Bayesian inference with informative priors is not inherently “subjective”

The quick way of saying this is that using a mathematical model informed by background information to set a prior distribution for logistic regression is no more “subjective” than deciding to run a logistic regression in the first place.

Here’s a longer version:

Every once in awhile you get people saying that Bayesian statistics is subjective bla bla bla, so every once in awhile it’s worth reminding people of my 2017 article with Christian Hennig, Beyond subjective and objective in statistics. Lots of good discussion there too. Here’s our abstract:

Decisions in statistical data analysis are often justified, criticized or avoided by using concepts of objectivity and subjectivity. We argue that the words ‘objective’ and ‘subjective’ in statistics discourse are used in a mostly unhelpful way, and we propose to replace each of them with broader collections of attributes, with objectivity replaced by transparency, consensus, impartiality and correspondence to observable reality, and subjectivity replaced by awareness of multiple perspectives and context dependence. Together with stability, these make up a collection of virtues that we think is helpful in discussions of statistical foundations and practice.

The advantage of these reformulations is that the replacement terms do not oppose each other and that they give more specific guidance about what statistical science strives to achieve. Instead of debating over whether a given statistical method is subjective or objective (or normatively debating the relative merits of subjectivity and objectivity in statistical practice), we can recognize desirable attributes such as transparency and acknowledgement of multiple perspectives as complementary goals. We demonstrate the implications of our proposal with recent applied examples from pharmacology, election polling and socio-economic stratification. The aim of the paper is to push users and developers of statistical methods towards more effective use of diverse sources of information and more open acknowledgement of assumptions and goals.