Search results for " Monte Carlo"
showing 10 items of 400 documents
Adaptive independent sticky MCMC algorithms
2018
In this work, we introduce a novel class of adaptive Monte Carlo methods, called adaptive independent sticky MCMC algorithms, for efficient sampling from a generic target probability density function (pdf). The new class of algorithms employs adaptive non-parametric proposal densities which become closer and closer to the target as the number of iterations increases. The proposal pdf is built using interpolation procedures based on a set of support points which is constructed iteratively based on previously drawn samples. The algorithm's efficiency is ensured by a test that controls the evolution of the set of support points. This extra stage controls the computational cost and the converge…
The Recycling Gibbs sampler for efficient learning
2018
Monte Carlo methods are essential tools for Bayesian inference. Gibbs sampling is a well-known Markov chain Monte Carlo (MCMC) algorithm, extensively used in signal processing, machine learning, and statistics, employed to draw samples from complicated high-dimensional posterior distributions. The key point for the successful application of the Gibbs sampler is the ability to draw efficiently samples from the full-conditional probability density functions. Since in the general case this is not possible, in order to speed up the convergence of the chain, it is required to generate auxiliary samples whose information is eventually disregarded. In this work, we show that these auxiliary sample…
Unbiased Estimators and Multilevel Monte Carlo
2018
Multilevel Monte Carlo (MLMC) and unbiased estimators recently proposed by McLeish (Monte Carlo Methods Appl., 2011) and Rhee and Glynn (Oper. Res., 2015) are closely related. This connection is elaborated by presenting a new general class of unbiased estimators, which admits previous debiasing schemes as special cases. New lower variance estimators are proposed, which are stratified versions of earlier unbiased schemes. Under general conditions, essentially when MLMC admits the canonical square root Monte Carlo error rate, the proposed new schemes are shown to be asymptotically as efficient as MLMC, both in terms of variance and cost. The experiments demonstrate that the variance reduction…
Conditional particle filters with diffuse initial distributions
2020
Conditional particle filters (CPFs) are powerful smoothing algorithms for general nonlinear/non-Gaussian hidden Markov models. However, CPFs can be inefficient or difficult to apply with diffuse initial distributions, which are common in statistical applications. We propose a simple but generally applicable auxiliary variable method, which can be used together with the CPF in order to perform efficient inference with diffuse initial distributions. The method only requires simulatable Markov transitions that are reversible with respect to the initial distribution, which can be improper. We focus in particular on random-walk type transitions which are reversible with respect to a uniform init…
Unbiased Inference for Discretely Observed Hidden Markov Model Diffusions
2021
We develop a Bayesian inference method for diffusions observed discretely and with noise, which is free of discretisation bias. Unlike existing unbiased inference methods, our method does not rely on exact simulation techniques. Instead, our method uses standard time-discretised approximations of diffusions, such as the Euler--Maruyama scheme. Our approach is based on particle marginal Metropolis--Hastings, a particle filter, randomised multilevel Monte Carlo, and importance sampling type correction of approximate Markov chain Monte Carlo. The resulting estimator leads to inference without a bias from the time-discretisation as the number of Markov chain iterations increases. We give conver…
Bayesian inference for the extremal dependence
2016
A simple approach for modeling multivariate extremes is to consider the vector of component-wise maxima and their max-stable distributions. The extremal dependence can be inferred by estimating the angular measure or, alternatively, the Pickands dependence function. We propose a nonparametric Bayesian model that allows, in the bivariate case, the simultaneous estimation of both functional representations through the use of polynomials in the Bernstein form. The constraints required to provide a valid extremal dependence are addressed in a straightforward manner, by placing a prior on the coefficients of the Bernstein polynomials which gives probability one to the set of valid functions. The…
Grapham: Graphical models with adaptive random walk Metropolis algorithms
2008
Recently developed adaptive Markov chain Monte Carlo (MCMC) methods have been applied successfully to many problems in Bayesian statistics. Grapham is a new open source implementation covering several such methods, with emphasis on graphical models for directed acyclic graphs. The implemented algorithms include the seminal Adaptive Metropolis algorithm adjusting the proposal covariance according to the history of the chain and a Metropolis algorithm adjusting the proposal scale based on the observed acceptance probability. Different variants of the algorithms allow one, for example, to use these two algorithms together, employ delayed rejection and adjust several parameters of the algorithm…
Efficient Bayesian generalized linear models with time-varying coefficients : The walker package in R
2020
The R package walker extends standard Bayesian general linear models to the case where the effects of the explanatory variables can vary in time. This allows, for example, to model the effects of interventions such as changes in tax policy which gradually increases their effect over time. The Markov chain Monte Carlo algorithms powering the Bayesian inference are based on Hamiltonian Monte Carlo provided by Stan software, using a state space representation of the model to marginalise over the regression coefficients for efficient low-dimensional sampling.
Simultaneous measurement of the muon neutrino charged-current cross section on oxygen and carbon without pions in the final state at T2K
2020
Authors: K. Abe,56 N. Akhlaq,45 R. Akutsu,57 A. Ali,32 C. Alt,11 C. Andreopoulos,54,34 L. Anthony,21 M. Antonova,19 S. Aoki,31 A. Ariga,2 T. Arihara,59 Y. Asada,69 Y. Ashida,32 E. T. Atkin,21 Y. Awataguchi,59 S. Ban,32 M. Barbi,46 G. J. Barker,66 G. Barr,42 D. Barrow,42 M. Batkiewicz-Kwasniak,15 A. Beloshapkin,26 F. Bench,34 V. Berardi,22 L. Berns,58 S. Bhadra,70 S. Bienstock,53 S. Bolognesi,6 T. Bonus,68 B. Bourguille,18 S. B. Boyd,66 A. Bravar,13 D. Bravo Berguño,1 C. Bronner,56 S. Bron,13 A. Bubak,51 M. Buizza Avanzini ,10 T. Campbell,7 S. Cao,16 S. L. Cartwright,50 M. G. Catanesi,22 A. Cervera,19 D. Cherdack,17 N. Chikuma,55 G. Christodoulou,12 M. Cicerchia,24,† J. Coleman,34 G. Collazu…
New insights into electron spin dynamics in the presence of correlated noise
2011
The changes of the spin depolarization length in zinc-blende semiconductors when an external component of correlated noise is added to a static driving electric field are analyzed for different values of field strength, noise amplitude and correlation time. Electron dynamics is simulated by a Monte Carlo procedure which keeps into account all the possible scattering phenomena of the hot electrons in the medium and includes the evolution of spin polarization. Spin depolarization is studied by examinating the decay of the initial spin polarization of the conduction electrons through the D'yakonov-Perel process, the only relevant relaxation mechanism in III-V crystals. Our results show that, f…