gaussianSynLikeGhuryeOlkin {BSL}

Estimate the Gaussian synthetic (log) 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

Ghurye SG, Olkin I (1969). “Unbiased Estimation of Some Multivariate Probability Densities and Related Functions.” Ann. Math. Statist., 40(4), 1261–1271.

Price LF, Drovandi CC, Lee A, Nott DJ (2018). “Bayesian Synthetic Likelihood.” Journal of Computational and Graphical Statistics, 27, 1–11. doi: 10.1080/10618600.2017.1302882.

See Also

Other available synthetic likelihood estimators: gaussianSynLike for the standard synthetic likelihood estimator, semiparaKernelEstimate for the semi-parametric likelihood estimator, synLikeMisspec for the Gaussian synthetic likelihood estimator for model misspecification.

Examples

data(ma2)
ssy <- ma2_sum(ma2$data)
m <- newModel(fnSim = ma2_sim, fnSum = ma2_sum, simArgs = ma2$sim_args,
              theta0 = ma2$start)
ssx <- simulation(m, n = 300, theta = c(0.6, 0.2), seed = 10)$ssx

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