Related papers: Bayesian Model Selection and Extrasolar Planet Det…

Estimating the marginal likelihoods is an essential feature of model selection in the Bayesian context. It is especially crucial to have good estimates when assessing the number of planets orbiting stars when the models explain the noisy…

Stellar radial velocity (RV) measurements have proven to be a very successful method for detecting extrasolar planets. Analysing RV data to determine the parameters of the extrasolar planets is a significant statistical challenge owing to…

In this paper, we present a method for computing the marginal likelihood, also known as the model likelihood or Bayesian evidence, from Markov Chain Monte Carlo (MCMC), or other sampled posterior distributions. In order to do this, one…

A Bayesian re-analysis of published radial velocity data sets is providing evidence for additional planetary candidates. The nonlinear model fitting is accomplished with a new hybrid Markov chain Monte Carlo (HMCMC) algorithm which…

Most applications of Bayesian Inference for parameter estimation and model selection in astrophysics involve the use of Monte Carlo techniques such as Markov Chain Monte Carlo (MCMC) and nested sampling. However, these techniques are time…

We obtain full information on the orbital parameters by combining radial velocity and astrometric measurements by means of Bayesian inference. We sample the parameter probability densities of orbital model parameters with a Markov chain…

Precise radial velocity measurements have led to the discovery of ~170 extrasolar planetary systems. Understanding the uncertainties in the orbital solutions will become increasingly important as the discovery space for extrasolar planets…

Bayesian inference under a set of priors, called robust Bayesian analysis, allows for estimation of parameters within a model and quantification of epistemic uncertainty in quantities of interest by bounded (or imprecise) probability.…

In this work, we propose a new flow-matching Markov chain Monte Carlo (FM-MCMC) algorithm for estimating the orbital parameters of exoplanetary systems, especially for those only one exoplanet is involved. Compared to traditional methods…

In many domains, we are interested in analyzing the structure of the underlying distribution, e.g., whether one variable is a direct parent of the other. Bayesian model-selection attempts to find the MAP model and use its structure to…

Recent advances in Markov chain Monte Carlo (MCMC) extend the scope of Bayesian inference to models for which the likelihood function is intractable. Although these developments allow us to estimate model parameters, other basic problems…

Computing the marginal likelihood or evidence is one of the core challenges in Bayesian analysis. While there are many established methods for estimating this quantity, they predominantly rely on using a large number of posterior samples…

It is common practice to use Laplace approximations to compute marginal likelihoods in Bayesian versions of generalised linear models (GLM). Marginal likelihoods combined with model priors are then used in different search algorithms to…

Inferring the number of planets $N$ in an exoplanetary system from radial velocity (RV) data is a challenging task. Recently, it has become clear that RV data can contain periodic signals due to stellar activity, which can be difficult to…

Markov Chain Monte Carlo (MCMC) proves to be powerful for Bayesian inference and in particular for exoplanet radial velocity fitting because MCMC provides more statistical information and makes better use of data than common approaches like…

Bayesian model selection enables comparison and ranking of conceptual subsurface models described by spatial prior models, according to the support provided by available geophysical data. Deep generative neural networks can efficiently…

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…

Bayesian inference for Markov processes has become increasingly relevant in recent years. Problems of this type often have intractable likelihoods and prior knowledge about model rate parameters is often poor. Markov Chain Monte Carlo…

We discuss a Bayesian approach to the analysis of radial velocities in planet searches. We use a combination of exact and approximate analytic and numerical techniques to efficiently evaluate chi-squared for multiple values of orbital…

Bayesian analysis often concerns an evaluation of models with different dimensionality as is necessary in, for example, model selection or mixture models. To facilitate this evaluation, transdimensional Markov chain Monte Carlo (MCMC)…