Optimal design of experiments for estimating the time of death in forensic medicineA preprint appeared as ZIB Report ZR 18-08

• Published in: Inverse problems 2018-10, Vol.34 (12)
• Main Authors: Weiser, Martin, Freytag, Yvonne, Erdmann, Bodo, Hubig, Michael, Mall, Gita
• Format: Article
• Language: English
• Subjects: Bayesian inversion; design of experiments; heat equation; parameter identification; time of death
• ISSN: 0266-5611; 1361-6420
• DOI: 10.1088/1361-6420/aae7a5

Estimation of time of death based on a single measurement of body core temperature is a standard procedure in forensic medicine. Mechanistic models using simulation of heat transport promise higher accuracy than established phenomenological models in particular in nonstandard situations, but involve many not exactly known physical parameters. Identifying both time of death and physical parameters from multiple temperature measurements is one possibility to reduce the uncertainty significantly. In this paper, we consider the inverse problem in a Bayesian setting and perform both local and sampling-based uncertainty quantification, where proper orthogonal decomposition is used as model reduction for fast solution of the forward model. Based on the local uncertainty quantification, optimal design of experiments is performed in order to minimize the uncertainty in the time of death estimate for a given number of measurements. For reasons of practicability, temperature acquisition points are selected from a set of candidates in different spatial and temporal locations. Applied to a real corpse model, a significant accuracy improvement is obtained already with a small number of measurements.