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Determining the physical characteristics of a star is an inverse problem consisting in estimating the parameters of models for the stellar structure and evolution, knowing certain observable quantities. We use a Bayesian approach to solve…
In this article we consider Bayesian estimation of static parameters for a class of partially observed McKean-Vlasov diffusion processes with discrete-time observations over a fixed time interval. This problem features several obstacles to…
Bayesian statistics and Markov Chain Monte Carlo (MCMC) algorithms have found their place in the field of Cosmology. They have become important mathematical and numerical tools, especially in parameter estimation and model comparison. In…
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…
Markov Chain Monte Carlo based Bayesian data analysis has now become the method of choice for analyzing and interpreting data in almost all disciplines of science. In astronomy, over the last decade, we have also seen a steady increase in…
Bayesian inverse problems often involve sampling posterior distributions on infinite-dimensional function spaces. Traditional Markov chain Monte Carlo (MCMC) algorithms are characterized by deteriorating mixing times upon mesh-refinement,…
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…
We present a novel algorithm that is based on a Bayesian Markov Chain Monte Carlo (MCMC) technique for performing robust profile analysis of a data cube from either single-dish or interferometric radio telescopes. It fits a set of models…
Advances in digital sensors, digital data storage and communications have resulted in systems being capable of accumulating large collections of data. In the light of dealing with the challenges that massive data present, this work proposes…
Giant molecular clouds (GMCs) are the primary reservoirs of cold, star-forming molecular gas in the Milky Way and similar galaxies, and thus any understanding of star formation must encompass a model for GMC formation, evolution, and…
This paper explores the versatility and depth of Bayesian modeling by presenting a comprehensive range of applications and methods, combining Markov chain Monte Carlo (MCMC) techniques and variational approximations. Covering topics such as…
Chemical models have been developed over the years by astrophysicists to study the pro- cesses at play in the various environments of the interstellar medium (ISM) that define the chemical composition of the gas and the dust. These…
Grain surface chemistry and its treatment in gas-grain chemical models is an area of large uncertainty. Whilst laboratory experiments are making progress, there is still much that is unknown about grain surface chemistry. Further, the…
In many hierarchical inverse problems, not only do we want to estimate high- or infinite-dimensional model parameters in the parameter-to-observable maps, but we also have to estimate hyperparameters that represent critical assumptions in…
Markov Chain Monte Carlo (MCMC) techniques are now widely used for cosmological parameter estimation. Chains are generated to sample the posterior probability distribution obtained following the Bayesian approach. An important issue is how…
We consider the simulation of Bayesian statistical inverse problems governed by large-scale linear and nonlinear partial differential equations (PDEs). Markov chain Monte Carlo (MCMC) algorithms are standard techniques to solve such…
We address the numerical solution of infinite-dimensional inverse problems in the framework of Bayesian inference. In the Part I companion to this paper (arXiv.org:1308.1313), we considered the linearized infinite-dimensional inverse…
Since the middle of the 1940's scientists have used Monte Carlo (MC) simulations to obtain information about physical processes. This has proved a accurate and and reliable method to obtain this information. Through out resent years…
Stellar oscillations can provide a wealth of information about a star, which can be extracted from observed time series of the star's brightness or radial velocity. In this paper we address the question of how to extract as much information…
Monte Carlo techniques have been used to evaluate the statistical and systematic uncertainties in the helium abundances derived from extragalactic H~II regions. The helium abundance is sensitive to several physical parameters associated…