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For large model spaces, the potential entrapment of Markov chain Monte Carlo (MCMC) based methods with spike-and-slab priors poses significant challenges in posterior computation in regression models. On the other hand, maximum a posteriori…
We consider parallel asynchronous Markov Chain Monte Carlo (MCMC) sampling for problems where we can leverage (stochastic) gradients to define continuous dynamics which explore the target distribution. We outline a solution strategy for…
We are concerned with a novel Bayesian statistical framework for the characterization of natural subsurface formations, a very challenging task. Because of the large dimension of the stochastic space of the prior distribution in the…
Markov Chain Monte Carlo (MCMC) methods are a powerful tool for computation with complex probability distributions. However the performance of such methods is critically dependant on properly tuned parameters, most of which are difficult if…
Using Markov chain Monte Carlo to sample from posterior distributions was the key innovation which made Bayesian data analysis practical. Notoriously, however, MCMC is hard to tune, hard to diagnose, and hard to parallelize. This…
Motivated by the physics of strings and branes, we introduce a general suite of Markov chain Monte Carlo (MCMC) "suburban samplers" (i.e., spread out Metropolis). The suburban algorithm involves an ensemble of statistical agents connected…
This paper proposes a new randomized strategy for adaptive MCMC using Bayesian optimization. This approach applies to non-differentiable objective functions and trades off exploration and exploitation to reduce the number of potentially…
Motivated by a challenging problem in financial trading we are presented with a mixture of regressions with variable selection problem. In this regard, one is faced with data which possess outliers, skewness and, simultaneously, due to the…
Random sampling of graph partitions under constraints has become a popular tool for evaluating legislative redistricting plans. Analysts detect partisan gerrymandering by comparing a proposed redistricting plan with an ensemble of sampled…
This paper develops a matrix-variate adaptive Markov chain Monte Carlo (MCMC) methodology for Bayesian Cointegrated Vector Auto Regressions (CVAR). We replace the popular approach to sampling Bayesian CVAR models, involving griddy Gibbs,…
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…
Markov chain Monte Carlo (MCMC) provides a feasible method for inferring Hidden Markov models, however, it is often computationally prohibitive, especially constrained by the curse of dimensionality, as the Monte Carlo sampler traverses…
The widespread use of Markov Chain Monte Carlo (MCMC) methods for high-dimensional applications has motivated research into the scalability of these algorithms with respect to the dimension of the problem. Despite this, numerous problems…
Sparsity has become a key concept for solving of high-dimensional inverse problems using variational regularization techniques. Recently, using similar sparsity-constraints in the Bayesian framework for inverse problems by encoding them in…
Decision trees have found widespread application within the machine learning community due to their flexibility and interpretability. This paper is directed towards learning decision trees from data using a Bayesian approach, which is…
In this paper, we present a method for computing the marginal likelihood, also known as the model likelihood or Bayesian evidence, from Markov Chain Monte Carlo (MCMC), or other sampled posterior distributions. In order to do this, one…
Multidimensional scaling (MDS) is widely used to reconstruct a low-dimensional representation of high-dimensional data while preserving pairwise distances. However, Bayesian MDS approaches based on Markov chain Monte Carlo (MCMC) face…
Traditional MCMC algorithms are computationally intensive and do not scale well to large data. In particular, the Metropolis-Hastings (MH) algorithm requires passing over the entire dataset to evaluate the likelihood ratio in each…
Efficient sampling of many-dimensional and multimodal density functions is a task of great interest in many research fields. We describe an algorithm that allows parallelizing inherently serial Markov chain Monte Carlo (MCMC) sampling by…
When working with multimodal Bayesian posterior distributions, Markov chain Monte Carlo (MCMC) algorithms have difficulty moving between modes, and default variational or mode-based approximate inferences will understate posterior…