A Way of Estimating the Standard Errors of Bayes Factor and Weight of Evidence – A Case Study (Theoretical Framework)

Published

March 27, 2023

Author(s)

Jin Chu Wu, John M. Libert

Abstract

The Weight of Evidence (WoE) is defined to be the logarithm of the Bayes factor (BF) with base 10, which is generally with single point hypothesis rather than diffuse hypothesis. They are used in applications such as forensic science, etc. To statistically estimate the standard error (SE) and the 95% confidence interval of BF and WoE, both parametric and nonparametric two-sample bootstrap algorithms are employed, respectively. Then, three challenging issues arise: 1. how to generate observed binomial variates; 2. how many variates are needed; 3. how to implement bootstrap algorithms. The observed binomial variates can be generated using either the stochastic function-call method (i.e., call rbinom in R Package) or the deterministic partition method via the expected binomial densities (i.e., call dbinom in R Package). To ensure the computational accuracies, the total number of observed binomial variates is determined by the root-mean-square deviation between the observed and expected binomial distributions, as well as the bootstrap variability caused by sampling. Thereafter, the parametric two-sample bootstrap algorithm is implemented on observed binomial variates generated using the stochastic function-call method, whereas the nonparametric two-sample bootstrap algorithm is carried out on observed binomial variates created using the deterministic partition method. In this article, a case study is carried out.

Citation

Technical Note (NIST TN) - 2250

Report Number

2250

NIST Pub Series

Technical Note (NIST TN)

Pub Type

NIST Pubs

Download Paper

https://doi.org/10.6028/NIST.TN.2250

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Keywords

weight of evidence, Bayes factor, standard error, binomial distribution, two-sample bootstrap, forensic science

Citation

Wu, J. and Libert, J. (2023), A Way of Estimating the Standard Errors of Bayes Factor and Weight of Evidence – A Case Study (Theoretical Framework), Technical Note (NIST TN), National Institute of Standards and Technology, Gaithersburg, MD, [online], https://doi.org/10.6028/NIST.TN.2250, https://tsapps.nist.gov/publication/get_pdf.cfm?pub_id=935689 (Accessed April 27, 2026)

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