sliceGammaVariance

This function updates the gamma parameter with a slice sampler
 Neal2003BSL. The target distribution is the variance
 inflated approximate posterior of BSL with model misspecification. See
 Frazier2019;textualBSL. Note this function is mainly
 designed for internal usage.

internal

Bayesian synthetic likelihood (BSL, Price et al. (2018) <doi:10.1080/10618600.2017.1302882>)
is an alternative to standard, non-parametric approximate Bayesian
computation (ABC). BSL assumes a multivariate normal distribution
for the summary statistic likelihood and it is suitable when the
distribution of the model summary statistics is sufficiently regular.
This package provides a Metropolis Hastings Markov chain Monte Carlo
implementation of four methods (BSL, uBSL, semiBSL and BSLmisspec) and two
shrinkage estimators (graphical lasso and Warton's estimator).
uBSL (Price et al. (2018) <doi:10.1080/10618600.2017.1302882>) uses
an unbiased estimator to the normal density. A semi-parametric version
of BSL (semiBSL, An et al. (2018) <arXiv:1809.05800>) is more robust
to non-normal summary statistics. BSLmisspec (Frazier et al. 2019
<arXiv:1904.04551>) estimates the Gaussian synthetic likelihood whilst
acknowledging that there may be incompatibility between the model and the
observed summary statistic. Shrinkage estimation can help to decrease the
number of model simulations when the dimension of the summary statistic is
high (e.g., BSLasso, An et al. (2019) <doi:10.1080/10618600.2018.1537928>).
Extensions to this package are planned. For a journal article describing how
to use this package, see An et al. (2022) <doi:10.18637/jss.v101.i11>.

Leah F. South

Bayesian Synthetic Likelihood

Ziwen An

Christopher C. Drovandi

sliceGammaVariance function

<dl><dt>ssy</dt>
<dd>The observed summary statisic.</dd>
<dt>ssx</dt>
<dd>A matrix of the simulated summary statistics. The number
of rows is the same as the number of simulations per iteration.</dd>
<dt>loglike</dt>
<dd>The current log synthetic likelihood. This is computed with
function <code>synLikeMisspec</code> with the current gamma value.</dd>
<dt>gamma</dt>
<dd>The additional latent parameter to account for possible
 incompatability between the model and observed summary statistic. In
 ``BSLmisspec'' method, this is updated with a slice sampler
 Neal2003BSL. The default gamma implies no model misspecification
and is equivalent to the standard <code>gaussianSynLike</code> estimator.</dd>
<dt>tau</dt>
<dd>Numeric. Scale (or inverse rate) parameter of the exponential
prior distribution.</dd>
<dt>w</dt>
<dd>Step size for the stepping out in the slice sampler. The default
step size is 1.</dd>
<dt>std</dt>
<dd>Standard deviation of the columns of ssx. If this is not
<code>NULL</code>, it will be used to save computation effort.</dd>
<dt>maxit</dt>
<dd>The maximum number of iteration of the stepping out and shrink
steps of slice sampler. The default is 1e3.</dd></dl>

Arguments

Generate a random sample of gamma for the R-BSL-V method of
Frazier2019;textualBSL using slice sampling — sliceGammaVariance

<dl>

<dt>ssy</dt>
<dd>The observed summary statisic.</dd>


<dt>ssx</dt>
<dd>A matrix of the simulated summary statistics. The number
of rows is the same as the number of simulations per iteration.</dd>


<dt>loglike</dt>
<dd>The current log synthetic likelihood. This is computed with
function <code>synLikeMisspec</code> with the current gamma value.</dd>


<dt>gamma</dt>
<dd>The additional latent parameter to account for possible
 incompatability between the model and observed summary statistic. In
 ``BSLmisspec'' method, this is updated with a slice sampler
 Neal2003BSL. The default gamma implies no model misspecification
and is equivalent to the standard <code>gaussianSynLike</code> estimator.</dd>


<dt>tau</dt>
<dd>Numeric. Scale (or inverse rate) parameter of the exponential
prior distribution.</dd>


<dt>w</dt>
<dd>Step size for the stepping out in the slice sampler. The default
step size is 1.</dd>


<dt>std</dt>
<dd>Standard deviation of the columns of ssx. If this is not
<code>NULL</code>, it will be used to save computation effort.</dd>


<dt>maxit</dt>
<dd>The maximum number of iteration of the stepping out and shrink
steps of slice sampler. The default is 1e3.</dd>

</dl>

sliceGammaVariance: Generate a random sample of gamma for the R-BSL-V method of Frazier2019;textualBSL using slice sampling

Description

Usage

Arguments

References

See Also