MCMC methods for diffusion bridges

摘要: We present and study a Langevin MCMC approach for sampling nonlinear diffusion bridges. The method is based on recent theory concerning stochastic partial differential equations (SPDEs) reversible with respect to the target bridge, derived by applying idea bridge pathspace. In process, Random-Walk Metropolis algorithm an Independence Sampler are also obtained. novel algorithmic of paper that proposed moves determined discretising SPDEs in time direction using implicit scheme, parametrised θ ∈ [0,1]. show resulting infinite-dimensional sampler well-defined only if = 1/2, when proposals have correct quadratic variation. Previous Langevin-based methods used explicit schemes, corresponding 0. significance choice 1/2 inherited finite-dimensional approximation practice. numerical results illustrating phenomenon explains it. Diffusion bridges (with additive noise) representative family laws defined as change measure from Gaussian distributions arbitrary separable Hilbert spaces; analysis this can be readily extended example signal processing illustrates fact.