getX

The function <code>getX</code> is used to get the matrix of covariates for the regression based on a specified polynomial order.

Stein control variates can be used to improve Monte Carlo estimates of expectations when the derivatives of the log target are available. This package implements a variety of such methods, including zero-variance control variates (ZV-CV, Mira et al. (2013) <doi:10.1007/s11222-012-9344-6>), regularised ZV-CV (South et al., 2023 <doi:10.1214/22-BA1328>), control functionals (CF, Oates et al. (2017) <doi:10.1111/rssb.12185>) and semi-exact control functionals (SECF, South et al., 2022 <doi:10.1093/biomet/asab036>). ZV-CV is a parametric approach that is exact for (low order) polynomial integrands with Gaussian targets. CF is a non-parametric alternative that offers better than the standard Monte Carlo convergence rates. SECF has both a parametric and a non-parametric component and it offers the advantages of both for an additional computational cost. Functions for applying ZV-CV and CF to two estimators for the normalising constant of the posterior distribution in Bayesian statistics are also supplied in this package. The basic requirements for using the package are a set of samples, derivatives and function evaluations.

Leah F. South

ZVCV

Zero-Variance Control Variates

getX function

<dl><dt>samples</dt>
<dd>An \(N\) by \(d\) matrix of samples from the target</dd>
<dt>derivatives</dt>
<dd>An \(N\) by \(d\) matrix of derivatives of the log target with respect to the parameters</dd>
<dt>polyorder</dt>
<dd>The order of the polynomial.</dd></dl>

Arguments

ZV-CV design matrix — getX

<dl>

<dt>samples</dt>
<dd>An \(N\) by \(d\) matrix of samples from the target</dd>


<dt>derivatives</dt>
<dd>An \(N\) by \(d\) matrix of derivatives of the log target with respect to the parameters</dd>


<dt>polyorder</dt>
<dd>The order of the polynomial.</dd>

</dl>

getX: ZV-CV design matrix

Description

Usage

Value

Arguments

See Also