Markov chain Monte Carlo algorithms for Gaussian processes
Seminar Room 1, Newton Institute
We discuss Markov chain Monte Carlo algorithms for sampling functions in Gaussian process models. A first algorithm is a local sampler that iteratively samples each local part of the function by conditioning on the remaining part of the function. The partitioning of the domain of the function into regions is automatically carried out during the burn-in sampling phase. A more advanced algorithm uses control variables which are auxiliary function values that summarize the properties of the function. At each iteration, the algorithm proposes new values for the control variables and then generates the function from the conditional Gaussian process prior. The control input locations are found by minimizing the total variance of the conditional prior. We apply these algorithms to estimate non-linear differential equations in Systems Biology.
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