Base rates and Bayes’ Theorem for decision support

Abstract

Purpose

The purpose of this paper is to discuss and demonstrate “best practices” for creating quantitative behavioural investigative advice (i.e. statements to assist police with psychological and behavioural aspects of investigations) where complex statistical modelling is not available.

Design/methodology/approach

Using a sample of 361 serial stranger sexual offenses and a cross-validation approach, the paper demonstrates prediction of offender characteristics using base rates and using Bayes’ Theorem. The paper predicts four dichotomous offender characteristic variables, first using simple base rates, then using Bayes’ Theorem with 16 categorical crime scene variable predictors.

Findings

Both methods consistently predict better than chance. By incorporating more information, analyses based on Bayes’ Theorem (74.6 per cent accurate) predict with 11.1 per cent more accuracy overall than analyses based on base rates (63.5 per cent accurate), and provide improved advising estimates in line with best practices.

Originality/value

The study demonstrates how useful predictions of offender characteristics can be acquired from crime information without large (i.e. >500 cases) data sets or “trained” statistical models. Advising statements are constructed for discussion, and results are discussed in terms of the pragmatic usefulness of the methods for police investigations.

Citation

Charles Allen, J., M. Goodwill, A., Watters, K. and Beauregard, E. (2014), "Base rates and Bayes’ Theorem for decision support", Policing: An International Journal, Vol. 37 No. 1, pp. 159-169. https://doi.org/10.1108/PIJPSM-03-2013-0025