Dimension-independent likelihood-informed MCMC

Dimension-independent likelihood-informed MCMC

Many Bayesian inference problems require exploring the posterior distribution of high-dimensional parameters that, in principle, can be described as functions. 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. Firs...

Likelihood-informed dimension reduction for nonlinear inverse problems

The intrinsic dimensionality of an inverse problem is affected by prior information, the accuracy and number of observations, and the smoothing properties of the forward operator. From a Bayesian perspective, changes from the prior to the posterior may, in many problems, be confined to a relatively lowdimensional subspace of the parameter space. We present a dimension reduction approach that de...

Conditional log-likelihood MDL and Evolutionary MCMC

Mcmc Perspectives on Simulated Likelihood Estimation

A major stumbling block in multivariate discrete data analysis is the problem of evaluating the outcome probabilities that enter the likelihood function. Calculation of these probabilities involves high-dimensional integration, making simulation methods indispensable in both Bayesian and frequentist estimation and model choice. We review several existing probability estimators and then show tha...

Adaptive independent sticky MCMC algorithms

Monte Carlo methods have become essential tools to solve complex Bayesian inference problems in different fields, such as computational statistics, machine learning, and statistical signal processing. In this work, we introduce a novel class of adaptive Monte Carlo methods, called adaptive independent sticky Markov Chain Monte Carlo (MCMC) algorithms, to sample efficiently from any bounded targ...