6533b827fe1ef96bd128715b
RESEARCH PRODUCT
Adaptive independent sticky MCMC algorithms
Roberto CasarinLuca MartinoFabrizio LeisenDavid Luengosubject
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)description
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 convergence of the proposal density to the target. Each part of the novel family of algorithms is discussed and several examples are provided. Although the novel algorithms are presented for univariate target densities, we show that they can be easily extended to the multivariate context within a Gibbs-type sampler. The ergodicity is ensured and discussed. Exhaustive numerical examples illustrate the efficiency of sticky schemes, both as a stand-alone methods to sample from complicated one-dimensional pdfs and within Gibbs in order to draw from multi-dimensional target distributions.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2018-01-11 | EURASIP Journal on Advances in Signal Processing |