Bayesian Handwriting Evidence Evaluation using MANOVA via Fourier-Based Extracted Features

TL;DR

This study develops a principled Bayesian framework for forensic handwriting evidence using Fourier-based loop descriptors of characters. It compares six models that arise from two likelihoods (Normal and Bayesian MANOVA) and three prior specifications (conjugate NIW, hierarchical NIW, and Normal-LogNormal-LKJ covariance), with marginal likelihoods estimated via bridge sampling to compute Bayes factors. Across 13 writers, the Bayesian MANOVA with Normal-LogNormal-LKJ priors consistently offers superior discrimination and robustness, while the sensitivity analyses map how prior choices and covariance parameters affect outcomes. The work provides a practical, multivariate approach to jointly analyze multiple character types, with implications for objective evidence evaluation and potential extensions to larger handwriting corpora.

Abstract

This paper proposes a novel statistical approach that aims at the identification of valid and useful patterns in handwriting examination via Bayesian modeling. Starting from a sample of characters selected among 13 French native writers, an accurate loop reconstruction can be achieved through Fourier analysis. The contour shape of handwritten characters can be described by the first four pairs of Fourier coefficients and by the surface size. Six Bayesian models are considered for such handwritten features. These models arise from two likelihood structures: (a) a multivariate Normal model, and (b) a MANOVA model that accounts for character-level variability. For each likelihood, three different prior formulations are examined, resulting in distinct Bayesian models: (i) a conjugate Normal-Inverse-Wishart prior, (ii) a hierarchical Normal-Inverse-Wishart prior, and (iii) a Normal-LogNormal-LKJ prior specification. The hierarchical prior formulations are of primary interest because they can incorporate the between-writers variability, a distinguishing element that sets writers apart. These approaches do not allow calculation of the marginal likelihood in a closed-form expression. Therefore, bridge sampling is used to estimate it. The Bayes factor is estimated to compare the performance of the proposed models and to evaluate their efficiency for discriminating purposes. Bayesian MANOVA with Normal-LogNormal-LKJ prior showed an overall better performance, in terms of discriminatory capacity and model fitting. Finally, a sensitivity analysis for the elicitation of the prior distribution parameters is performed.

Figures (18)

• Figure 1: Image analysis procedure: from the original loop to polar coordinates. Adapted from marquis2005quantification.
• Figure 2: Harmonics contribution obtained by the sum of the unit circle (h=0) and the specific harmonics of interest, $\alpha_h = 0.5$ and $b_h = 0$
• Figure 3: Reconstructed loop characters shown for the average Fourier coefficients per writer and character using the first four pairs of Fourier coefficients (H = 4; red curve) and the first ten pairs (H = 10; black curve).
• Figure 4: Logarithmic Bayes factors for handwriting evaluation ($\log\rm{BF}$) for same writer (a) and different writers comparisons (b), using the data modeling approaches described in Sections \ref{['normal-inverse-wishart']} and \ref{['bayesian_manova']}.
• Figure 5: Boxplots of Logarithmic Bayes factors ($\log\mathrm{BF}$) for handwriting evaluation for the same writer scenarios over different subsamples of background data for the Bayesian MANOVA approach.