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

Flávio Codeço Coelho,Claudia Codeço

doi:10.1038/npre.2009.4044.1

Flávio Codeço Coelho, Claudia Codeço

Open Access

https://doi.org/10.1038/npre.2009.4044.1

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Journal: Nature Precedings	Publication Date: Dec 3, 2009
Citations: 21	License type: CC BY 3.0

Affiliation: Instituto Gulbenkian de Ciência

Abstract

AbstractMathematical 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.

Highlights

Mathematical models have long played a key role in understanding infectious disease epidemiology [1] as well other biological dynamical systems
A mathematical model is by definition a simplified and idealized representation of a real system
How well a model’s dynamics reproduce the real system’s depends in part on how well we can set the parameters of the model to correspond to their real-world counterparts

Summary

Introduction

Mathematical models have long played a key role in understanding infectious disease epidemiology [1] as well other biological dynamical systems Their ability to combine established theory and data to predict empirical observation is unique and cannot be achieved by other methods [2]. Proper representation of the intrinsic uncertainty associated with dynamic models of biological systems, has been under increasing scrutiny through the develop of a number of methods for parameter estimation and model calibration. Such methods, to be effective, must strive to be as comprehensible as possible in the treatment of all identifiable sources of uncertainty related to a given mathematical representation of a biological system [3]. Tend to be closely coupled to a specific model or class of models, being less generally applicable [4,5,6,7]

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