medianTune

This function calculates the median heuristic for use in e.g. the Gaussian, Matern and rational quadratic kernels.

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

medianTune function

<dl><dt>samples</dt>
<dd>An \(N\) by \(d\) matrix of samples from the target</dd>
<dt>Z</dt>
<dd>(optional) An NxN matrix of square norms, which can be calculated
using <code>squareNorm</code>, as long as the <code>nystrom_inds</code> are <code>NULL</code>.</dd></dl>

Arguments

Author

Median heuristic — medianTune

<dl>

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


<dt>Z</dt>
<dd>(optional) An NxN matrix of square norms, which can be calculated
using <code>squareNorm</code>, as long as the <code>nystrom_inds</code> are <code>NULL</code>.</dd>

</dl>

medianTune: Median heuristic

Description

Usage

Value

Arguments

Author

References

See Also