sample_lm_ridge

Sample the parameters for a linear regression model assuming a
ridge prior for the (non-intercept) coefficients. The number of predictors
<code>p</code> may exceed the number of observations <code>n</code>.

internal

For Bayesian and classical inference and prediction with count-valued data,
Simultaneous Transformation and Rounding (STAR) Models provide a flexible, interpretable,
and easy-to-use approach. STAR models the observed count data using a rounded
continuous data model and incorporates a transformation for greater flexibility.
Implicitly, STAR formalizes the commonly-applied yet incoherent procedure of
(i) transforming count-valued data and subsequently
(ii) modeling the transformed data using Gaussian models.
STAR is well-defined for count-valued data, which is reflected in predictive accuracy,
and is designed to account for zero-inflation, bounded or censored data, and over- or underdispersion.
Importantly, STAR is easy to combine with existing MCMC or point estimation
methods for continuous data, which allows seamless adaptation of continuous data
models (such as linear regressions, additive models, BART, random forests,
and gradient boosting machines) for count-valued data. The package also includes several
methods for modeling count time series data, namely via warped Dynamic Linear Models.
For more details and background on these methodologies, see the works of
Kowal and Canale (2020) <doi:10.1214/20-EJS1707>,
Kowal and Wu (2022) <doi:10.1111/biom.13617>,
King and Kowal (2022) <arXiv:2110.14790>, and
Kowal and Wu (2023) <arXiv:2110.12316>.

Brian King

countSTAR

Flexible Modeling of Count Data

Dan Kowal

sample_lm_ridge function

<dl><dt>y</dt>
<dd><code>n x 1</code> vector of data</dd>
<dt>X</dt>
<dd><code>n x p</code> matrix of predictors</dd>
<dt>params</dt>
<dd>the named list of parameters containing<ol>
<li><code>mu</code>: vector of conditional means (fitted values)</li>
<li><code>sigma</code>: the conditional standard deviation</li>
<li><code>coefficients</code>: a named list of parameters that determine <code>mu</code></li>
</ol></dd>
<dt>A</dt>
<dd>the prior scale for <code>sigma_beta</code>, which we assume follows a Uniform(0, A) prior.</dd>
<dt>XtX</dt>
<dd>the <code>p x p</code> matrix of <code>crossprod(X)</code> (one-time cost);
if NULL, compute within the function</dd>
<dt>X_test</dt>
<dd>matrix of predictors at test points (default is NULL)</dd></dl>

Arguments

Sample linear regression parameters assuming a ridge prior — sample_lm_ridge

<dl>

<dt>y</dt>
<dd><code>n x 1</code> vector of data</dd>


<dt>X</dt>
<dd><code>n x p</code> matrix of predictors</dd>


<dt>params</dt>
<dd>the named list of parameters containing<ol>
<li><code>mu</code>: vector of conditional means (fitted values)</li>
<li><code>sigma</code>: the conditional standard deviation</li>
<li><code>coefficients</code>: a named list of parameters that determine <code>mu</code></li>
</ol></dd>


<dt>A</dt>
<dd>the prior scale for <code>sigma_beta</code>, which we assume follows a Uniform(0, A) prior.</dd>


<dt>XtX</dt>
<dd>the <code>p x p</code> matrix of <code>crossprod(X)</code> (one-time cost);
if NULL, compute within the function</dd>


<dt>X_test</dt>
<dd>matrix of predictors at test points (default is NULL)</dd>

</dl>

sample_lm_ridge: Sample linear regression parameters assuming a ridge prior

Description

Usage

Value

Arguments