A simple method is introduced for assessing the evidentiary value of fire debris samples. The method relies on models built by random draws from a database of ignitable liquid and substrate pyrolysis samples. A stratified random draw from database records belonging to each ASTM E1618 ignitable liquid class and the substrate class is taken in proportion to a prescribed distribution. The likelihood ratios are estimated by direct calculation from a one-level Gaussian kernel density model based on the covariance structure and multivariate means resulting from each random draw. Multiple draws result in model-related variation in the calculated likelihood ratios. The method is demonstrated for 500 random draws with replacement based on three distributions. Ten-fold cross-validation is performed for each model, with subsequent testing on laboratory burn samples. The average cross-validated receiver operating characteristic areas under the curve were 0.959, 0.956 and 0.947, for the three distributions. The mean log (base 10) of the likelihood ratio (LLR) values for the laboratory test burns of gasoline on polyester carpet and carpet padding were in the range of 1.5 to −3.1 and were qualitatively consistent with the observed gasoline contributions to the total ion chromatograms for the samples. The LLR values for laboratory test burns of a petroleum distillate on polyester carpet and carpet padding, 1.7 to −3.3, were also in qualitative agreement with the observed chromatographic patterns. The calculated LLR values for laboratory burns of a set of polyester carpet and padding samples were in the range −0.9 to −6.7.
