Practitioners of Bayesian statistics have long depended on Markov chain Monte Carlo (MCMC) to obtain samples from intractable posterior distributions. Unfortunately, MCMC algorithms are typically serial, and do not scale to the large datasets typical of modern machine learning. The recently proposed consensus Monte Carlo algorithm removes this limitation by partitioning the data and drawing sam...

Many commonly used models in statistics can be formulated as (Bayesian) hierarchical Gaussian Markov random field models. These are characterised by assuming a (often large) Gaussian Markov random field (GMRF) as the second stage in the hierarchical structure and a few hyperparameters at the third stage. Markov chain Monte Carlo is the common approach for Bayesian inference in such models. The ...

We report the characterization of a transiting hot Jupiter WASP-18b at optical wavelengths measured by exoplanet survey satellite (TESS). analyze publicly available data collected TESS in sector 2. Here, we model systematic noise using Gaussian processes (GPs) and fit it to Markov Chain Monte Carlo (MCMC) method.

The evolution of DNA sequences can be described by discrete state continuous time Markov processes on a phylogenetic tree. We consider neighbor-dependent evolutionary models where the instantaneous rate of substitution at a site depends on the states of the neighboring sites. Neighbor-dependent substitution models are analytically intractable and must be analyzed using either approximate or sim...

This paper describes and illustrates functionality of the spNNGP R package. The package provides a suite spatial regression models for Gaussian non-Gaussian pointreferenced outcomes that are spatially indexed. implements several Markov chain Monte Carlo (MCMC) MCMC-free nearest neighbor process (NNGP) inference about large data. Non-Gaussian modeled using NNGP Pólya-Gamma latent variable. OpenM...

An intriguing new class of piecewise deterministic Markov processes (PDMPs) has recently been proposed as an alternative to chain Monte Carlo (MCMC). We propose a PDMPs termed Gibbs zig-zag samplers, which allow parameters be updated in blocks with sampler applied certain and traditional MCMC-style updates others. demonstrate the flexibility this framework on posterior sampling for logistic mod...

We present a Hidden Markov Model (HMM) for inferring the hidden psychological state (or neural activity) during single trial fMRI activation experiments with blocked task paradigms. Inference is based on Bayesian methodology, using a combination of analytical and a variety of Markov Chain Monte Carlo (MCMC) sampling techniques. The advantage of this method is that detection of short time learni...

Michael Lavine Duke University, Durham, NC, USA. Summary. In recent years there have been several papers giving examples of Markov Chain Monte Carlo (MCMC) algorithms whose invariant measures are improper (have infinite mass) and which therefore are not positive recurrent, yet which have subchains from which valid inference can be derived. These are nonergodic (not having a limiting distributio...