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*Correspondence:

This article was submitted to Cognition, a section of the journal Frontiers in Psychology.

Edited by: Gorka Navarrete, Universidad Diego Portales, Chile

Reviewed by: Vittorio Girotto, University IUAV of Venice, Italy; Miroslav Sirota, King's College London, UK

This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) or licensor are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.

Most psychological research on Bayesian reasoning since the 1970s has used a type of problem that tests a certain kind of statistical reasoning performance. The subject is given statistical facts within a hypothetical scenario. Those facts include a base-rate statistic and one or two diagnostic probabilities. The subject is meant to use that information to arrive at a “posterior” probability estimate. For instance, in one well-known problem (Eddy,

The probability of breast cancer is 1% for a woman at age forty who participates in routine screening. If a woman has breast cancer, the probability is 80% that she will get a positive mammography. If a woman does not have breast cancer, the probability is 9.6% that she will also get a positive mammography. A woman in this age group had a positive mammography in a routine screening. What is the probability that she actually has breast cancer? __ %.

The information in such problems can be mapped onto common expressions that use

Bayes' theorem states:

Thus, it yields a posterior probability of 0.078 in the mammography problem. Yet even the majority of physicians who were queried by Eddy (

Well-established findings such as these have supported the view that expert and naïve subjects alike are non-Bayesian (Kahneman and Tversky,

This estimate is closer to the modal estimate but is still off by about ten percentage points. Another explanation is that people commit the

It is also known that steps can be taken to increase agreement with Bayes' theorem. Since Bayes' theorem can be simplified as

task reformulations that directly provide these values or make them easily computable increase the proportion of Bayesian responses (e.g., Gigerenzer and Hoffrage,

Bayesian reasoning also benefits from the use of visual representations of pertinent statistical information, such as Euler circles (Sloman et al.,

A remarkable feature of the standard approach to studying Bayesian reasoning is its inability to reveal how people

It is instead conveniently assumed that the base rate represents the subject's prior belief,

Priors need not equal base rates, as many have noted (e.g., de Finetti,

Clearly, the ideal base rate in such personal cases would be a sample of people who are just like the patient, yet since each of us is unique no such sample exists. In the absence of a single, ideal base rate, one must decide among a range of imperfect ones—a task involving decision under uncertainty. It might be sensible for the woman getting the screening to anchor on a relevant, available base rate, such as for women in her cohort, and then adjust it in light of other diagnostic characteristics that she knows she possesses. Yet, if people are overly optimistic (Taylor and Brown,

Given that standard Bayesian reasoning tasks involve no assessment of a prior probability, they should be seen for what they are: conditional probability judgment tasks that require the combination of statistical information. When that information is fleshed out, it reveals the fours cells of a 2 × 2 contingency table, where

From this perspective, it is perhaps unsurprising why a greater proportion of subjects conform to Bayes theorem when they are given the frequencies

I do not intend for my observations to imply that the well-established findings I summarized earlier are incorrect. However, I believe greater care should be taken in labeling the type of performance measured in such experiments. “Statistical inference” would seem to be more appropriate than “Bayesian reasoning” given the limitations I have noted.

Future research on Bayesian reasoning would benefit from a richer conceptualization of what it is to “be Bayesian” and from better discussion of whether being non-Bayesian is necessarily irrational (Lewis,

The staging of information with repeated assessments was in fact a common methodological approach in Bayesian research prior to the 1970s, culminating in the classic work on conservatism by Ward Edwards and others (for a review, see Slovic and Lichtenstein,

For example, Williams and Mandel (

The issues I have raised, non-exhaustive as they are, draw attention to some important problems with the conventional approach to studying Bayesian reasoning in psychology that has been dominant since the 1970s. Rather than fostering pessimism, I hope my comments illustrate that there are good opportunities for future work to advance our understanding of how people revise or update their beliefs.

The author declares that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.

I thank Baruch Fischhoff, Vittorio Girotto, Gorka Navarrete, and Miroslav Sirota for helpful comments on earlier drafts of this paper.