bbemkr (version 2.0)

logdensity_gaussian: Calculate an estimate of log posterior ordinate used in the log marginal density of Chib (1995).

Description

Log marginal likelihood = Log likelihood + Log prior - Log density

Usage

logdensity_gaussian(tau2, cpost)

Arguments

tau2

Square of re-parameterized bandwidths and square of normal error variance

cpost

Simulation output of tau2 obtained from the MCMC iterations

Value

Value of the log density

Details

It should be noted that the posterior mode or maximum likelihood estimate can be computed from the simulation output at least approximately, if it is easy to evaluate the log-likelihood function for each draw in the simulation. Alternatively, one can make use of the posterior mean provided that there is no concern that it is a low density point.

References

S. Chib and I. Jeliazkov (2001) Marginal likelihood from the Metropolis-Hastings output, Journal of the American Statistical Association, 96, 453, 270-281.

S. Chib (1995) Marginal likelihood from the Gibbs output, Journal of the American Statistical Association, 90, 432, 1313-1321.

M. A. Newton and A. E. Raftery (1994) Approximate Bayesian inference by the weighted likelihood bootstrap (with discussion), Journal of the Royal Statistical Society, 56, 3-48.

See Also

logpriors_gaussian, loglikelihood_gaussian, mcmcrecord_gaussian