Conditional probability distribution (CPD) method in temperature based death time estimation: Error propagation analysis

Abstract

Bayesian estimation applied to temperature based death time estimation was recently introduced as conditional probability distribution or CPD-method by Biermann and Potente. The CPD-method is useful, if there is external information that sets the boundaries of the true death time interval (victim last seen alive and found dead). CPD allows computation of probabilities for small time intervals of interest (e.g. no-alibi intervals of suspects) within the large true death time interval. In the light of the importance of the CPD for conviction or acquittal of suspects the present study identifies a potential error source. Deviations in death time estimates will cause errors in the CPD-computed probabilities. We derive formulae to quantify the CPD error as a function of input error. Moreover we observed the paradox, that in cases, in which the small no-alibi time interval is located at the boundary of the true death time interval, adjacent to the erroneous death time estimate, CPD-computed probabilities for that small no-alibi interval will increase with increasing input deviation, else the CPD-computed probabilities will decrease. We therefore advise not to use CPD if there is an indication of an error or a contra-empirical deviation in the death time estimates, that is especially, if the death time estimates fall out of the true death time interval, even if the 95%-confidence intervals of the estimate still overlap the true death time interval.