Machine learning (ML) is increasingly shaping forensic science by enabling more accurate and objective evidence analysis. This study applies ML algorithms to classify gunshot residue (GSR) particles using spectral data obtained through scanning electron microscopy with energy-dispersive X-ray spectroscopy (SEM-EDX). Conventional GSR identification relies on detecting characteristic inorganic particles containing lead (Pb), barium (Ba), and antimony (Sb), which point to firearm discharge residue. Twelve spectra were collected from four hand swabs taken during a simulated shooting scenario, alongside control samples that yielded no residue signal. The particles were analysed for elemental distribution and subjected to ML-assisted classification. A statistical framework combining probabilistic modelling with likelihood ratios (LRs) was then used to weigh the evidential strength of competing hypotheses. Results revealed marked differences in elemental composition across samples, underscoring the importance of rigorous statistical treatment rather than relying solely on visual or qualitative assessment. Three of the four swab classes offered strong support for GSR presence, yielding high LRs favouring the prosecution hypothesis. One sample, however, deviated from the model's underlying assumptions, illustrating how elemental signatures alone can be misleading if interpreted without appropriate methodological safeguards. Overall, integrating ML with probabilistic modelling offers a robust framework for forensic GSR analysis. Nonetheless, the findings highlight that methodological rigor cannot be sacrificed for computational convenience, and analysts should remain attentive to cases where statistical assumptions break down.