Consensus Monte Carlo is an algorithm for conducting Monte Carlo based Bayesian inference on large data sets distributed across many worker machines in a data center. The algorithm operates by running a separate Monte Carlo algorithm on each worker machine, which only sees a portion of the full data set. The worker-level posterior samples are then combined to form a Monte Carlo approximation to the full posterior distribution based on the complete data set. We compare several methods of carrying out the combination, including a new method based on approximating worker-level simulations using a mixture of multivariate Gaussian distributions. We find that resampling and kernel density based methods break down after 10 or sometimes fewer dimensions, while the new mixture-based approach works well, but the necessary mixture models take too long to fit.

We discuss Bayesian analysis of multivariate time series with dynamic factor models that exploit time-adaptive sparsity in model parametrizations via the latent threshold approach. One central focus is on the transfer responses of multiple interrelated series to underlying, dynamic latent factor processes. Structured priors on model hyper-parameters are key to the efficacy of dynamic latent thresholding, and MCMC-based computation enables model fitting and analysis. A detailed case study of electroencephalographic (EEG) data from experimental psychiatry highlights the use of latent threshold extensions of time-varying vector autoregressive and factor models. This study explores a class of dynamic transfer response factor models, extending prior Bayesian modeling of multiple EEG series and highlighting the practical utility of the latent thresholding concept in multivariate, non-stationary time series analysis.

In this expository paper, we abstract and describe a simple MCMC scheme for sampling from intractable target densities. The approach has been introduced in Gonçalves, Łatuszyński and Roberts (2017a) in the specific context of jump-diffusions, and is based on the Barker’s algorithm paired with a simple Bernoulli factory type scheme, the so called 2-coin algorithm. In many settings, it is an alternative to standard Metropolis–Hastings pseudo-marginal method for simulating from intractable target densities. Although Barker’s is well known to be slightly less efficient than Metropolis–Hastings, the key advantage of our approach is that it allows to implement the “marginal Barker’s” instead of the extended state space pseudo-marginal Metropolis–Hastings, owing to the special form of the accept/reject probability. We shall illustrate our methodology in the context of Bayesian inference for discretely observed Wright–Fisher family of diffusions.

In any sports competition, strong interest is devoted to the knowledge on the team that will be champion. The result of a match, the chance of a team either qualifying for a specific tournament, or relegating, the best attack and defense are all topics of interest. This paper presents a Bayesian methodology for modeling the number of goals scored by a team based on Zero-Modified Poisson distribution. An important advantage of this distribution is the flexibility in modeling count data without previous knowledge of the sampling characteristic with respect to the frequency of zeros (inflated, standard, deflation). These characteristics are present in the data sets referring to the number of goals scored by different teams. Inference procedures and computational simulation studies are also discussed. The proposed methodology was applied to the 2012–13 La Liga and the results were compared with those of the Poisson model using the De Finetti measure an percentage of correct predictions.

The Multiregression Dynamic Model (MDM) is a multivariate graphical model for a multidimensional time series that allows the estimation of time-varying effective connectivity. An MDM is a state space model where connection weights reflect the contemporaneous interactions between brain regions. Because the marginal likelihood has a closed form, model selection across a large number of potential connectivity networks is easy to perform. With application of the Integer Programming Algorithm, we can quickly find optimal models that satisfy acyclic graph constraints and, due to a factorisation of the marginal likelihood, the search over all possible directed (acyclic or cyclic) graphical structures is even faster. These methods are illustrated using recent resting-state and steady-state task fMRI data.

In extreme value theory, the generalized Pareto distribution (GPD) is a family of continuous distribution used to model the tail of the distribution to values higher than a threshold $u$. Several works have used this method to approximate the tail of distribution. In this paper, we propose two extensions of GPD, including an additional shape parameter, to provide a more flexible distribution for exceedance. Some properties of these approximations are presented. Inference for these extensions were performed under the Bayesian paradigm, and the results showed fit improvement when compared with the standard GPD in applications to environmental and financial data.