Illia Horenko, University of Lugano:

**What is the Bayesian relation model? On a data-driven Bayesian model reduction and applications.**

In the "What is ..." part of the talk Bayesian relation models (BRM) and Bayesian networks, their relation to Markov processes will be introduced. Next, issues related to a data-driven inference of BRMs (like "curse of dimension", quantification of uncertainty and computational cost) will be discussed. A particular focus will be on the model reduction aspect - since applicability of many computational approaches for multiscale systems is dwelling on identification of reduced dynamical models defined on a small set of collective variables (colvars). The popular approaches to Bayesian and Markovian model reduction rely on the knowledge of the full matrix of relations between the systems components. In many application areas these matrices are not directly available and must first be estimated from the data, resulting in the uncertainty of the obtained models and colvars that can grow exponentially with the physical dimension of the system.

A simple-to-implement but still rigorous clustering methodology for probability-preserving identification of reduced dynamical models and colvars directly from the data will be presented - not relying on the availability of full relation matrices or models at any stage of the resulting algorithm. Newly-developed open-access Bayesian Model Reduction Toolbox in Matlab will be introduced. Methodology will be demonstrated on an application to analysis and modeling of interactions between global teleconnections in the atmosphere and on a biomolecular dynamics application.

The talk will describe the work from the following papers:

[1] S. Gerber and I. Horenko: On inference of causality for discrete state models in a multiscale context, PNAS, 111(41), pp.14651–14656, 2014.

[2] S. Gerber and I. Horenko: Improving clustering by imposing network information, Science Advances (AAAS), 1(7), 2015.

[3] S. Gerber and I. Horenko: Towards a direct identification of reduced dynamical models for categorical processes, under review in PNAS, 2017