Dimension-independent likelihood-informed MCMC
- Massachusetts Institute of Technology, Cambridge, MA 02139 (United States)
Many Bayesian inference problems require exploring the posterior distribution of high-dimensional parameters that represent the discretization of an underlying function. This work introduces a family of Markov chain Monte Carlo (MCMC) samplers that can adapt to the particular structure of a posterior distribution over functions. Two distinct lines of research intersect in the methods developed here. First, we introduce a general class of operator-weighted proposal distributions that are well defined on function space, such that the performance of the resulting MCMC samplers is independent of the discretization of the function. Second, by exploiting local Hessian information and any associated low-dimensional structure in the change from prior to posterior distributions, we develop an inhomogeneous discretization scheme for the Langevin stochastic differential equation that yields operator-weighted proposals adapted to the non-Gaussian structure of the posterior. The resulting dimension-independent and likelihood-informed (DILI) MCMC samplers may be useful for a large class of high-dimensional problems where the target probability measure has a density with respect to a Gaussian reference measure. Two nonlinear inverse problems are used to demonstrate the efficiency of these DILI samplers: an elliptic PDE coefficient inverse problem and path reconstruction in a conditioned diffusion.
- OSTI ID:
- 22570206
- Journal Information:
- Journal of Computational Physics, Vol. 304; Other Information: Copyright (c) 2015 Elsevier Science B.V., Amsterdam, The Netherlands, All rights reserved.; Country of input: International Atomic Energy Agency (IAEA); ISSN 0021-9991
- Country of Publication:
- United States
- Language:
- English
Exact and computationally efficient likelihood-based estimation for discretely observed diffusion processes (with discussion)
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journal | June 2006 |
Optimal scaling for various Metropolis-Hastings algorithms
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journal | November 2001 |
| Diffusion limits of the random walk Metropolis algorithm in high dimensions | text | January 2010 |
| Optimal scaling and diffusion limits for the Langevin algorithm in high dimensions | text | January 2011 |
| A Hierarchical Multilevel Markov Chain Monte Carlo Algorithm with Applications to Uncertainty Quantification in Subsurface Flow | preprint | January 2013 |
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