bbelogdensity: Calculate an estimate of log posterior ordinate used in the log marginal density of Chib(1995).
Description
The calculation of the log posterior ordinate estimate does not suffer from any instability problem,
because it is a density value that is averaged rather than its inverse.
Usage
bbelogdensity(x, sigma, data_post)
Arguments
x
Estimated averaged bandwidths of the regressors
sigma
Estimated averaged variance of the error density
data_post
Gibbs output 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
Gibbs 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 (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.