### Forensic Probability and Statistics - 8EC - M1

Prerequisites

Basic course in (discrete and continuous) probability theory and statistics, including at least the following topics: events, random variables, conditional probability, independence, basics of estimation theory, basics of hypotheses testing. No knowledge in biology, philosophy or forensic science is assumed since we will introduce the necessary background.

Aim of the course

The aim of this course is to understand the basics of forensic statistics and probability, and to apply these to concrete problems. The course is a natural mixture of rigorous probabilistic and statistical theory on the one hand, and elements from biology, forensic science, legal science, and philosophy on the other. The theory is not only applied but actually developed as an answer to new challenges in a rapidly changing environment.

We will discuss the following topics:

1. The Bayesian framework with prior odds, posterior odds, and likelihood ratios. Likelihood ratios as measure of the strength of evidence.
2. The probability and statistics of DNA evidence for trace-person matches, family relatedness, and database searches.
3. Understanding likelihood ratios and likelihood ratio distributions when likelihood ratios are interpreted as random variables.
4. The role of p-values in reporting forensic evidence. In particular we address the issue that p-values do not measure the strength of evidence and should not be used for that purpose.
5. The classical island problems: assigning evidential weight to a shared characteristic in a closed population. We distinguish between the cold case, when an individual is randomly selected, and the search case in which the first matching individual is considered. The difference is relevant for the evidential value of a match. Also subpopulations are discussed.
6. The philosophy of probabilities in a forensic context. The way we interpret probability is crucial for the applicability. We will argue that only an epistemic and subjective interpretation is tenable, and discuss consequences.
7. Classical probability cannot deal with complete ignorance, but this ignorance is desirable in many priors. The theory of belief functions provides a solution to this. We introduce these and their role in forensic statistics.
8. Bayesian networks - theory and applications.
9. Combination of evidence.
10. Familial search and statistical and probabilistic aspects of database searches. Databases can lead to a direct match or may point at a relative of the donor of a DNA profile. We discuss these issues.