Related papers: Individual adaptation: an adaptive MCMC scheme for…

Factors models are routinely used to analyze high-dimensional data in both single-study and multi-study settings. Bayesian inference for such models relies on Markov Chain Monte Carlo (MCMC) methods which scale poorly as the number of…

Elliptical slice sampling is a widely used gradient-free Markov chain Monte Carlo algorithm that is tuning-free and capable of adapting to local characteristics of the target distribution. However, its primary limitation is that sampling…

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…

Posterior sampling by Monte Carlo methods provides a more comprehensive solution approach to inverse problems than computing point estimates such as the maximum posterior using optimization methods, at the expense of usually requiring many…

Inverse problems involving partial differential equations (PDEs) are widely used in science and engineering. Although such problems are generally ill-posed, different regularisation approaches have been developed to ameliorate this problem.…

We consider the recently introduced Transformation-based Markov Chain Monte Carlo (TMCMC) (Dutta and Bhattacharya (2014)), a methodology that is designed to update all the parameters simultaneously using some simple deterministic…

Markov Chain Monte Carlo approach is frequently used within Bayesian framework to sample the target posterior distribution. Its efficiency strongly depends on the proposal used to build the chain. The best jump proposal is the one that…

Adaptive Monte Carlo methods are very efficient techniques designed to tune simulation estimators on-line. In this work, we present an alternative to stochastic approximation to tune the optimal change of measure in the context of…

The 21st century has seen an enormous growth in the development and use of approximate Bayesian methods. Such methods produce computational solutions to certain intractable statistical problems that challenge exact methods like Markov chain…

In the field of decision trees, most previous studies have difficulty ensuring the statistical optimality of a prediction of new data and suffer from overfitting because trees are usually used only to represent prediction functions to be…

In this paper, the minimization of computational cost on evaluating multi-dimensional integrals is explored. More specifically, a method based on an adaptive scheme for error variance selection in Monte Carlo integration (MCI) is presented.…

We investigate lower bounds on the subgeometric convergence of adaptive Markov chain Monte Carlo under any adaptation strategy. In particular, we prove general lower bounds in total variation and on the weak convergence rate under general…

High-dimensional Bayesian variable selection problems are often solved using computationally expensive Markov Chain Montle Carlo (MCMC) techniques. Recently, a Bayesian variable selection technique was developed for continuous data using…

We demonstrate the use of a variational method to determine a quantitative lower bound on the rate of convergence of Markov Chain Monte Carlo (MCMC) algorithms as a function of the target density and proposal density. The bound relies on…

Understanding how stochastic gene expression is regulated in biological systems using snapshots of single-cell transcripts requires state-of-the-art methods of computational analysis and statistical inference. A Bayesian approach to…

Bayesian Neural Networks (BNNs) provide a promising framework for modeling predictive uncertainty and enhancing out-of-distribution robustness (OOD) by estimating the posterior distribution of network parameters. Stochastic Gradient Markov…

In many practices, scientists are particularly interested in detecting which of the predictors are truly associated with a multivariate response. It is more accurate to model multiple responses as one vector rather than separating each…

We propose a very fast approximate Markov Chain Monte Carlo (MCMC) sampling framework that is applicable to a large class of sparse Bayesian inference problems, where the computational cost per iteration in several models is of order…

Developing an efficient computational scheme for high-dimensional Bayesian variable selection in generalised linear models and survival models has always been a challenging problem due to the absence of closed-form solutions for the…

Bayesian analyses combine information represented by different terms in a joint Bayesian model. When one or more of the terms is misspecified, it can be helpful to restrict the use of information from suspect model components to modify…