Search results for "Metropolis-within-Gibbs"

showing 2 items of 2 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…

FOS: Computer and information sciencesMathematical optimizationAdaptive Markov chain Monte Carlo (MCMC)Monte Carlo methodBayesian inferenceHASettore SECS-P/05 - Econometrialcsh:TK7800-8360Machine Learning (stat.ML)02 engineering and technologyBayesian inference01 natural sciencesStatistics - Computationlcsh:Telecommunication010104 statistics & probabilitysymbols.namesakeAdaptive Markov chain Monte Carlo (MCMC); Adaptive rejection Metropolis sampling (ARMS); Bayesian inference; Gibbs sampling; Hit and run algorithm; Metropolis-within-Gibbs; Monte Carlo methods; Signal Processing; Hardware and Architecture; Electrical and Electronic EngineeringGibbs samplingStatistics - Machine Learninglcsh:TK5101-67200202 electrical engineering electronic engineering information engineeringComputational statisticsMetropolis-within-GibbsHit and run algorithm0101 mathematicsElectrical and Electronic EngineeringGaussian processComputation (stat.CO)MathematicsSignal processinglcsh:Electronics020206 networking & telecommunicationsMarkov chain Monte CarloMonte Carlo methodsHardware and ArchitectureSignal ProcessingSettore SECS-S/03 - Statistica EconomicasymbolsSettore SECS-S/01 - StatisticaStatistical signal processingGibbs samplingAdaptive rejection Metropolis sampling (ARMS)EURASIP Journal on Advances in Signal Processing
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Uniform ergodicity of the iterated conditional SMC and geometric ergodicity of particle Gibbs samplers

2018

We establish quantitative bounds for rates of convergence and asymptotic variances for iterated conditional sequential Monte Carlo (i-cSMC) Markov chains and associated particle Gibbs samplers. Our main findings are that the essential boundedness of potential functions associated with the i-cSMC algorithm provide necessary and sufficient conditions for the uniform ergodicity of the i-cSMC Markov chain, as well as quantitative bounds on its (uniformly geometric) rate of convergence. Furthermore, we show that the i-cSMC Markov chain cannot even be geometrically ergodic if this essential boundedness does not hold in many applications of interest. Our sufficiency and quantitative bounds rely on…

Statistics and ProbabilityMetropoliswithin-Gibbsgeometric ergodicity01 natural sciencesCombinatorics010104 statistics & probabilitysymbols.namesakeFOS: MathematicsMetropolis-within-GibbsApplied mathematicsErgodic theory0101 mathematicsGibbs measureQAMathematics65C40 (Primary) 60J05 65C05 (Secondary)Particle GibbsMarkov chainGeometric ergodicity010102 general mathematicsErgodicityuniform ergodicityProbability (math.PR)iterated conditional sequential Monte CarloMarkov chain Monte CarloIterated conditional sequential Monte CarloRate of convergencesymbolsUniform ergodicityparticle GibbsParticle filterMathematics - ProbabilityGibbs sampling
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