Objectives This thesis is based on 4 papers that were all written with the same intent, which was to describe and demonstrate how epidemiologic concepts and data can serve as a basis for improved validity of probabilistic conclusions in forensic medicine (FM). Conclusions based on probability are common in FM, and the validity of probabilistic conclusions is dependant on their foundation, which is often no more than personal experience. Forensic epidemiology (FE) describes the use and application of epidemiologic methods and data to questions encountered in the practice of FM, as a means of providing an evidence-based foundation, and thus increased validity, for certain types of opinions. The 4 papers comprising this thesis describe 4 unique applications of FE that have the common goal of assessing probabilities associated with evidence gathered during the course of the investigation of traumatic injury and death.   Materials and Methods Paper I used a case study of a fatal traffic crash in which the seat position of the surviving occupant was uncertain as an example for describing a probabilistic approach to the investigation of occupant position in a fatal crash. The methods involved the matching of the occupants’ injuries to the vehicular and crash evidence in order to assess the probability that the surviving occupant was either the driver or passenger of the vehicle at the time of the crash. In the second and third papers, epidemiologic data pertaining to traffic crash-related injuries from the National Automotive Sampling System-Crashworthiness Data System (NASS-CDS) was used to assess the utility and strength of evidence, such as vehicle deformation and occupant injury of a particular severity and pattern, as a means of assessing the probability of an uncertain issue of interest. The issue of interest in Paper II was the seat position of the occupant at the time of a rollover crash (similar to Paper I), and the association that was investigated was the relationship between the degree of downward roof deformation and likelihood of a serious head and neck injury in the occupant. The analysis was directed at the circumstance in which a vehicle has sustained roof deformation on one side but not the other, and only one of the occupants has sustained a serious head or neck injury. In Paper III the issue of interest was whether an occupant was using a seat belt prior to being ejected from a passenger vehicle, when there was evidence that the seat belt could have unlatched during a crash, and thus it was uncertain whether the occupant was restrained and then ejected after the seat belt unlatched, or unrestrained. Of particular interest was the relative frequency of injury to the upper extremity closest to the side window (the outboard upper extremity [OUE]), as several prior authors have postulated that during ejection when the seat belt has become unlatched the retracting seat belt would invariably cinch around the OUE and cause serious injury. In Paper IV the focus of the analysis was the predictability of the distribution of skull and cervical spine fractures associated with fatal falls as a function of the fall circumstances. Swedish autopsy data were used as the source material for this study. Results In Paper I the indifferent pre-crash probability that the survivor was the driver (0.5) was modified by the evidence to arrive at a post-test odds of 19 to 1 that he was driving. In Paper II NASS-CDS data for 960 (unweighted) occupants of rollover crashes were included in the analysis. The association between downward roof deformation and head and neck injury severity (as represented by a composite numerical value [HNISS] ranging from 1 to 75) was as follows: for each unit increase of the HNISS there were increased odds of 4% that the occupant was exposed to >8 cm of roof crush versus <8 cm; 6% for >15 cm compared to <8 cm, and 11% for >30 cm of roof crush compared to <8 cm. In Paper III NASS-CDS data for 232,931 (weighted) ejected occupants were included in the analysis, with 497 coded as seat belt failures, and 232,434 coded as unbelted. Of the 7 injury types included in the analysis, only OUE and serious head injury were found to have a significant adjusted association with seat belt failure, (OR=3.87, [95% CI 1.2, 13.0] and 3.1, [95% CI 1.0, 9.7], respectively). The results were used to construct a table of post-test probabilities that combined the derived sensitivity and (1 - specificity) rates with a range of pre-crash seat belt use rates so that the results could be used in an investigation of a suspected case of belt latch failure. In Paper IV, the circumstances of 1,008 fatal falls were grouped in 3 categories of increasing fall height; falls occurring at ground level, falls from a height of <3 meters or down stairs, and falls from ≥3 meters. Logistic regression modeling revealed significantly increased odds of skull base and lower cervical fracture in the middle (<3 m) and upper (≥3 m) fall height groups, relative to ground level falls, as follows: (lower cervical <3 m falls, OR = 2.55 [1.32, 4.92]; lower cervical ≥3 m falls, OR = 2.23 [0.98, 5.08]; skull base <3 m falls, OR = 1.82 [1.32, 2.50]; skull base ≥3 m falls, OR = 2.30 [1.55, 3.40]). Additionally, C0-C1 dislocations were strongly related to fall height, with an OR of 8.3 for the injury in a ≥3 m fall versus ground level. Conclusions In this thesis 4 applications of FE methodology were described. In all of the applications epidemiologic data resulting from prior FM investigations were analyzed in order to draw probabilistic conclusions that could be reliably applied to the circumstances of a specific investigation. It is hoped that this thesis will serve to demonstrate the utility of FE in enhancing evidence-based practice in FM.

Many have used the principles of statistics and Bayesian decision theory to model specific learning problems. It is less common to see models of the processes of learning in general. One exception is the model of the supervised learning process known as the "Extended Bayesian Formalism" or EBF. This model is descriptive, in that it can describe and compare learning algorithms. Thus the EBF is capable of modeling both effective and ineffective learning algorithms. We extend the EBF to model un-supervised learning, semi-supervised learning, supervised learning, and empirical function optimization. We also generalize the utility model of the EBF to deal with non-deterministic outcomes, and with utility functions other than 0-1 loss. Finally, we modify the EBF to create a "prescriptive" learning model, meaning that, instead of describing existing algorithms, our model defines how learning should optimally take place. We call the resulting model the Unified Bayesian Decision Theoretical Model, or the UBDTM. WE show that this model can serve as a cohesive theory and framework in which a broad range of questions can be analyzed and studied. Such a broadly applicable unified theoretical framework is one of the major missing ingredients of machine learning theory. Using the UBDTM, we concentrate on supervised learning and empirical function optimization. We then use the UBDTM to reanalyze many important theoretical issues in Machine Learning, including No-Free-Lunch, utility implications, and active learning. We also point forward to future directions for using the UBDTM to model learnability, sample complexity, and ensembles. We also provide practical applications of the UBDTM by using the model to train a Bayesian variation to the CMAC supervised learner in closed form, to perform a practical empirical function optimization task, and as part of the guiding principles behind an ongoing project to create an electronic and print corpus of tagged ancient Syriac texts using active learning.