Related papers: Geometric MCMC for Infinite-Dimensional Inverse Pr…

Recently Dutta and Bhattacharya (2013) introduced a novel Markov Chain Monte Carlo methodology that can simultaneously update all the components of high dimensional parameters using simple deterministic transformations of a one-dimensional…

This study introduces a computationally efficient algorithm, delayed acceptance Markov chain Monte Carlo (DA-MCMC), designed to improve posterior simulation in quasi-Bayesian inference. Quasi-Bayesian methods, which do not require fully…

We consider the problem of Bayesian inference for changepoints where the number and position of the changepoints are both unknown. In particular, we consider product partition models where it is possible to integrate out model parameters…

The identification of parameters in mathematical models using noisy observations is a common task in uncertainty quantification. We employ the framework of Bayesian inversion: we combine monitoring and observational data with prior…

Markov Chain Monte Carlo (MCMC) is a computational approach to fundamental problems such as inference, integration, optimization, and simulation. The field has developed a broad spectrum of algorithms, varying in the way they are motivated,…

We consider Markov chain Monte Carlo (MCMC) algorithms for Bayesian high-dimensional regression with continuous shrinkage priors. A common challenge with these algorithms is the choice of the number of iterations to perform. This is…

Bayesian max-margin models have shown superiority in various practical applications, such as text categorization, collaborative prediction, social network link prediction and crowdsourcing, and they conjoin the flexibility of Bayesian…

Quasi-Monte Carlo (QMC) methods for estimating integrals are attractive since the resulting estimators typically converge at a faster rate than pseudo-random Monte Carlo. However, they can be difficult to set up on arbitrary posterior…

Performing numerical integration when the integrand itself cannot be evaluated point-wise is a challenging task that arises in statistical analysis, notably in Bayesian inference for models with intractable likelihood functions. Markov…

Decision trees are flexible models that are well suited for many statistical regression problems. In a Bayesian framework for regression trees, Markov Chain Monte Carlo (MCMC) search algorithms are required to generate samples of tree…

Monte Carlo (MC) sampling methods are widely applied in Bayesian inference, system simulation and optimization problems. The Markov Chain Monte Carlo (MCMC) algorithms are a well-known class of MC methods which generate a Markov chain with…

Variable selection is a key issue when analyzing high-dimensional data. The explosion of data with large sample sizes and dimensionality brings new challenges to this problem in both inference accuracy and computational complexity. To…

Convergence analysis of Markov chain Monte Carlo methods in high-dimensional statistical applications is increasingly recognized. In this paper, we develop general mixing time bounds for Metropolis-Hastings algorithms on discrete spaces by…

Inverse problems defined on the sphere arise in many fields, including seismology and cosmology where problems are defined on the globe and the cosmic sphere. These are generally high-dimensional and computationally very complex and, as a…

Bayesian formulation of modern day signal processing problems has called for improved Markov chain Monte Carlo (MCMC) sampling algorithms for inference. The need for efficient sampling techniques has become indispensable for high…

Monte Carlo (MC) methods are widely used for Bayesian inference and optimization in statistics, signal processing and machine learning. A well-known class of MC methods are Markov Chain Monte Carlo (MCMC) algorithms. In order to foster…

The Bayesian elastic net regression model is characterized by the regression coefficient prior distribution, the negative log density of which corresponds to the elastic net penalty function. While Markov chain Monte Carlo (MCMC) methods…

Gaussian Process (GP) models are a powerful and flexible tool for non-parametric regression and classification. Computation for GP models is intensive, since computing the posterior density, $\pi$, for covariance function parameters…

A Riemannian geometric framework for Markov chain Monte Carlo (MCMC) is developed where using the Fisher-Rao metric on the manifold of probability density functions (pdfs), informed proposal densities for Metropolis-Hastings (MH) algorithms…

We present a novel Bayesian inference tool that uses a neural network to parameterise efficient Markov Chain Monte-Carlo (MCMC) proposals. The target distribution is first transformed into a diagonal, unit variance Gaussian by a series of…