# A Bayesian Hierarchical Model for Evaluating Forensic Footwear Evidence

## TL;DR

This paper introduces a Bayesian hierarchical model for forensic footwear evidence, improving the estimation of random match probabilities by incorporating shoe tread patterns and spatial accidentals, addressing limitations of previous models.

## Contribution

The paper develops a new spatial point process model within a hierarchical Bayesian framework that leverages shoe tread pattern data for better forensic evidence evaluation.

## Key findings

- Model fits data significantly better than existing models.
- Including tread pattern information improves accuracy.
- Demonstrated on a large heterogeneous shoe database.

## Abstract

When a latent shoeprint is discovered at a crime scene, forensic analysts inspect it for distinctive patterns of wear such as scratches and holes (known as accidentals) on the source shoe's sole. If its accidentals correspond to those of a suspect's shoe, the print can be used as forensic evidence to place the suspect at the crime scene. The strength of this evidence depends on the random match probability---the chance that a shoe chosen at random would match the crime scene print's accidentals. Evaluating random match probabilities requires an accurate model for the spatial distribution of accidentals on shoe soles. A recent report by the President's Council of Advisors in Science and Technology criticized existing models in the literature, calling for new empirically validated techniques. We respond to this request with a new spatial point process model for accidental locations, developed within a hierarchical Bayesian framework. We treat the tread pattern of each shoe as a covariate, allowing us to pool information across large heterogeneous databases of shoes. Existing models ignore this information; our results show that including it leads to significantly better model fit. We demonstrate this by fitting our model to one such database.