Related papers: Detecting Extra-solar Planets with a Bayesian hybr…
An automatic Bayesian Kepler periodogram has been developed for identifying and characterizing multiple planetary orbits in precision radial velocity data. The periodogram is powered by a parallel tempering MCMC algorithm which is capable…
Radial velocity (RV) planet searches are increasingly finding planets with small velocity amplitudes, with long orbital periods, or in multiple planet systems. Bayesian inference has the potential to improve the interpretation of existing…
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…
A Bayesian multi-planet Kepler periodogram has been developed for the analysis of precision radial velocity data (Gregory 2005b and 2007). The periodogram employs a parallel tempering Markov chain Monte Carlo algorithm. The HD 11964 data…
In the 20+ years of Doppler observations of stars, scientists have uncovered a diverse population of extrasolar multi-planet systems. A common technique for characterizing the orbital elements of these planets is Markov chain Monte Carlo…
Bayesian max-margin models have shown superiority in various practical applications, such as text categorization, collaborative prediction, social network link prediction and crowdsourcing, and they conjoin the flexibility of Bayesian…
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…
Retrieval of orbital parameters of extrasolar planets poses considerable statistical challenges.Due to sparse sampling, measurement errors, parameters degeneracy and modelling limitations, there are no unique values of basic parameters,…
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…
The coalescence of binary neutron stars are one of the main sources of gravitational waves for ground-based gravitational wave detectors. As Bayesian inference for binary neutron stars is computationally expensive, more efficient and faster…
Bayesian inference in the presence of an intractable likelihood function is computationally challenging. When following a Markov chain Monte Carlo (MCMC) approach to approximate the posterior distribution in this context, one typically…
Hamiltonian Monte Carlo (HMC) is a popular Markov chain Monte Carlo (MCMC) algorithm that generates proposals for a Metropolis-Hastings algorithm by simulating the dynamics of a Hamiltonian system. However, HMC is sensitive to large time…
A Bayesian analysis of 47 Ursae Majoris (47 UMa) radial velocity data confirms and refines the properties of two previously reported planets with periods of 1079 and 2325 days and finds evidence for an additional long period planet with a…
The hybrid Monte Carlo (HMC) algorithm is applied for the Bayesian inference of the stochastic volatility (SV) model. We use the HMC algorithm for the Markov chain Monte Carlo updates of volatility variables of the SV model. First we…
Hamiltonian Monte Carlo (HMC) is a powerful Markov chain Monte Carlo (MCMC) method for performing approximate inference in complex probabilistic models of continuous variables. In common with many MCMC methods, however, the standard HMC…
Traditional Markov Chain Monte Carlo methods suffer from low acceptance rate, slow mixing and low efficiency in high dimensions. Hamiltonian Monte Carlo resolves this issue by avoiding the random walk. Hamiltonian Monte Carlo (HMC) is a…
The hybrid Monte Carlo (HMC) algorithm is used for Bayesian analysis of the generalized autoregressive conditional heteroscedasticity (GARCH) model. The HMC algorithm is one of Markov chain Monte Carlo (MCMC) algorithms and it updates all…
Particle Markov Chain Monte Carlo (PMCMC) is a general computational approach to Bayesian inference for general state space models. Our article scales up PMCMC in terms of the number of observations and parameters by generating the…
We consider the so-called Keplerian periodogram, in which the putative detectable signal is modelled by a highly non-linear Keplerian radial velocity function, appearing in Doppler exoplanetary surveys. We demonstrate that for planets on…
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…