Information-Theoretical Assessment of the Performance of Likelihood Ratio Computation Methods

Performance of likelihood ratio (LR) methods for evidence evaluation has been represented in the past using, for example, Tippett plots. We propose empirical cross-entropy (ECE) plots as a metric of accuracy based on the statistical theory of proper scoring rules, interpretable as information given by the evidence according to information theory, which quantify calibration of LR values. We present results with a case example using a glass database from real casework, comparing performance with both Tippett and ECE plots. We conclude that ECE plots allow clearer comparisons of LR methods than previous metrics, allowing a theoretical criterion to determine whether a given method should be used for evidence evaluation or not, which is an improvement over Tippett plots. A set of recommendations for the use of the proposed methodology by practitioners is also given.