam\n", - "\n", - "jax.config.update(\"jax_enable_x64\", True)\n", - "\n", - "total_time_start = time.time()" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "## Fetch the detector data\n", - "We first fetch the 4s segment detector data centered on GW150914. " - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": {}, - "outputs": [], - "source": [ - "gps = 1126259462.4\n", - "duration = 4\n", - "post_trigger_duration = 2\n", - "start_pad = duration - post_trigger_duration\n", - "end_pad = post_trigger_duration\n", - "fmin = 20.0\n", - "fmax = 1024.0\n", - "\n", - "ifos = [H1, L1]\n", - "\n", - "f_ref = 20.0\n", - "\n", - "for ifo in ifos:\n", - " ifo.load_data(gps, start_pad, end_pad, fmin, fmax, psd_pad=16, tukey_alpha=0.2)" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "## Set up Prior\n", - "Prior is the prior knowledge you have on the probability distribution of the event parameters $\\theta_{prior}$. There is a few prior classes available: UniformPrior,..." - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": {}, - "outputs": [], - "source": [ - "M_c_min, M_c_max = 10.0, 80.0\n", - "q_min, q_max = 0.125, 1.0\n", - "m_1_prior = UniformPrior(Mc_q_to_m1_m2(M_c_min, q_max)[0], Mc_q_to_m1_m2(M_c_max, q_min)[0], parameter_names=[\"m_1\"])\n", - "m_2_prior = UniformPrior(Mc_q_to_m1_m2(M_c_min, q_min)[1], Mc_q_to_m1_m2(M_c_max, q_max)[1], parameter_names=[\"m_2\"])\n", - "theta_jn_prior = SinePrior(parameter_names=[\"theta_jn\"])\n", - "phi_jl_prior = UniformPrior(0.0, 2 * jnp.pi, parameter_names=[\"phi_jl\"])\n", - "theta_1_prior = SinePrior(parameter_names=[\"theta_1\"])\n", - "theta_2_prior = SinePrior(parameter_names=[\"theta_2\"])\n", - "phi_12_prior = UniformPrior(0.0, 2 * jnp.pi, parameter_names=[\"phi_12\"])\n", - "a_1_prior = UniformPrior(0.0, 1.0, parameter_names=[\"a_1\"])\n", - "a_2_prior = UniformPrior(0.0, 1.0, parameter_names=[\"a_2\"])\n", - "dL_prior = PowerLawPrior(10.0, 2000.0, 2.0, parameter_names=[\"d_L\"])\n", - "t_c_prior = UniformPrior(-0.05, 0.05, parameter_names=[\"t_c\"])\n", - "phase_c_prior = UniformPrior(0.0, 2 * jnp.pi, parameter_names=[\"phase_c\"])\n", - "psi_prior = UniformPrior(0.0, jnp.pi, parameter_names=[\"psi\"])\n", - "ra_prior = UniformPrior(0.0, 2 * jnp.pi, parameter_names=[\"ra\"])\n", - "dec_prior = CosinePrior(parameter_names=[\"dec\"])\n", - "\n", - "prior = CombinePrior(\n", - " [\n", - " m_1_prior,\n", - " m_2_prior,\n", - " theta_jn_prior,\n", - " phi_jl_prior,\n", - " theta_1_prior,\n", - " theta_2_prior,\n", - " phi_12_prior,\n", - " a_1_prior,\n", - " a_2_prior,\n", - " dL_prior,\n", - " t_c_prior,\n", - " phase_c_prior,\n", - " psi_prior,\n", - " ra_prior,\n", - " dec_prior,\n", - " ]\n", - ")" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "## Set up Sample Transform\n", - "Sometimes the same event can be described by multiple different set of event parameters, and it exists some transform that transform from one set of parameters to another set of parameters. Suppose we want to define prior on one set of event parameters $\\theta_1$, but sample on another set of event parameters $\\theta_2$, sample transform becomes useful. " - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": {}, - "outputs": [], - "source": [ - "sample_transforms = [\n", - " ComponentMassesToChirpMassMassRatioTransform(name_mapping=[[\"m_1\", \"m_2\"], [\"M_c\", \"q\"]]),\n", - " BoundToUnbound(name_mapping = [[\"M_c\"], [\"M_c_unbounded\"]], original_lower_bound=10.0, original_upper_bound=80.0),\n", - " BoundToUnbound(name_mapping = [[\"q\"], [\"q_unbounded\"]], original_lower_bound=0.125, original_upper_bound=1.),\n", - " BoundToUnbound(name_mapping = [[\"theta_jn\"], [\"theta_jn_unbounded\"]] , original_lower_bound=0.0, original_upper_bound=jnp.pi),\n", - " BoundToUnbound(name_mapping = [[\"phi_jl\"], [\"phi_jl_unbounded\"]] , original_lower_bound=0.0, original_upper_bound=2 * jnp.pi),\n", - " BoundToUnbound(name_mapping = [[\"theta_1\"], [\"theta_1_unbounded\"]] , original_lower_bound=0.0, original_upper_bound=jnp.pi),\n", - " BoundToUnbound(name_mapping = [[\"theta_2\"], [\"theta_2_unbounded\"]] , original_lower_bound=0.0, original_upper_bound=jnp.pi),\n", - " BoundToUnbound(name_mapping = [[\"phi_12\"], [\"phi_12_unbounded\"]] , original_lower_bound=0.0, original_upper_bound=2 * jnp.pi),\n", - " BoundToUnbound(name_mapping = [[\"a_1\"], [\"a_1_unbounded\"]] , original_lower_bound=0.0, original_upper_bound=1.0),\n", - " BoundToUnbound(name_mapping = [[\"a_2\"], [\"a_2_unbounded\"]] , original_lower_bound=0.0, original_upper_bound=1.0),\n", - " BoundToUnbound(name_mapping = [[\"d_L\"], [\"d_L_unbounded\"]] , original_lower_bound=10.0, original_upper_bound=2000.0),\n", - " BoundToUnbound(name_mapping = [[\"t_c\"], [\"t_c_unbounded\"]] , original_lower_bound=-0.05, original_upper_bound=0.05),\n", - " BoundToUnbound(name_mapping = [[\"phase_c\"], [\"phase_c_unbounded\"]] , original_lower_bound=0.0, original_upper_bound=2 * jnp.pi),\n", - " BoundToUnbound(name_mapping = [[\"psi\"], [\"psi_unbounded\"]], original_lower_bound=0.0, original_upper_bound=jnp.pi),\n", - " SkyFrameToDetectorFrameSkyPositionTransform(name_mapping = [[\"ra\", \"dec\"], [\"zenith\", \"azimuth\"]], gps_time=gps, ifos=ifos),\n", - " BoundToUnbound(name_mapping = [[\"zenith\"], [\"zenith_unbounded\"]], original_lower_bound=0.0, original_upper_bound=jnp.pi),\n", - " BoundToUnbound(name_mapping = [[\"azimuth\"], [\"azimuth_unbounded\"]], original_lower_bound=0.0, original_upper_bound=2 * jnp.pi),\n", - "]" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "## Set up Likelihood Transform\n", - "To make the issue even more complicated, sometimes the model could takes another set of parameters. Therefore, we would define likelihood transforms that transform $\\theta_2$ into $\\theta_3$." - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": {}, - "outputs": [], - "source": [ - "likelihood_transforms = [\n", - " ComponentMassesToChirpMassMassRatioTransform(name_mapping=[[\"m_1\", \"m_2\"], [\"M_c\", \"q\"]]),\n", - " SpinToCartesianSpinTransform(name_mapping=[[\"theta_jn\", \"phi_jl\", \"theta_1\", \"theta_2\", \"phi_12\", \"a_1\", \"a_2\"], [\"iota\", \"s1_x\", \"s1_y\", \"s1_z\", \"s2_x\", \"s2_y\", \"s2_z\"]], freq_ref=f_ref),\n", - " MassRatioToSymmetricMassRatioTransform(name_mapping=[[\"q\"], [\"eta\"]]),\n", - "]" - ] - } - ], - "metadata": { - "language_info": { - "name": "python" - } - }, - "nbformat": 4, - "nbformat_minor": 2 -} From 53f3de4bed17167ecfc755f52c744f97a539b462 Mon Sep 17 00:00:00 2001 From: xuyuon <116078673+xuyuon@users.noreply.github.com> Date: Fri, 23 Aug 2024 18:20:43 +0800 Subject: [PATCH 29/31] Update prior_system.md --- docs/tutorials/prior_system.md | 4 ++-- 1 file changed, 2 insertions(+), 2 deletions(-) diff --git a/docs/tutorials/prior_system.md b/docs/tutorials/prior_system.md index afc5a5ef3..27be9683e 100644 --- a/docs/tutorials/prior_system.md +++ b/docs/tutorials/prior_system.md @@ -7,7 +7,7 @@ The parameterization of some fundamental quantities can have significant impacts On the other hand, defining a prior in the component mass space is much more intuitive. The common prior of choice is uniform in the component mass space with some maximum and minimum mass. One may want to define the prior in the component mass space then sample in the chirp mass space. To make the problem even worse, there is yet another set of paraemeters one may want to choose, which is the set of parameters the model may want to take. For example, the waveform generator in ripple takes the symmetric mass ratio $\eta$ as input instead of the mass ratio. -So in a general setting, there could be three sets of parametrizations we can choose for our problem: a parameterization $\vec{\theta}_{prior}$ which we want to define our prior in, a parameterization $\vec{z}$ which we want the sampler to see, and a parameterization $\vec{\theta}_{model}$ which the model takes. To facilitate the transformation between these parameterizations, we introduce a naming system and a transform system to handle this. +So in a general setting, there could be three sets of parametrizations we can choose for our problem: a parameterization $\vec{\theta_{prior}}$ which we want to define our prior in, a parameterization $\vec{z}$ which we want the sampler to see, and a parameterization $\vec{\theta}_{model}$ which the model takes. To facilitate the transformation between these parameterizations, we introduce a naming system and a transform system to handle this. A sketch of the transform system is shown below: ![A sketch of the transform system](prior_system_diagram.png) @@ -126,4 +126,4 @@ likelihood_transforms = [ ] ``` -Again when the transformations are executed in `Jim`, they will be applied in the order as they appear in the list. \ No newline at end of file +Again when the transformations are executed in `Jim`, they will be applied in the order as they appear in the list. From 59324b4a8ee4b821f70a124f4c44ed730a5258e4 Mon Sep 17 00:00:00 2001 From: xuyuon <116078673+xuyuon@users.noreply.github.com> Date: Fri, 23 Aug 2024 18:25:02 +0800 Subject: [PATCH 30/31] Update prior_system.md --- docs/tutorials/prior_system.md | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/docs/tutorials/prior_system.md b/docs/tutorials/prior_system.md index 27be9683e..08cacd526 100644 --- a/docs/tutorials/prior_system.md +++ b/docs/tutorials/prior_system.md @@ -75,7 +75,7 @@ To handle these different parameterizations, Jim provides a naming system and a ## Setting up Sample Transformations ![Sample Transformations](sample_transform.png) -As mentioned earlier, we may have different parameterizations for defining the priors (θ_prior) and for the sampler to see (z). Therefore, we have to set up sample transformations that can convert between these two parameterizations. +As mentioned earlier, we may have different parameterizations for defining the priors ($\theta_{prior}$) and for the sampler to see ($z$). Therefore, we have to set up sample transformations that can convert between these two parameterizations. ### Bound-to-unbound Transformations In general, we want the sampler to sample in an unconstrained parameter space, in which the set of parameters $z$ are well-defined over the entire real space. This prevents the samples from crossing into regions of the parameter space where the value is not well-defined. From a4bde2092d3a566e6ccb1aea6611d3180e2b924f Mon Sep 17 00:00:00 2001 From: xuyuon <116078673+xuyuon@users.noreply.github.com> Date: Fri, 23 Aug 2024 18:25:41 +0800 Subject: [PATCH 31/31] Update prior_system.md --- docs/tutorials/prior_system.md | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/docs/tutorials/prior_system.md b/docs/tutorials/prior_system.md index 08cacd526..16a1225f1 100644 --- a/docs/tutorials/prior_system.md +++ b/docs/tutorials/prior_system.md @@ -80,7 +80,7 @@ As mentioned earlier, we may have different parameterizations for defining the p ### Bound-to-unbound Transformations In general, we want the sampler to sample in an unconstrained parameter space, in which the set of parameters $z$ are well-defined over the entire real space. This prevents the samples from crossing into regions of the parameter space where the value is not well-defined. -However, the parameterization that we use to define the priors, $θ_prior$, often contain parameters with hard bounds. Therefore, we need a bound-to-unbound transformation to map the bounded parameters into an unbounded representation. In a nutshell, bound-to-unbound transformation in Jim utilize the logit function to map real numbers from $(0, 1)$ to real numbers in $(-\infty, +\infty)$. The logit function is given by: +However, the parameterization that we use to define the priors, $\theta_{prior}$, often contain parameters with hard bounds. Therefore, we need a bound-to-unbound transformation to map the bounded parameters into an unbounded representation. In a nutshell, bound-to-unbound transformation in Jim utilize the logit function to map real numbers from $(0, 1)$ to real numbers in $(-\infty, +\infty)$. The logit function is given by: $$ logit(\theta) = \ln{\frac{\theta}{1-\theta}}