Models, Parameters and Priors in Bayesian Inference
Batchelder and Smith (2004) critiqued the use of Bayesian statistical inference for model selection and evaluation, arguing that it can lead to invalid and contradictory conclusions. Their argument centered around a series of concrete examples purporting to show the problems inherent in adopting the Bayesian approach. This paper addresses Batchelder and Smith’s critique by re-analyzing their examples using correct Bayesian methods, and demonstrates that their negative conclusions are not warranted. Throughout the re-analysis, the central role of information in the Bayesian approach is emphasized. In particular, it is argued a careful consideration of available information is required to understand the relationship between parameters, models, and data, and the setting of prior probability distributions.