BAYESIAN MODEL SELECTION AND PRIOR IMPACT ASSESSMENT WITH A FOCUS ON DYNAMICAL SYSTEMS

There are many models for prediction. These models differ in the number of parameters and therefore scientists are faced with the problem of model selection. Model selection techniques seek a simple model with similar accuracy to complex models for in-sample data. While the Bayesian approach to parameter estimation is frequently used, fully Bayesian model selection is seldom used because of the high computational cost of computing the marginal likelihood, a key component of Bayesian model selection. This thesis introduces a gradient-based algorithm, Replica exchange Hamiltonian Monte Carlo (REHMC), which accurately computes the marginal likelihood when used with thermodynamic integration (TI). It also examines the often-overlooked impact of prior choices in Bayesian analysis on model outcomes, especially in Ordinary differential equation (ODE)
models. The thesis extends prior impact assessment to models with more than two parameters using algorithms from computational optimal transport. It introduces a new interpretable prior impact measure based on the Wasserstein Impact Measure (WIM). Power posteriors are used to provide insights into the transitions from prior to posterior
distributions. The source codes are made publicly available to encourage their adoption.