Are informative priors “[in]compatible with standards of research integrity”? Click to find out!!

A couple people asked me what I thought of this article by Miguel Ángel García-Pérez, Bayesian Estimation with Informative Priors is Indistinguishable from Data Falsification, which states:

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.

I agree with the mathematical point. Once you’ve multiplied the prior with the likelihood, you can’t separate what came from where. The prior is exactly equivalent to a measurement; conversely, any factor of the likelihood is exactly equivalent to prior information, from a mathematical perspective.

I don’t think it’s so helpful to label this procedure as “data falsification.” The prior is an assumption, just as the likelihood is an assumption. All the assumptions we use in applied statistics are false, so, sure the prior is a falsification, just as every normal distribution you use is a falsification, every logistic regression is a falsification, etc. Whatever. The point is, yes, the prior and the likelihood have equal mathematical status when they come together to form the posterior.

The article continues:

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.

Huh? Where does “research integrity” come in here? That’s just nuts. I guess now we know what comes after Vixra. In all seriousness, I guess there’s always a market for over-the-top claims that tell (some) people what they want to hear (in this case, in a bit of an old-fashioned way).

To get to the larger issue: I do think there are interesting questions regarding the interactions between ethics and the use of prior information. No easy answers but the issue is worth thinking about. As I summarized in my 2012 article:

I believe we are ethically required to clearly state our assumptions and, to the best of our abilities, explain the rationales for these assumptions and our sources of information.