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Efficient Bayesian Model Comparison with Differential Equations: a Population MCMC Approach via the Thermodynamic Integral

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Abstract: In this talk I shall present some Bayesian methodology based on Population MCMC and thermodynamic integration, which simultaneously addresses the commonly encountered issue of sampling from multimodal posterior distributions, as well as accurately estimating the marginal likelihoods of statistical models.

I shall characterise the method and compare to other approaches with some results using simple linear models, before looking at more complex models based on nonlinear differential equations. Such differential equation models are employed in many fields of science to describe processes occurring in the natural world, and discrimination of plausible model hypotheses is vital to the application of the scientific method.

Finally, I shall discuss a sampling scheme in which inference over differential equation models may be accelerated by employing auxiliary Gaussian processes to avoid solving the dynamical systems explicitly.

This talk is part of the Microsoft Research Cambridge, public talks series.

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