truncated PRNGs

[bob-carpenter]

It'd be nice to be able to match our models and do something like this:

sigma_sim <- normal_rng(mu, sigma) T[lb, ];

to get a truncated form of the normal (and so on for upper and lower bounds and just upper bounds).

What we need in this repo is truncated forms of the PRNGs. Rejection sampling won't be robust enough and writing a slice sampler seems like a huge pain and I'm not even clear it'll work for fat tails like the Cauchy or constrained distributions without transformed. Will this have to wait until we have inverse CDFs?

[sakrejda]

On Sat, Dec 5, 2015 at 9:24 PM, Bob Carpenter notifications@github.com
wrote:

Not for fat tails, but other than that slice sampling is pretty generic in 1D, what do you mean by constrained distributions (?)

[avehtari]

1D slice sampling is one of the simplest and most robust algorithms. It would be useful also 1) to make it easy to sample from a user defined (log) density function, without need to implement CDF, and 2) to check new 1D rng implementations.

Inverse CDF would be otherwise better choice. Some truncated distributions (e.g. truncated normal) have special algorithms which are more efficient,

[sakrejda]

On Dec 6, 2015 4:47 AM, "Aki Vehtari" notifications@github.com wrote:

1D slice sampling is one of the simplest and most robust algorithms. It
would be useful also 1) to make it easy to sample from a user defined (log)
density function, without need to implement CDF, and 2) to check new 1D rng
implementations.

I could add Neal's step-out generic slice sampler pretty easily, but it
still has two ways of failing: 1) for user defined log densities I don't
know how to calculate a step size generically without adaptation and I'm
concerned about having a nested adaptation that can fail even if the rest
of the program runs fine. I imagine there's something we could do with the
curvature from ad to get into the ballpark, but I haven't thought it
through. 2) for multi-modal densities, say a user defined mixture, it can
also get stuck in a single mode. I've implemented a slice sampler for
specific densities that used the companion matrix to find all the modes and
include them in the step-out procedure but again I wonder if we couldn't
just use the ad with some different starting points to find all the modes.

So implementing is relatively simple but we should decide if we want 1 and
2 in there as well.

Inverse CDF would be otherwise better choice. Some truncated
distributions (e.g. truncated normal) have special algorithms which are
more efficient,

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[betanalpha]

If…if only we had some method for efficiently sampling
from complex distributions.

Seriously, though, the problem with a slice sampler is
that it’s a Markov chain which means there’s no guarantee
of exact samples unlike our current RNGs. Without being
able to guarantee the existence of RNGs I think our best
bet is a smart rejection sampler. In particular, knowledge
of the transformed density along with the Jacobian should
be enough to admit a good guess at an initial envelope.
Hell, we could even do an adaptive rejection sampler
on the constrained space directly.

On Dec 6, 2015, at 2:50 PM, Krzysztof Sakrejda notifications@github.com wrote:

On Dec 6, 2015 4:47 AM, "Aki Vehtari" notifications@github.com wrote:

1D slice sampling is one of the simplest and most robust algorithms. It
would be useful also 1) to make it easy to sample from a user defined (log)
density function, without need to implement CDF, and 2) to check new 1D rng
implementations.

I could add Neal's step-out generic slice sampler pretty easily, but it
still has two ways of failing: 1) for user defined log densities I don't
know how to calculate a step size generically without adaptation and I'm
concerned about having a nested adaptation that can fail even if the rest
of the program runs fine. I imagine there's something we could do with the
curvature from ad to get into the ballpark, but I haven't thought it
through. 2) for multi-modal densities, say a user defined mixture, it can
also get stuck in a single mode. I've implemented a slice sampler for
specific densities that used the companion matrix to find all the modes and
include them in the step-out procedure but again I wonder if we couldn't
just use the ad with some different starting points to find all the modes.

So implementing is relatively simple but we should decide if we want 1 and
2 in there as well.

Inverse CDF would be otherwise better choice. Some truncated
distributions (e.g. truncated normal) have special algorithms which are
more efficient,

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Reply to this email directly or view it on GitHub.
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[sakrejda]

On Dec 6, 2015 10:34 AM, "Michael Betancourt" notifications@github.com
wrote:

If…if only we had some method for efficiently sampling
from complex distributions.

Sure, that's where we're at with high dimensional distributions, but for 1d
distributions the set of problems is much smaller.

Seriously, though, the problem with a slice sampler is
that it’s a Markov chain which means there’s no guarantee
of exact samples unlike our current RNGs.

The Markov chain issue only becomes relevant with far trails, is a
rejection sampler going to solve that somehow?

Without being

able to guarantee the existence of RNGs I think our best
bet is a smart rejection sampler. In particular, knowledge
of the transformed density along with the Jacobian should
be enough to admit a good guess at an initial envelope.

This is the same thing you need for the slice sampler to work well.

Hell, we could even do an adaptive rejection sampler
on the constrained space directly.

On Dec 6, 2015, at 2:50 PM, Krzysztof Sakrejda notifications@github.com
wrote:

On Dec 6, 2015 4:47 AM, "Aki Vehtari" notifications@github.com wrote:

1D slice sampling is one of the simplest and most robust algorithms.
It
would be useful also 1) to make it easy to sample from a user defined
(log)
density function, without need to implement CDF, and 2) to check new 1D
rng
implementations.

I could add Neal's step-out generic slice sampler pretty easily, but it
still has two ways of failing: 1) for user defined log densities I don't
know how to calculate a step size generically without adaptation and I'm
concerned about having a nested adaptation that can fail even if the
rest
of the program runs fine. I imagine there's something we could do with
the
curvature from ad to get into the ballpark, but I haven't thought it
through. 2) for multi-modal densities, say a user defined mixture, it
can
also get stuck in a single mode. I've implemented a slice sampler for
specific densities that used the companion matrix to find all the modes
and
include them in the step-out procedure but again I wonder if we couldn't
just use the ad with some different starting points to find all the
modes.

So implementing is relatively simple but we should decide if we want 1
and
2 in there as well.

Inverse CDF would be otherwise better choice. Some truncated
distributions (e.g. truncated normal) have special algorithms which are
more efficient,

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Reply to this email directly or view it on GitHub.
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[betanalpha]

Slice sampler: Markov chain
(Adaptive) rejection sampler: exact samples

In some sense the rejection envelope is similar
to an importance distribution or a proposal distribution,
but it gives exact samples and is ever so slightly
easier to tune.

On Dec 6, 2015, at 4:07 PM, Krzysztof Sakrejda notifications@github.com wrote:

On Dec 6, 2015 10:34 AM, "Michael Betancourt" notifications@github.com
wrote:

If…if only we had some method for efficiently sampling
from complex distributions.

Sure, that's where we're at with high dimensional distributions, but for 1d
distributions the set of problems is much smaller.

Seriously, though, the problem with a slice sampler is
that it’s a Markov chain which means there’s no guarantee
of exact samples unlike our current RNGs.

The Markov chain issue only becomes relevant with far trails, is a
rejection sampler going to solve that somehow?

Without being

able to guarantee the existence of RNGs I think our best
bet is a smart rejection sampler. In particular, knowledge
of the transformed density along with the Jacobian should
be enough to admit a good guess at an initial envelope.

This is the same thing you need for the slice sampler to work well.

Hell, we could even do an adaptive rejection sampler
on the constrained space directly.

On Dec 6, 2015, at 2:50 PM, Krzysztof Sakrejda notifications@github.com
wrote:

On Dec 6, 2015 4:47 AM, "Aki Vehtari" notifications@github.com wrote:

1D slice sampling is one of the simplest and most robust algorithms.
It
would be useful also 1) to make it easy to sample from a user defined
(log)
density function, without need to implement CDF, and 2) to check new 1D
rng
implementations.

I could add Neal's step-out generic slice sampler pretty easily, but it
still has two ways of failing: 1) for user defined log densities I don't
know how to calculate a step size generically without adaptation and I'm
concerned about having a nested adaptation that can fail even if the
rest
of the program runs fine. I imagine there's something we could do with
the
curvature from ad to get into the ballpark, but I haven't thought it
through. 2) for multi-modal densities, say a user defined mixture, it
can
also get stuck in a single mode. I've implemented a slice sampler for
specific densities that used the companion matrix to find all the modes
and
include them in the step-out procedure but again I wonder if we couldn't
just use the ad with some different starting points to find all the
modes.

So implementing is relatively simple but we should decide if we want 1
and
2 in there as well.

Inverse CDF would be otherwise better choice. Some truncated
distributions (e.g. truncated normal) have special algorithms which are
more efficient,

—
Reply to this email directly or view it on GitHub.
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[sakrejda]

On Dec 6, 2015 11:15 AM, "Michael Betancourt" notifications@github.com
wrote:

Slice sampler: Markov chain

Slice sampler on U(0,1): exact samples
Slice sampler on Cauchy(0,1): junk

I think there's enough room in between those two extremes to make it useful
but if there's an automatic way to generate a good generic envelope for
rejection sampling i can see how that would be preferable.

(Adaptive) rejection sampler: exact samples

In some sense the rejection envelope is similar
to an importance distribution or a proposal distribution,
but it gives exact samples and is ever so slightly
easier to tune.

On Dec 6, 2015, at 4:07 PM, Krzysztof Sakrejda notifications@github.com
wrote:

On Dec 6, 2015 10:34 AM, "Michael Betancourt" notifications@github.com
wrote:

If…if only we had some method for efficiently sampling
from complex distributions.

Sure, that's where we're at with high dimensional distributions, but
for 1d
distributions the set of problems is much smaller.

Seriously, though, the problem with a slice sampler is
that it’s a Markov chain which means there’s no guarantee
of exact samples unlike our current RNGs.

The Markov chain issue only becomes relevant with far trails, is a
rejection sampler going to solve that somehow?

Without being

able to guarantee the existence of RNGs I think our best
bet is a smart rejection sampler. In particular, knowledge
of the transformed density along with the Jacobian should
be enough to admit a good guess at an initial envelope.

This is the same thing you need for the slice sampler to work well.

Hell, we could even do an adaptive rejection sampler
on the constrained space directly.

On Dec 6, 2015, at 2:50 PM, Krzysztof Sakrejda <
notifications@github.com>
wrote:

On Dec 6, 2015 4:47 AM, "Aki Vehtari" notifications@github.com
wrote:

1D slice sampling is one of the simplest and most robust
algorithms.
It
would be useful also 1) to make it easy to sample from a user
defined
(log)
density function, without need to implement CDF, and 2) to check
new 1D
rng
implementations.

I could add Neal's step-out generic slice sampler pretty easily,
but it
still has two ways of failing: 1) for user defined log densities I
don't
know how to calculate a step size generically without adaptation
and I'm
concerned about having a nested adaptation that can fail even if the
rest
of the program runs fine. I imagine there's something we could do
with
the
curvature from ad to get into the ballpark, but I haven't thought it
through. 2) for multi-modal densities, say a user defined mixture,
it
can
also get stuck in a single mode. I've implemented a slice sampler
for
specific densities that used the companion matrix to find all the
modes
and
include them in the step-out procedure but again I wonder if we
couldn't
just use the ad with some different starting points to find all the
modes.

So implementing is relatively simple but we should decide if we
want 1
and
2 in there as well.

Inverse CDF would be otherwise better choice. Some truncated
distributions (e.g. truncated normal) have special algorithms which
are
more efficient,

—
Reply to this email directly or view it on GitHub.
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Reply to this email directly or view it on GitHub.

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[avehtari]

Of course it would be nice to get independent samples, and it would be good to implement known efficient algorithms for specific distributions (e.g. truncated normal) and use inverse CDF. If the focus is in the built-in distributions, then I guess there is no need for generic adaptive rejection sampling or slice sampling.

[bob-carpenter]

I think I made an issue out of this prematurely. The advantage of the truncated PRNGs over just throwing things into the model is that they don't interact with the rest of sampling and they can interact with the rest of generated quantities.

[nschiett]

Hi! I realize this issue is closed, but is there an example available on how to finally do truncated normal rngs?

[bgoodri]

https://discourse.mc-stan.org/t/rng-for-truncated-distributions/3122/7?u=bgoodri

…

On Wed, Sep 5, 2018 at 9:28 AM nschiett ***@***.***> wrote: Hi! I realize this issue is closed, but is there an example available on how to finally do truncated normal rngs? — You are receiving this because you are subscribed to this thread. Reply to this email directly, view it on GitHub <#214 (comment)>, or mute the thread <https://github.com/notifications/unsubscribe-auth/ADOrqkp23lggqeuWnczZN-tllqqEsrNRks5uX9GBgaJpZM4GvkT-> .