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To sample from a given target distribution, Markov chain Monte Carlo (MCMC) sampling relies on constructing an ergodic Markov chain with the target distribution as its invariant measure. For any MCMC method, an important question is how to…

Probability · Mathematics 2023-08-15 Federica Milinanni , Pierre Nyquist

Markov-chain Monte Carlo sampling has become a standard technique for exploring the posterior distribution of cosmological parameters constrained by observations of CMB anisotropies. Given an infinite amount of time, any MCMC sampler will…

Astrophysics · Physics 2007-05-23 Anze Slosar , Michael Hobson

This paper studies a new and highly efficient Markov chain Monte Carlo (MCMC) methodology to perform Bayesian inference in low-photon imaging problems, with particular attention to situations involving observation noise processes that…

We describe a hierarchical data analysis pipeline for coherently searching for gravitational wave (GW) signals from non-spinning compact binary coalescences (CBCs) in the data of multiple earth-based detectors. It assumes no prior…

Instrumentation and Methods for Astrophysics · Physics 2015-05-27 Sukanta Bose , Thilina Dayanga , Shaon Ghosh , Dipongkar Talukder

We study the Electrical Impedance Tomography Bayesian inverse problem for recovering the conductivity given noisy measurements of the voltage on some boundary surface electrodes. The uncertain conductivity depends linearly on a countable…

Numerical Analysis · Mathematics 2023-06-16 Quang Huy Pham , Viet Ha Hoang

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…

Precessing black hole-neutron star (BH-NS) binaries produce a rich gravitational wave signal, encoding the binary's nature and inspiral kinematics. Using the lalinference\_mcmc Markov-chain Monte Carlo parameter estimation code, we use two…

General Relativity and Quantum Cosmology · Physics 2015-06-19 R. O'Shaughnessy , B. Farr , E. Ochsner , H. S. Cho , V. Raymond , C. Kim , C. H. Lee

State-transition models are essential across epidemiology and ecology, but statistical inference remains challenging owing to high-dimensional latent state spaces, temporal dependence, and intractable likelihood functions. Bayesian…

Computation · Statistics 2026-05-12 Alin Morariu , Jess Bridgen , Chris Jewell

We elaborate the idea behind Markov chain Monte Carlo (MCMC) methods in a mathematically coherent, yet simple and understandable way. To this end, we proof a pivotal convergence theorem for finite Markov chains and a minimal version of the…

Statistics Theory · Mathematics 2019-07-30 Tobias Siems

We propose a new class of learning algorithms that combines variational approximation and Markov chain Monte Carlo (MCMC) simulation. Naive algorithms that use the variational approximation as proposal distribution can perform poorly…

Machine Learning · Computer Science 2013-01-14 Nando de Freitas , Pedro Hojen-Sorensen , Michael I. Jordan , Stuart Russell

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…

Astrophysics of Galaxies · Physics 2019-05-22 Se-Heon Oh , Lister Staveley-Smith , Bi-Qing For

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…

Instrumentation and Methods for Astrophysics · Physics 2023-09-20 James J. Buchanan , Michael D. Schneider , Kerianne Pruett , Robert E. Armstrong

We study the benefits and limits of parallelised Markov chain Monte Carlo (MCMC) sampling in cosmology. MCMC methods are widely used for the estimation of cosmological parameters from a given set of observations and are typically based on…

Cosmology and Nongalactic Astrophysics · Physics 2013-10-03 Joël Akeret , Sebastian Seehars , Adam Amara , Alexandre Refregier , André Csillaghy

Bayesian analysis of LISA data sets based on Markov chain Monte Carlo methods has been shown to be a challenging problem, in part due to the complicated structure of the likelihood function consisting of several isolated local maxima that…

General Relativity and Quantum Cosmology · Physics 2015-05-13 Miquel Trias , Alberto Vecchio , John Veitch

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…

Computational Finance · Quantitative Finance 2010-12-30 Tetsuya Takaishi

Tasks such as record linkage and multi-target tracking, which involve reconstructing the set of objects that underlie some observed data, are particularly challenging for probabilistic inference. Recent work has achieved efficient and…

Artificial Intelligence · Computer Science 2012-07-02 Brian Milch , Stuart Russell

The standard Bayesian technique for searching pulsar timing data for gravitational wave (GW) bursts with memory (BWMs) using Markov Chain Monte Carlo (MCMC) sampling is very computationally expensive to perform. In this paper, we explain…

General Relativity and Quantum Cosmology · Physics 2023-08-02 Jerry Sun , Paul T. Baker , Aaron D. Johnson , Dustin R. Madison , Xavier Siemens

There has been remarkable progress in numerical relativity recently. This has led to the generation of gravitational waveform signals covering what has been traditionally termed the three phases of the coalescence of a compact binary - the…

General Relativity and Quantum Cosmology · Physics 2009-06-10 Benjamin Farr , Stephen Fairhurst , B. S. Sathyaprakash

Exponential random graph models are extremely difficult models to handle from a statistical viewpoint, since their normalising constant, which depends on model parameters, is available only in very trivial cases. We show how inference can…

Applications · Statistics 2010-09-30 Alberto Caimo , Nial Friel

Recent observations support the hypothesis that a large fraction of "short-hard" gamma-ray bursts (SHBs) are associated with compact binary inspiral. Since gravitational-wave (GW) measurements of well-localized inspiraling binaries can…

Cosmology and Nongalactic Astrophysics · Physics 2010-11-23 Samaya Nissanke , Daniel E. Holz , Scott A. Hughes , Neal Dalal , Jonathan L. Sievers