bbelogdensity: Calculate an estimate of log posterior ordinate used in the log marginal density of Chib (1995).
Description
The calculation of 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
Bandwidths of the regressors
sigma
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 a modal value such as the posterior mode, or the 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.