Stochastic models in population biology: from dynamic noise to Bayesian description and model comparison for given data sets

Abstract

We study some stochastic models from population biology, namely epidemiology, which can be solved analytically. From the solution of the stochastic processes we construct the likelihood function and compare the maximum likelihood parameter estimation procedure with the Bayesian approach of obtaining an explicit probability for the parameters given the available data. Finally, we compare one model against the other in the Bayesian framework, both models performing on the same simulated data set. In some cases of data obtained under one model with specific parameter values, the model comparison favours the model not underlying the simulated data. This apparently paradoxical situation arises in parameter regions which do not easily give sufficient information to the simulated data to reject simpler models.

Keywords:

• Markov processes in continuous time
• linear infection model
• Poisson process
• Bayes factor

2010 AMS Subject Classifications:

• 92B05
• 37A50
• 62M02
• 62M05
• 62F15

Acknowledgements

This work has been supported by the European Union under FP7 in the projects EPIWORK and DENFREE and by FCT, Portugal, in various ways, especially via the project PTDC/MAT/115168/2009.