A large, irregular red paint splatter with two smaller splashes on a light gray background.

Journal: Computational Statistics & Data Analysis

Published: 2024

Primary Author: Tong Zou

Secondary Authors: Hal Stern

Type: Publication

Research Area: Bloodstain, Forensic Statistics

Directional data require specialized models because of the non-Euclidean nature of their domain. When a directional variable is observed jointly with linear variables, modeling their dependence adds an additional layer of complexity. A Bayesian nonparametric approach is introduced to analyze directional-linear data. Firstly, the projected normal distribution is extended to model the joint distribution of linear variables and a directional variable with arbitrary dimension projected from a higher-dimensional augmented multivariate normal distribution. The new distribution is called the semi-projected normal distribution (SPN) and can be used as the mixture distribution in a Dirichlet process model to obtain a more flexible class of models for directional-linear data. Then, a conditional inverse-Wishart distribution is proposed as part of the prior distribution to address an identifiability issue inherited from the projected normal and preserve conjugacy with the SPN. The SPN mixture model shows superior performance in clustering on synthetic data compared to the semi-wrapped Gaussian model. The experiments show the ability of the SPN mixture model to characterize bloodstain patterns. A hierarchical Dirichlet process model with the SPN distribution is built to estimate the likelihood of bloodstain patterns under a posited causal mechanism for use in a likelihood ratio approach to the analysis of forensic bloodstain pattern evidence.

View Full Article

Related Resources

A thick gray wavy line forming an abstract, looping shape on a light gray background.

An Introduction to the Forensic Handwriting Analysis Software handwriter

July 18, 2025

Full Article

Blue shoeprint with a tread pattern on a white background.

Forensic Footwear: A Retrospective of the Development of the MANTIS Shoe Scanning System

July 10, 2025

There currently are no shoe-scanning devices developed in the United States that can operate in a real-world, variable-weather environment in …

Full Article

A green fingerprint icon on a light gray background.

Examiner consistency in perceptions of fingerprint minutia rarity

July 10, 2025

Friction ridge examiners (FREs) identify distinctive features (minutiae) in fingerprints and consider how rare these observed minutiae are in their …

Full Article