In forensic science, one of the major questions of interest is whether the suspect can be linked to the crime scene through the evidence. Forensic scientists are often tasked with addressing source-level questions and need to develop a method to statistically assess the evidence for traditional feature-comparison analyses, such as examiners perform for firearms, toolmarks, hair, glass fragments, fingerprints, shoe prints, handwriting and so on. In this thesis, we propose a two-step statistical approach that is applicable to a variety of forensic evidence types; (1) Develop a statistical method to assign the score, a measure of similarity, between questioned and recovered samples, (2) Assess the value of evidence through the score-based likelihood ratio (SLR). There are three chapters dedicated to developing methods of quantifying the similarity between two items on numerical trace evidence in glass fragments and on the two-dimensional pattern evidence of shoe outsole impressions. First, we develop a non-parametric method through statistical learning techniques for the comparison of glass fragments by computing a similarity score and showing that our score-based approach outperforms a number of existing methods. Secondly, we develop an algorithm to quantify the degree of correspondence between two shoe outsole impressions. By defining a good representative signature of shoe impressions, the methods we developed can take the class characteristic and unique wear and tear pattern into account when quantifying the similarity between two images, being able to discriminate two shoe impressions that share the same pattern. Finally, we research the performance of the SLR using the scores from the methods that we developed. We show how different SLRs are strengthened by increasing the discriminating power of the scoring metric and illustrate the range of SLR values for a variety of reasonable model choices.