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Bootstrap

The bootstrap method is used to generate empirical distributions of the parameters, thus avoiding the difficulties with the usual methods of statistical inference described above.

CML provides two types of bootstrap methods, a simple bootstrap that generates a simulated distribution of parameters by random re-sampling with replacement, and a weighted re-sampling that generates a simulation of the Bayesian posterior distribution of the parameters.

Additional procedures are available in CML for generating kernel density plots, histograms, contour plots of bivariate distributions, and confidence limits, from the data sets containing the simulated distributions of parameters.

Bayesian Inference. CML procedure can generate a simulation of the posterior distribution of the parameters using a weighted bootstrap method described by Newton and Raftery (1994). Here weighted Dirichlet random variates are used for weights. After generating the weighted bootstrapped parameters, ``importance'' weights are computed:

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where tex2html_wrap_inline719 is the prior distribution of the parameters, and tex2html_wrap_inline721 is a normal kernel density estimate of the joint density of the parameters using Terrell's (1990) method of maximum smoothing. The SIR algorithm, described in Rubin (1988), is applied to the bootstrapped parameters using these importance weights.



R. Schoenberg
Fri Sep 12 09:21:35 PDT 1997