BEN CALDERHEAD THESIS

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Differential geometric MCMC methods and applications

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ben calderhead thesis

ccalderhead Lecturer in Statistics, Imperial College London. Unusually for a biological system, one can obtain vast numbers of relatively accurate measurements of open and closed states on an incredibly small time scale. Resource geometric combination definable notation. Neural Information Processing Systems.

ben calderhead thesis

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The performance of these Riemannian manifold Markov chain Monte Carlo algorithms is rigorously assessed by performing Bayesian inference on logistic regression models, log-Gaussian Cox point process models, stochastic volatility models, and both parameter and model level inference of dynamical systems described by nonlinear differential equations.

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During this time, I developed novel Markov chain Monte Carlo methodology that exploits the natural representation of the parameter space of a statistical model as a Riemannian manifold.

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The methods developed provide generalisations of the Metropolis-adjusted Langevin algorithm and the Hybrid Monte Carlo algorithm for Bayesian statistical inference, and resolve many shortcomings of existing Monte Carlo algorithms when sampling from target densities that may be high dimensional and exhibit strong correlation structure.

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