An overview of Bayesian reasoning in the analysis of delay‐discounting data
Bayesian stats turn delay-discounting data into plain probability statements you can act on.
01Research in Context
What this study did
Franck and colleagues wrote a how-to guide. They show step-by-step Bayesian re-analysis of delay-discounting data.
The paper uses old data from people with and without substance-use issues. No new experiment was run.
What they found
Bayesian methods give straight probability answers. You can say, "There is an 85 percent chance this person is impulsive."
Old p-values only tell you the chance of the data if the null is true. Bayesian output is easier to explain to clients and teams.
How this fits with other research
Alaimo et al. (2015) already offered a Bayesian tool that picks the best discounting curve for each person. Franck et al. widen the lens and show how to add prior knowledge and get full probability curves.
Gilroy et al. (2018) created a model-based area-under-the-curve using numerical integration. Franck folds that same metric into the Bayesian framework, so you can now get a credible interval around AUC.
Bacon et al. (1998) say, "Skip inferential stats—just use visual analysis." Franck does not reject stats; instead, they swap p-values for Bayesian probabilities. The two papers seem to clash, but one targets single-case clinical decisions while the other targets group-level parameter estimation.
Why it matters
If you run discounting assessments for impulsive clients, Bayesian output gives clearer numbers for reports and treatment plans. Try adding a prior based on past clinic data and report the 95 percent credible interval next time you graph a client’s delay curve.
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02At a glance
03Original abstract
Statistical inference (including interval estimation and model selection) is increasingly used in the analysis of behavioral data. As with many other fields, statistical approaches for these analyses traditionally use classical (i.e., frequentist) methods. Interpreting classical intervals and p-values correctly can be burdensome and counterintuitive. By contrast, Bayesian methods treat data, parameters, and hypotheses as random quantities and use rules of conditional probability to produce direct probabilistic statements about models and parameters given observed study data. In this work, we reanalyze two data sets using Bayesian procedures. We precede the analyses with an overview of the Bayesian paradigm. The first study reanalyzes data from a recent study of controls, heavy smokers, and individuals with alcohol and/or cocaine substance use disorder, and focuses on Bayesian hypothesis testing for covariates and interval estimation for discounting rates among various substance use disorder profiles. The second example analyzes hypothetical environmental delay-discounting data. This example focuses on using historical data to establish prior distributions for parameters while allowing subjective expert opinion to govern the prior distribution on model preference. We review the subjective nature of specifying Bayesian prior distributions but also review established methods to standardize the generation of priors and remove subjective influence while still taking advantage of the interpretive advantages of Bayesian analyses. We present the Bayesian approach as an alternative paradigm for statistical inference and discuss its strengths and weaknesses.
Journal of the Experimental Analysis of Behavior, 2019 · doi:10.1002/jeab.504