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Bayesian phylogenetics typically estimates a posterior distribution, or aspects thereof, using Markov chain Monte Carlo methods. These methods integrate over tree space by applying local rearrangements to move a tree through its space as a…

Many optimization problems in science and engineering are highly nonlinear, and thus require sophisticated optimization techniques to solve. Traditional techniques such as gradient-based algorithms are mostly local search methods, and often…

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…

Bayesian inference is now a leading technique for reconstructing phylogenetic trees from aligned sequence data. In this short note, we formally show that the maximum posterior tree topology provides a statistically consistent estimate of a…

In machine learning and statistics, probabilistic inference involving multimodal distributions is quite difficult. This is especially true in high dimensional problems, where most existing algorithms cannot easily move from one mode to…

Bayesian averaging over classification models allows the uncertainty of classification outcomes to be evaluated, which is of crucial importance for making reliable decisions in applications such as financial in which risks have to be…

Markov chain Monte Carlo (MCMC) methods have not been broadly adopted in Bayesian neural networks (BNNs). This paper initially reviews the main challenges in sampling from the parameter posterior of a neural network via MCMC. Such…

In the context of Bayesian inversion for scientific and engineering modeling, Markov chain Monte Carlo sampling strategies are the benchmark due to their flexibility and robustness in dealing with arbitrary posterior probability density…

Employing Bayesian inference to calibrate constitutive model parameters has grown substantially in recent years. Among the available techniques, Markov Chain Monte Carlo (MCMC) sampling remains one of the most widely used approaches for…

Approximate Bayesian computation (ABC) methods provide an elaborate approach to Bayesian inference on complex models, including model choice. Both theoretical arguments and simulation experiments indicate, however, that model posterior…

In this paper we present an extension of population-based Markov chain Monte Carlo (MCMC) to the trans-dimensional case. One of the main challenges in MCMC-based inference is that of simulating from high and trans-dimensional target…

There is increasing interest to develop Bayesian inferential algorithms for point process models with intractable likelihoods. A purpose of this paper is to illustrate the utility of using simulation based strategies, including Approximate…

In large domains, Monte-Carlo tree search (MCTS) is required to estimate the values of the states as efficiently and accurately as possible. However, the standard update rule in backpropagation assumes a stationary distribution for the…

Leaving posterior sensitivity concerns aside, non-identifiability of the parameters does not raise a difficulty for Bayesian inference as far as the posterior is proper, but multi-modality or flat regions of the posterior induced by the…

Determining subgroups that respond especially well (or poorly) to specific interventions (medical or policy) requires new supervised learning methods tailored specifically for causal inference. Bayesian Causal Forest (BCF) is a recent…

Novel Markov Chain Monte Carlo (MCMC) methods have enabled the generation of large ensembles of redistricting plans through graph partitioning. However, existing algorithms such as Reversible Recombination (RevReCom) and Metropolized Forest…

We study weighted particle systems in which new generations are resampled from current particles with probabilities proportional to their weights. This covers a broad class of sequential Monte Carlo (SMC) methods, widely-used in applied…

Approximate Bayesian computation (ABC) is a well-established family of Monte Carlo methods for performing approximate Bayesian inference in the case where an ``implicit'' model is used for the data: when the data model can be simulated, but…

In geostatistics, Gaussian random fields are often used to model heterogeneities of soil or subsurface parameters. To give spatial approximations of these random fields, they are discretized. Then, different techniques of geostatistical…

Bayesian methods hold significant promise for improving the uncertainty quantification ability and robustness of deep neural network models. Recent research has seen the investigation of a number of approximate Bayesian inference methods…