Are Bayesian Inferences Weak for Wasserman's Example?

ISSN： 0361-0918

Source： Communications in Statistics: Simulation and Computation, Vol.39, Iss.3, 2010-03, pp. : 655-667

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Abstract

An example was given in the textbook All of Statistics (Wasserman, 2004, pp. 186-188) for arguing that, in the problems with a great many parameters Bayesian inferences are weak, because they rely heavily on the likelihood function that captures information of only a tiny fraction of the total parameters. Alternatively, he suggested non Bayesian Horwitz-Thompson estimator, which cannot be obtained from a likelihood-based approaches, including Bayesian approaches. He argued that Horwitz-Thompson estimator is good since it is unbiased and consistent. In this article, the mean square errors of Horwitz-Thompson estimator is compared with a Bayes estimator at a wide range of parameter configurations. These two estimators are also simulated to visualize them directly. From these comparisons, the conclusion is that the simple Bayes estimator works better than Horwitz-Thompson estimator for most parameter configurations. Hence, Bayesian inferences are not weak for this example.