A Bayesian Analysis of a Cognitive-Behavioral Therapy Intervention for High-Risk People on Probation

Abstract

This analysis employs a Bayesian framework to estimate the impact of a Cognitive-Behavioral Therapy (CBT) intervention on the recidivism of high-risk people under community supervision. The study relies on the reanalysis of experimental datal using a Bayesian logistic regression model. In doing so, new estimates of programmatic impact were produced using weakly informative Cauchy priors and the Hamiltonian Monte Carlo method. The Bayesian analysis indicated that CBT reduced the prevalence of new charges for total, non-violent, property, and drug crimes. However, the effectiveness of the CBT program varied meaningfully depending on the participant's age. The probability of the successful reduction of drug offenses was high only for younger individuals (<26 years old), while there was an impact on property offenses only for older individuals (>26 years old). In general, the probability of the successful reduction of new charges was higher for the older group of people on probation. Generally, this study demonstrates that Bayesian analysis can complement the more commonplace Null Hypothesis Significance Test (NHST) analysis in experimental research by providing practically useful probability information. Additionally, the specific findings of the reestimation support the principles of risk-needs responsivity and risk-stratified community supervision and align with related findings, though important differences emerge. In this case, the Bayesian estimations suggest that the effect of the intervention may vary for different types of crime depending on the age of the participants. This is informative for the development of evidence-based correctional policy and effective community supervision programming.