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Comparing Markov Chain Monte Carlo Proposal Densities for Diffusion Processes
Citation key Stimberg:2010:CMC
Author Florian Stimberg
Year 2010
Month mar
School TU Berlin
Abstract Inference for discretely observed diffusion processes has been of interest for some time. Analytical solutions are only possible for special types of models and therefore sampling strategies haven recently been increasingly popular for models of this type. In this thesis a Markov chain Monte Carlo approach is applied to reaction systems approximated by a diffusion process. The quality of Markov chain Monte Carlo methods depends heavily on the employed proposal distributions, thus their influence is the focus of this thesis. Besides a modified diffusion bridge, a variational approach to the inference problem is adapted as a path proposal. Simulations of system biology models are used to compare these methods and determine how they react to different values of observation noise and discretization among other simulation parameters. Although not generally applicable, the variational proposals proved to give good results for a number of models. Additionally, a Gaussian random walk and a maximum likelihood approach are used for parameter proposals and applied on the models to test their performance. The maximum likelihood method is found to be not practical to be used on its own, therefore possible enhancements are discussed.
Bibtex Type of Publication Diploma Thesis
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