[Paper Review] Two-stage approach for the inference of the source of high-dimension and complex chemical data in forensic science

Madeline Ausdemore, Cédric Neumann+3 more|arXiv (Cornell University)|Apr 3, 2018

Forensic and Genetic Research20 references3 citations

TL;DR

This paper proposes a two-stage kernel-based method for forensic source inference of high-dimensional chemical data, such as FTIR spectra of paint, enabling statistically rigorous, likelihood-free Bayesian-like inference without requiring complex probability models. The approach uses kernel functions to handle complex, high-dimensional data and demonstrates that paint evidence carries substantial probative value, especially when source characteristics are rare.

ABSTRACT

Forensic scientists are often criticised for the lack of quantitative support for the conclusions of their examinations. While scholars advocate for the use of a Bayes factor to quantify the weight of forensic evidence, it is often impossible to assign the necessary probability measures to perform likelihood-based inference for high-dimensional and complex data. To address this issue, we revisit a two-stage inference framework and leverage the properties of kernel functions to offer a method that allows for statistically supporting the inference of the identity of source of sets of trace and control objects by way of a single test. Our method is generic in that it can be easily tailored to any type of data encountered in forensic science or pattern recognition, and our method does not depend on the dimension or the type of the considered data. The application of our method to paint evidence shows that this type of evidence carries substantial probative value. Finally, our approach can easily be extended to other evidence types such as glass, fibres and dust.

Motivation & Objective

• To address the lack of quantitative support in forensic source attribution for high-dimensional, complex chemical data such as paint, glass, or fibre spectra.
• To develop a statistically rigorous, likelihood-free inference framework that supports Bayesian reasoning without requiring explicit probability models for complex data.
• To enable practical forensic inference using small sample sizes typical in casework (e.g., 3–10 observations), avoiding the need for extensive training data.
• To demonstrate the method’s applicability and probative value using real-world FTIR data from paint evidence.
• To provide a generic, extensible framework applicable to diverse forensic evidence types beyond paint.

Proposed method

• The method employs a two-stage inference framework originally proposed by Parker (1966), reinterpreted using kernel functions to enable statistical inference on high-dimensional, heterogeneous data.
• A kernel function is used to compute similarity between trace and control objects, forming the basis of a test statistic that is invariant to data type and dimension.
• The approach relies on a single key assumption—satisfied through kernel design—that ensures consistency as data dimension increases.
• Posterior distributions of model parameters are sampled efficiently using algorithms that handle parameter uncertainty, enabling robust inference.
• The framework replaces traditional likelihood-based inference with a kernel-based test statistic, allowing inference even when probability measures are infeasible to assign.
• The method is generic and can be adapted to any data type by modifying the kernel function, including compositional, continuous, or discrete data.

Experimental results

Research questions

• RQ1 Can a two-stage inference framework be adapted to provide statistically rigorous, likelihood-free inference for high-dimensional forensic chemical data?
• RQ2 Does the proposed kernel-based method enable reliable source attribution when traditional likelihood-based inference is infeasible due to data complexity?
• RQ3 What is the probative value of paint evidence characterized by FTIR spectra, and how does it vary with source rarity?
• RQ4 Can the method be extended to other forensic evidence types such as glass, fibres, or dust?
• RQ5 How does the method perform under typical casework constraints, such as small sample sizes and limited background data?

Key findings

• The proposed method successfully enables statistically rigorous inference for high-dimensional chemical data, such as FTIR spectra of paint, where traditional likelihood-based inference is infeasible.
• FTIR spectra of paint contain highly specific information that allows for effective discrimination between samples from different sources.
• The probative value of paint evidence is significantly higher when the source characteristics are rare, indicating that rare features enhance forensic discrimination.
• The method performs well with small sample sizes typical in forensic casework, supporting practical application in real-world scenarios.
• The two-stage kernel-based framework provides a robust, generic solution applicable to diverse forensic evidence types, including paint, glass, fibres, and dust.
• The approach supports a shift toward quantitative, evidence-based source attribution, addressing longstanding criticisms of forensic science regarding lack of statistical support.