**[Fall 2020]**

**Prerequisites**

1. Basic course in (discrete and continuous) probability theory, including at least the following topics: events, random variables, conditional probability, independence. For instance, a course on the level of Sheldon Ross:" A first course in probability" suffices.

2. It may help if the student is familiar with the very basics of statistics, in particular basic estimation theory and hypotheses testing, but this is not strictly necessary.

3. 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 the theory and philosophy 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:

- The Bayesian framework with prior odds, posterior odds, and likelihood ratios. Likelihood ratios as measure of the strength of evidence.
- The probability and statistics of DNA evidence for trace-person matches, family relatedness, and database searches.
- Understanding likelihood ratios and likelihood ratio distributions when likelihood ratios are interpreted as random variables.
- 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.
- 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.
- The philosophy of probability 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.
- Classical probability cannot deal with complete ignorance, but this ignorance is desirable in many priors. The theory of belief functions provides a partial solution to this. We introduce these and their role in forensic statistics.
- Bayesian networks - theory and applications.
- Statistical and probabilistic aspects of database searches, including familial search. Databases can lead to a direct match or may point at a relative of the donor of a DNA profile.
- The uncertainty of likelihood ratios and how to deal with this.

**Lecturers**

Ronald Meester (VU 6 weeks), Klaas Slooten (NFI/VU 6 weeks) & Marjan Sjerps (NFI/UvA 3 weeks)

- Docent: Ronald Meester
- Docent: Marjan Sjerps
- Docent: Klaas Slooten