gaussianSynLikeGhuryeOlkin {BSL} | R Documentation |

## 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 |

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

### 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)
```

*BSL*version 3.2.5 Index]