A Bayesian Framework for Parameter Estimation in Dynamical Models with Applications to Forecasting

Mathematical models in Biology are powerful tools for the study and exploration of complex dynamics. Nevertheless, bringing theoretical results to an agreement with experimental observations involves acknowledging a great deal of uncertainty intrinsic to our theoretical representation of a real system.
Proper handling of such uncertainties, is key to the successful usage of models to predict experimental or field observations. This problem has been addressed over the years by many tools for model calibration an parameter estimation. In this article we present a general framework for uncertainty analysis and parameter estimation which is designed to handle uncertainties associated with the modeling of dynamic biological systems while remaining agnostic as to the type of model used. We apply the framework to two Influenza transmission models: one deterministic and the other stochastic. The results show that the framework can be applied without modifications to the two types of models and that it performs equally well on both. We also discuss the application of the framework to calibrate models for forecasting purposes.
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The Bayesian boom: good thing or bad?

A series of high-profile critiques of Bayesian models of cognition have recently sparked controversy. These critiques question the contribution of rational, normative considerations in the study of cognition. The present article takes central claims from these critiques and evaluates them in light of specific models. Closer consideration of actual examples of Bayesian treatments of different cognitive phenomena allows one to defuse these critiques showing that they cannot be sustained across the diversity of applications of the Bayesian framework for cognitive modeling. More generally, there is nothing in the Bayesian framework that would inherently give rise to the deficits that these critiques perceive, suggesting they have been framed at the wrong level of generality. At the same time, the examples are used to demonstrate the different ways in which consideration of rationality uniquely benefits both theory and practice in the study of cognition