feat(docs): improve baseline modeling explanation and update theming

- Refined and condensed explanations in `baseline_modeling.rst` for better clarity and conciseness.
- Introduced a new custom CSS file for improved documentation design, including centered math rendering.
- Updated `conf.py` to include `custom.css` and configure centered MathJax alignment.

Author: hpparvi

doc/source/_static/css/custom.css

@@ -8,4 +8,4 @@ blocks.frontpage > h1 {
     font-weight: 300;
     padding-top: 0.5em;
     padding-bottom: 0.5em;
-}
+}

doc/source/_static/custom.css

@@ -0,0 +1,21 @@
+/*
+ * ExoIris: fast, flexible, and easy exoplanet transmission spectroscopy in Python.
+ * Copyright (C) 2026 Hannu Parviainen
+ *
+ * This program is free software: you can redistribute it and/or modify
+ * it under the terms of the GNU General Public License as published by
+ * the Free Software Foundation, either version 3 of the License, or
+ * (at your option) any later version.
+ *
+ * This program is distributed in the hope that it will be useful,
+ * but WITHOUT ANY WARRANTY; without even the implied warranty of
+ * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+ * GNU General Public License for more details.
+ *
+ * You should have received a copy of the GNU General Public License
+ * along with this program.  If not, see <https://www.gnu.org/licenses/>.
+ */
+
+div.math {
+    text-align: center;
+}

doc/source/conf.py

@@ -13,10 +13,8 @@
 extensions = [
     'sphinx.ext.autodoc',
     'sphinx.ext.autosummary',
-#    'sphinx_automodapi.automodapi',
     'sphinx.ext.mathjax',
     'sphinx.ext.intersphinx',
-    'sphinx.ext.imgmath',
     'sphinx.ext.viewcode',
     'sphinx.ext.githubpages',
     'sphinx.ext.napoleon',
@@ -35,15 +33,18 @@
 
 pygments_style = 'sphinx'
 
-#html_theme = 'furo'
 html_theme = 'sphinx_book_theme'
-#html_theme = 'pydata_sphinx_theme'
-
 html_title = f'ExoIris v{version}'
-html_theme_options = {
-    'sidebar_hide_name': False,
-}
 html_static_path = ['_static']
+html_css_files = [
+    'custom.css',
+]
+
+mathjax3_config = {
+    'chtml': {
+        'displayAlign': 'center',
+    },
+}
 
 default_role = 'py:obj'
 

doc/source/features/baseline_modeling.rst

@@ -18,54 +18,37 @@ ExoIris describes the observed flux at each wavelength channel as
 where :math:`\boldsymbol{\Phi}` is an :math:`n_t \times k` covariate (design) matrix and
 :math:`\mathbf{c}(\lambda)` is a vector of per-wavelength baseline coefficients. The first column of
 :math:`\boldsymbol{\Phi}` is always a column of ones that captures the out-of-transit flux level; the
-remaining columns describe systematic trends.
-
-The covariates can be:
-
-- **Time polynomials** --- the default when no custom covariates are supplied. ``TSData`` automatically
-  builds a design matrix with columns :math:`1, \hat{t}, \hat{t}^2, \ldots`, where :math:`\hat{t}` is
-  centred and normalised time, up to the order set by ``n_baseline``.
-- **Measured auxiliary variables** such as detector temperature, pointing drift, airmass, or
-  PSF width, recorded simultaneously with the spectroscopic time series.
-- **Common-mode systematics** extracted from the observations (e.g., wavelength-independent trends
-  derived from the white light curve residuals).
-- **Any user-supplied matrix** passed via the ``covs`` parameter of :class:`~exoiris.tsdata.TSData`.
-  When ``covs`` is provided it replaces the default polynomial construction entirely, so it should
-  include a constant (ones) column if an additive offset is desired.
+remaining columns describe systematic trends. The covariates can be time polynomials (the default),
+measured auxiliary variables such as detector temperature or pointing drift, common-mode systematics
+extracted from the white light curve residuals, or any user-supplied matrix that replaces the default
+polynomial construction entirely.
 
 Profiled Baseline
 -----------------
 
-When the noise model is set to ``white_profiled`` (the default), ExoIris estimates the baseline
-coefficients :math:`\mathbf{c}(\lambda)` by ordinary linear least squares at every likelihood
-evaluation. Concretely, given the current transit model :math:`F_\mathrm{transit}`, the residual
-:math:`F_\mathrm{obs} / F_\mathrm{transit}` is regressed against :math:`\boldsymbol{\Phi}` to obtain
-the best-fit coefficients, which are then multiplied back into the transit model. Because the
-coefficients are determined analytically at each step, they are *profiled out* of the likelihood and
-add no extra parameters to the MCMC sampler. This keeps the parameter space compact and speeds up
-convergence.
+In the default profiled mode, ExoIris estimates the baseline coefficients by ordinary linear least
+squares at every likelihood evaluation. The residual between the data and the current transit model is
+regressed against the design matrix, and the resulting best-fit coefficients are folded back into the
+model. Because the coefficients are determined analytically at each step, they are *profiled out* of the
+likelihood and add no extra parameters to the sampler. This keeps the parameter space compact and speeds
+up convergence.
 
 Analytically Marginalized Baseline
 -----------------------------------
 
-Setting the noise model to ``white_marginalized`` activates Bayesian analytic marginalisation of the
-baseline coefficients. Instead of plugging in point estimates, ExoIris integrates the coefficients out
-under a broad isotropic Gaussian prior :math:`\mathbf{c} \sim \mathcal{N}(\mathbf{0},\,\tau^2 \mathbf{I})`
-with :math:`\tau = 10^6`. The marginal likelihood is
+As an alternative, ExoIris can analytically marginalise the baseline coefficients under a broad Gaussian
+prior instead of plugging in point estimates. The marginal likelihood integrates the coefficients out in
+closed form,
 
 .. math::
 
    \mathcal{L}(\theta) = \int p\!\left(F_\mathrm{obs} \mid \theta, \mathbf{c}\right)\, p(\mathbf{c})\, \mathrm{d}\mathbf{c}
 
-which can be evaluated in closed form because the model is linear in :math:`\mathbf{c}`. Defining
-:math:`\boldsymbol{\Phi}_m = \mathrm{diag}(F_\mathrm{transit}) \, \boldsymbol{\Phi}`, the marginal
-covariance of the data is :math:`C = \Sigma + \tau^2 \boldsymbol{\Phi}_m \boldsymbol{\Phi}_m^\top`,
-where :math:`\Sigma = \mathrm{diag}(\sigma^2)`. ExoIris evaluates :math:`C^{-1}` and
-:math:`\lvert C \rvert` efficiently using the Woodbury matrix identity and the matrix determinant
-lemma, working with :math:`k \times k` matrices rather than :math:`n_t \times n_t` matrices.
+because the model is linear in :math:`\mathbf{c}`. The resulting covariance is evaluated efficiently via
+the Woodbury matrix identity and the matrix determinant lemma, keeping the cost proportional to the
+number of covariates rather than the number of time points.
 
 Compared to the profiled approach, marginalisation properly propagates baseline uncertainty into the
-posterior distributions of all transit parameters. The transit model is evaluated *without* a baseline
-factor; the likelihood accounts for the baseline analytically. This can yield more conservative---and
-more accurate---uncertainty estimates, particularly when the covariate model is flexible or the
-out-of-transit coverage is limited.
+posterior distributions of all transit parameters. This can yield more conservative---and more
+accurate---uncertainty estimates, particularly when the covariate model is flexible or the out-of-transit
+coverage is limited.