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Weighted Maximum Likelihood Bayesian Simulation

CML procedure generates a simulation of the posterior distribution using the method of Newton and Raftery (1994).

In this method an SIR adjustment (Rubin, 1988) is made incorporating a prior to a weighted maximum likelihood using Dirichlet random variates for weights. The SIR weights are computed:


where tex2html_wrap_inline550 is the prior distribution of the parameters, and tex2html_wrap_inline552 is a normal kernel density estimate of the joint density of the parameters using Terrell's (1990) method of maximum smoothing.

This method is quite easy to program. Moreover it is possible to write a general program that applies to any maximum likelihood estimation. Gibbs samplers and other Markov chain simulation methods require special programming for each type of model, and require substantially greater numbers of re-samplings. Experience suggests that reasonable accuracy is achieved with the weighted likelihood bootstrap on the order of the simple bootstrap. Thus for three places of accuracy, about 1000 re-samples are sufficient. Smaller numbers of re-samples will produce at least two places of accuracy, but the larger number of re-samples are generally required for kernel density plots.

R. Schoenberg
Fri Sep 12 09:47:41 PDT 1997