The characterization of Monte Carlo errors for the quantification of the value of forensic evidence

ABSTRACT

Recent developments in forensic science have lead to a proliferation of methods for quantifying the probative value of evidence by constructing a Bayes Factor that allows a decision-maker to select between the prosecution and defense models. Unfortunately, the analytical form of a Bayes Factor is often computationally intractable. A typical approach in statistics uses Monte Carlo integration to numerically approximate the marginal likelihoods composing the Bayes Factor. This article focuses on developing a generally applicable method for characterizing the numerical error associated with Monte Carlo integration techniques used in constructing the Bayes Factor. The derivation of an asymptotic Monte Carlo standard error (MCSE) for the Bayes Factor will be presented and its applicability to quantifying the value of evidence will be explored using a simulation-based example involving a benchmark data set. The simulation will also explore the effect of prior choice on the Bayes Factor approximations and corresponding MCSEs.

KEYWORDS:

• Bayes factor
• forensic science
• Monte Carlo
• standard error
• Gibbs sampling
• Bayesian
• model selection

AMS SUBJECT CLASSIFICATION:

• 62F15
• 62P99
• 65C05
• 65C60

Acknowledgements

We would like to thank the two anonymous reviewers for their time and for improving this article with their helpful comments.

Disclosure statement

No potential conflict of interest was reported by the authors.

ORCID

Danica M. Ommen  http://orcid.org/0000-0001-9955-3817

Additional information

Funding

The writing of this article was supported in part by Award No. 2014-IJ-CX-K088 awarded by the National Institute of Justice, Office of Justice Programs, US Department of Justice. The opinions, findings, and conclusions or recommendations expressed in this publication are those of the authors and do not necessarily reflect those of the Department of Justice.