MCMC methods for diffusion bridges. (English) Zbl 1159.65007
This interesting work may be useful for the specialists in various subjects: Markov chain Monte Carlo (MCMC) methods; stochastic partial differential equations (SPDEs), and SDEs on Hilbert space; implicit schemes for SPDEs; and relevant numerical studies.
The authors present and study a Langevin MCMC approach for sampling nonlinear diffusion bridges. The proposed moves for the MCMC algorithm are determined by discretising the SPDEs. Of all innovations the part, which deals with implicit schemes for Langevin SPDEs, is the key one. The only one value of the scheme parameter is proved to be good, and the authors study this fact in detail, including the numerical examples.
Several adjoining themes are considered briefly, for example, a random-walk Metropolis and an independence sampler on the pathspace.
The authors present and study a Langevin MCMC approach for sampling nonlinear diffusion bridges. The proposed moves for the MCMC algorithm are determined by discretising the SPDEs. Of all innovations the part, which deals with implicit schemes for Langevin SPDEs, is the key one. The only one value of the scheme parameter is proved to be good, and the authors study this fact in detail, including the numerical examples.
Several adjoining themes are considered briefly, for example, a random-walk Metropolis and an independence sampler on the pathspace.
Reviewer: Serghey G. Suvorov (Donetsk)
MSC:
65C30 | Numerical solutions to stochastic differential and integral equations |
65C05 | Monte Carlo methods |
60H35 | Computational methods for stochastic equations (aspects of stochastic analysis) |
60H15 | Stochastic partial differential equations (aspects of stochastic analysis) |
35R60 | PDEs with randomness, stochastic partial differential equations |
65C40 | Numerical analysis or methods applied to Markov chains |
60G50 | Sums of independent random variables; random walks |
Keywords:
diffusion bridge; Langevin sampling; Gaussian measure; implicit Euler scheme; quadratic variation; Metropolis-adjusted Langevin algorithm; Markov chain Monte Carlo methods; stochastic partial differential equations; numerical examples; random-walkReferences:
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