BSL (version 3.0.0)

gaussianSynLike: Estimating the Gaussian synthetic likelihood

Description

This function estimates the Gaussian synthetic likelihood function of Wood (2010). Shrinkage on the Gaussian covariance matrix is also available (see An et al 2019).

Usage

gaussianSynLike(ssy, ssx, shrinkage = NULL, penalty = NULL,
  standardise = FALSE, GRC = FALSE, 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.

shrinkage

A string argument indicating which shrinkage method to be used. The default is NULL, which means no shrinkage is used. Shrinkage estimation is only available for method ``BSL'' and ``semiBSL''. Current options are ``glasso'' for the graphical lasso method of Friedman et al (2008) and ``Warton'' for the ridge regularisation method of Warton (2008).

penalty

The penalty value to be used for the specified shrinkage method. Must be between zero and one if the shrinkage method is ``Warton''.

standardise

A logical argument that determines whether to standardise the summary statistics before applying the graphical lasso. This is only valid if method is ``BSL'', shrinkage is ``glasso'' and penalty is not NULL. The diagonal elements will not be penalised if the shrinkage method is ``glasso''. The default is FALSE.

GRC

A logical argument indicating whether the Gaussian rank correlation matrix (Boudt et al., 2012) should be used to estimate the covariance matrix in ``BSL'' method. The default is FALSE, which uses the sample covariance by default.

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

An, Z., South, L. F., Nott, D. J. & Drovandi, C. C. (2019). Accelerating Bayesian synthetic likelihood with the graphical lasso. Journal of Computational and Graphical Statistics. https://doi.org/10.1080/10618600.2018.1537928

Friedman, J., Hastie, T., Tibshirani, R. (2008). Sparse inverse covariance estimation with the graphical lasso. Biostatistics. https://doi.org/10.1093/biostatistics/kxm045

Warton, D. I. (2008). Penalized Normal Likelihood and Ridge Regularization of Correlation and Covariance Matrices, Journal of the American Statistical Association. https://doi.org/10.1198/016214508000000021

See Also

gaussianSynLikeGhuryeOlkin for the unbiased 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)

# the standard Gaussian synthetic likelihood (the likelihood estimator used in BSL)
gaussianSynLike(y, x)
# the Gaussian synthetic likelihood with glasso shrinkage estimation
# (the likelihood estimator used in BSLasso)
gaussianSynLike(y, x, shrinkage = 'glasso', penalty = 0.1)
# the Gaussian synthetic likelihood with Warton shrinkage estimation
gaussianSynLike(y, x, shrinkage = 'Warton', penalty = 0.9)

# }