Thomas Hamelryck (Bioinformatics Center, University of Copenhagen)

Inference of protein structure and ensembles using Bayesian statistics and probability kinematics

The so-called protein folding problem is the loose designation for an amalgam of closely related, unsolved problems that include protein structure prediction, protein design and the simulation of the protein folding process. We adopt a unique Bayesian approach to modelling bio-molecular structure, based on graphical models, directional statistics and probability kinematics. Notably, we developed a generative probabilistic model of protein structure in full atomic detail. I will give an overview of how rigorous probabilistic models of something as complicated as a protein's atomic structure can be formulated, focusing on the use of graphical models and directional statistics to model angular degrees of freedom. I will also discuss the reference ratio method, which is needed to "glue" several probabilistic models of protein structure together in a consistent way. The reference ratio method is based on "probability kinematics", a little known method to perform Bayesian inference proposed by the philosopher Richard C. Jeffrey at the end of the fifties. Probability kinematics might find widespread application in statistics and machine learning as a way to formulate complex, high dimensional probabilistic models for multi-scale problems by combining several simpler models.

Anjali Mazumder (University of Warwick)

Probabilistic Graphical Models for planning and reasoning of scientific evidence in the courts

The use of probabilistic graphical models (PGMs) has gained prominence in the forensic science and legal literature when evaluating evidence under uncertainty. The graph-theoretic and modular nature of the PGMs provide a flexible and graphical representation of the inference problem, and propagation algorithms facilitate the calculation of laborious marginal and conditional probabilities of interest. In giving expert testimony regarding, for example, the source of a DNA sample, forensic scientists under much scrutiny, are often asked to justify their decision-making-process. Using information-theoretic concepts and a decision-theoretic framework, we define a value of evidence criterion as a general measure of informativeness for a forensic query and collection of evidence to determine which and how much evidence contributes to the reduction of uncertainty. In this talk, we demonstrate how this approach can be used for a variety of planning problems and the utility of PGMs for scientific and legal reasoning.