BSL (version 3.0.0)

gaussianSynLikeGhuryeOlkin: Estimating the Gaussian synthetic likelihood with an unbiased estimator

Description

This function computes an unbiased, nonnegative estimate of a normal density function from simulations assumed to be drawn from it. See Price et al. (2018) and Ghurye and Olkin (1969).

Usage

gaussianSynLikeGhuryeOlkin(ssy, ssx, log = TRUE, verbose = FALSE)

Arguments

ssy

The observed summary statisic.

ssx

A matrix of the simulated summary statistics. The number of rows is the same as the number of simulations per iteration.

log

A logical argument indicating if the log of likelihood is given as the result. The default is TRUE.

verbose

A logical argument indicating whether an error message should be printed if the function fails to compute a likelihood. The default is FALSE.

Value

The estimated synthetic (log) likelihood value.

References

Price, L. F., Drovandi, C. C., Lee, A., & Nott, D. J. (2018). Bayesian synthetic likelihood. Journal of Computational and Graphical Statistics. https://doi.org/10.1080/10618600.2017.1302882

Ghurye, S. G., & Olkin, I. (1969). Unbiased estimation of some multivariate probability densities and related functions. The Annals of Mathematical Statistics. https://projecteuclid.org/euclid.aoms/1177697501

See Also

gaussianSynLike for the standard synthetic likelihood estimator, semiparaKernelEstimate for the semi-parametric likelihood estimator.

Examples

# NOT RUN {
data(ma2)
y <- ma2$data # the observed data

theta_true <- c(0.6, 0.2)
x <- matrix(0, 300, 50)
set.seed(100)
for(i in 1:300) x[i, ] <- ma2_sim(theta_true, 50)

# unbiased estimate of the Gaussian synthetic likelihood
# (the likelihood estimator used in uBSL)
gaussianSynLikeGhuryeOlkin(y, x)

# }