Bayesian inference for psychology. Part I: Theoretical advantages and practical ramifications

Abstract

Bayesian parameter estimation and Bayesian hypothesis testing present attractive alternatives to classical inference using confidence intervals and p values. In part I of this series we outline ten prominent advantages of the Bayesian approach. Many of these advantages translate to concrete opportunities for pragmatic researchers. For instance, Bayesian hypothesis testing allows researchers to quantify evidence and monitor its progression as data come in, without needing to know the intention with which the data were collected. We end by countering several objections to Bayesian hypothesis testing. Part II of this series discusses JASP, a free and open source software program that makes it easy to conduct Bayesian estimation and testing for a range of popular statistical scenarios (Wagenmakers et al. this issue).

Why Do I Have to Drive Now? Post Hoc Explanations of Takeover Requests

“…Consistent to the prior the prior width for the expected range of effect 359 sizes was set to r = 0.5 (medium), which correspondents to the prior width of r = 1 √2 ⁄ for the Bayesian 360 t test (Wagenmakers et al, 2017). Participant was included as a random factor.…”

Introduction to Bayesian Inference for Psychology

“…Once the models were built, the researcher had only to "turn the crank" of probabilistic inference and posterior probabilities are obtained through standard mechanisms that rely on little other than the sum and product rules of probability. As this example illustrates, the practical computation of posterior probabilities will often rely on calculus or numerical integration methods; several papers in this special issue deal with computational software that is available (39,58,64,65).…”

“…By reporting only the amount of evidence, in the form of a Bayes factor, every individual reader can combine that evidence with their own prior and form their own conclusions. This is now a widely-recommended approach (e.g., (65); but see (47), for words of caution; and see (28), for a discussion of scenarios in which the Bayes factor should not be the final step of an analysis) that is taken in the final example. If the coin is fair, and there is no cheating, then the Irish team captain should win the toss with 50% probability on each occasion (M0 : θ = θ0 = 0.5).…”

“…Recent computational developments have made the computation of Bayes factors more tractable, especially for common scenarios (64,65). For uncommon or complex scenarios, one might resort to reporting a different model comparison metric that does not rely on the marginal likelihood, such as the various information criteria (AIC, BIC, DIC, WAIC) or leave-one-out cross validation (LOOCV; see 56,59,60).…”

“…While we maintain that the mathematical underpinnings serve understanding of these methods in important ways, we should also point out that recent developments regarding Bayesian statistical software packages (e.g., 39,58,64,65) have made it possible to perform many kinds of Bayesian analyses without the need to carry out any of the technical mathematical derivations. The mathematical basis we present here remains, of course, more general.…”