Exact active subspace Metropolis-Hastings, with applications to the Lorenz-96 system

Ingmar Schuster; Paul G. Constantine; T.J. Sullivan

Exact active subspace Metropolis-Hastings, with applications to the Lorenz-96 system

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arxiv 1712.02749 v1 pith:AMBEAHAQ submitted 2017-12-07 stat.CO stat.AP

Ingmar Schuster , Paul G. Constantine , T.J. Sullivan This is my paper · ORCID

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keywords activealgorithmformulationlorenz-96metropolis-hastingsproblemsystema2779-a2805

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We consider the application of active subspaces to inform a Metropolis-Hastings algorithm, thereby aggressively reducing the computational dimension of the sampling problem. We show that the original formulation, as proposed by Constantine, Kent, and Bui-Thanh (SIAM J. Sci. Comput., 38(5):A2779-A2805, 2016), possesses asymptotic bias. Using pseudo-marginal arguments, we develop an asymptotically unbiased variant. Our algorithm is applied to a synthetic multimodal target distribution as well as a Bayesian formulation of a parameter inference problem for a Lorenz-96 system.

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