Are Bayesian Inferences Weak for Wasserman's Example?

作者：Li Longhai^*

来源：Communications in Statistics - Simulation and Computation, 2010, 39(3): 655-667.

DOI：10.1080/03610910903576540

• Bayes estimator
• Critique of Bayesian inference
• Decision theory
• Horwitz-Thompson estimator
• Wasserman's example

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.

• 出版日期2010
• 单位Saskatoon; Saskatchewan