Bayesian Estimation with Informative Priors is Indistinguishable from Data Falsification

Abstract

Abstract Criticism of null hypothesis significance testing, confidence intervals, and frequentist statistics in general has evolved into advocacy of Bayesian analyses with informative priors for strong inference. This paper shows that Bayesian analysis with informative priors is formally equivalent to data falsification because the information carried by the prior can be expressed as the addition of fabricated observations whose statistical characteristics are determined by the parameters of the prior. This property of informative priors makes clear that only the use of non-informative, uniform priors in all types of Bayesian analyses is compatible with standards of research integrity. At the same time, though, Bayesian estimation with uniform priors yields point and interval estimates that are identical or nearly identical to those obtained with frequentist methods. At a qualitative level, frequentist and Bayesian outcomes have different interpretations but they are interchangeable when uniform priors are used. Yet, Bayesian interpretations require either the assumption that population parameters are random variables (which they are not) or an explicit acknowledgment that the posterior distribution (which is thus identical to the likelihood function except for a scale factor) only expresses the researcher’s beliefs and not any information about the parameter of concern.