estimateLoglike {BSL}  R Documentation 
Estimate the synthetic likelihood
Description
This function computes the estimated synthetic (log) likelihood using one of the four methods (“BSL”, “uBSL”, “semiBSL” and “BSLmisspec”). Please find the links below in the see also section for more details.
Usage
estimateLoglike(
ssy,
ssx,
method = c("BSL", "uBSL", "semiBSL", "BSLmisspec"),
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. 
method 
A string argument indicating the method to be used. The default, “BSL”, runs standard BSL. “uBSL” uses the unbiased estimator of a normal density of Ghurye and Olkin (1969). “semiBSL” runs the semiparametric BSL algorithm and is more robust to nonnormal summary statistics. “BSLmisspec” estimates the Gaussian synthetic likelihood whilst acknowledging that there may be incompatibility between the model and the observed summary statistic (Frazier and Drovandi 2021). 
log 
A logical argument indicating if the log of likelihood is
given as the result. The default is 
verbose 
A logical argument indicating whether an error message
should be printed if the function fails to compute a likelihood. The
default is 
... 
Arguments to be passed to methods.

Value
The estimated synthetic (log) likelihood value.
References
Boudt K, Cornelissen J, Croux C (2012).
“The Gaussian Rank Correlation Estimator: Robustness Properties.”
Statistics and Computing, 22(2), 471–483.
doi: 10.1007/s1122201192370.
Frazier DT, Drovandi C (2021).
“Robust Approximate Bayesian Inference with Synthetic Likelihood.”
Journal of Computational and Graphical Statistics (In Press).
https://arxiv.org/abs/1904.04551.
Friedman J, Hastie T, Tibshirani R (2008).
“Sparse Inverse Covariance Estimation with the Graphical Lasso.”
Biostatistics, 9(3), 432–441.
Ghurye SG, Olkin I (1969).
“Unbiased Estimation of Some Multivariate Probability Densities and Related Functions.”
Ann. Math. Statist., 40(4), 1261–1271.
Neal RM (2003).
“Slice sampling.”
The Annals of Statistics, 31(3), 705–767.
Warton DI (2008).
“Penalized Normal Likelihood and Ridge Regularization of Correlation and Covariance Matrices.”
Journal of the American Statistical Association, 103(481), 340–349.
doi: 10.1198/016214508000000021.
See Also
gaussianSynLike
,
gaussianSynLikeGhuryeOlkin
,
semiparaKernelEstimate
and synLikeMisspec
.
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
estimateLoglike(ssy, ssx, method = "BSL")
estimateLoglike(ssy, ssx, method = "uBSL")
estimateLoglike(ssy, ssx, method = "semiBSL")
estimateLoglike(ssy, ssx, method = "BSLmisspec", type = "mean", gamma = rep(0.1, 50))