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Bayesian formulations of inverse problems are attractive for their ability to incorporate prior knowledge and update probabilistic models as new data become available. Markov chain Monte Carlo (MCMC) methods sample posterior probability…

Markov Chain Monte Carlo (MCMC) methods have become a cornerstone of many modern scientific analyses by providing a straightforward approach to numerically estimate uncertainties in the parameters of a model using a sequence of random…

Markov Chain Monte Carlo (MCMC) is a well-established family of algorithms primarily used in Bayesian statistics to sample from a target distribution when direct sampling is challenging. Existing work on Bayesian decision trees uses MCMC.…

We review the use of Bayesian Model Averaging in astrophysics. We first introduce the statistical basis of Bayesian Model Selection and Model Averaging. We discuss methods to calculate the model-averaged posteriors, including Markov Chain…

This book aims to provide a graduate-level introduction to advanced topics in Markov chain Monte Carlo (MCMC) algorithms, as applied broadly in the Bayesian computational context. Most, if not all of these topics (stochastic gradient MCMC,…

We present a highly efficient proximal Markov chain Monte Carlo methodology to perform Bayesian computation in imaging problems. Similarly to previous proximal Monte Carlo approaches, the proposed method is derived from an approximation of…

Markov chain Monte Calro methods (MCMC) are commonly used in Bayesian statistics. In the last twenty years, many results have been established for the calculation of the exact convergence rate of MCMC methods. We introduce another rate of…

We apply Markov Chain Monte Carlo (MCMC) to the problem of parametric galaxy modeling, estimating posterior distributions of galaxy properties such as ellipticity and brightness for more than 100,000 images of galaxies taken from DC2, a…

Recently the number of main-sequence and subgiant stars exhibiting solar-like oscillations that are resolved into individual mode frequencies has increased dramatically. While only a few such data sets were available for detailed modeling…

High resolution observations have permitted to resolve the solar prominences/filaments as sets of threads/fibrils. However, the values of the physical parameters of these threads and their structuring remain poorly constrained. We use…

Over the past two decades, helioseismology has revolutionized our understanding of the interior structure and dynamics of the Sun. Asteroseismology will soon place this knowledge into a broader context by providing structural data for…

In this article we consider Bayesian parameter inference associated to partially-observed stochastic processes that start from a set B0 and are stopped or killed at the first hitting time of a known set A. Such processes occur naturally…

We present the first detections by the NASA K2 Mission of oscillations in solar-type stars, using short-cadence data collected during K2 Campaign\,1 (C1). We understand the asteroseismic detection thresholds for C1-like levels of…

The usual procedure for estimating the significance of a peak in a power spectrum is to calculate the probability of obtaining that value or a larger value by chance, on the assumption that the time series contains only noise (e.g. that the…

Owing to the remarkable photometric precision of space observatories like Kepler, stellar and planetary systems beyond our own are now being characterized en masse for the first time. These characterizations are pivotal for endeavors such…

We introduce zeus, a well-tested Python implementation of the Ensemble Slice Sampling (ESS) method for Bayesian parameter inference. ESS is a novel Markov chain Monte Carlo (MCMC) algorithm specifically designed to tackle the computational…

Bayesian Decision Trees (DTs) are generally considered a more advanced and accurate model than a regular Decision Tree (DT) because they can handle complex and uncertain data. Existing work on Bayesian DTs uses Markov Chain Monte Carlo…

Decision tree learning is a popular approach for classification and regression in machine learning and statistics, and Bayesian formulations---which introduce a prior distribution over decision trees, and formulate learning as posterior…

A novel approach of accurately reconstructing storage ring's linear optics from turn-by-turn (TbT) data containing measurement error is introduced. This approach adopts a Bayesian inference based on the Markov Chain Monte-Carlo (MCMC)…

We propose a sequential Monte Carlo (SMC) method to efficiently and accurately compute cut-Bayesian posterior quantities of interest, variations of standard Bayesian approaches constructed primarily to account for model misspecification. We…