Search results for "Metropolis–Hastings algorithm"

showing 4 items of 14 documents

Componentwise adaptation for high dimensional MCMC

2005

We introduce a new adaptive MCMC algorithm, based on the traditional single component Metropolis-Hastings algorithm and on our earlier adaptive Metropolis algorithm (AM). In the new algorithm the adaption is performed component by component. The chain is no more Markovian, but it remains ergodic. The algorithm is demonstrated to work well in varying test cases up to 1000 dimensions.

Statistics and ProbabilityMathematical optimization010504 meteorology & atmospheric sciencesMonte Carlo methodMarkov processMarkov chain Monte Carlo01 natural sciencesStatistics::Computation010104 statistics & probabilityComputational Mathematicssymbols.namesakeMetropolis–Hastings algorithmTest caseChain (algebraic topology)Component (UML)symbolsStatistics::MethodologyErgodic theory0101 mathematicsStatistics Probability and Uncertainty0105 earth and related environmental sciencesMathematicsComputational Statistics
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Adaptive Metropolis algorithm using variational Bayesian adaptive Kalman filter

2013

Markov chain Monte Carlo (MCMC) methods are powerful computational tools for analysis of complex statistical problems. However, their computational efficiency is highly dependent on the chosen proposal distribution, which is generally difficult to find. One way to solve this problem is to use adaptive MCMC algorithms which automatically tune the statistics of a proposal distribution during the MCMC run. A new adaptive MCMC algorithm, called the variational Bayesian adaptive Metropolis (VBAM) algorithm, is developed. The VBAM algorithm updates the proposal covariance matrix using the variational Bayesian adaptive Kalman filter (VB-AKF). A strong law of large numbers for the VBAM algorithm is…

Statistics and ProbabilityMathematical optimizationCovariance matrixApplied MathematicsBayesian probabilityRejection samplingMathematics - Statistics TheoryMarkov chain Monte CarloStatistics Theory (math.ST)Kalman filterStatistics::ComputationComputational Mathematicssymbols.namesakeComputingMethodologies_PATTERNRECOGNITIONMetropolis–Hastings algorithmComputational Theory and MathematicsConvergence (routing)FOS: MathematicsKernel adaptive filtersymbolsMathematicsComputational Statistics & Data Analysis
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On the stability and ergodicity of adaptive scaling Metropolis algorithms

2011

The stability and ergodicity properties of two adaptive random walk Metropolis algorithms are considered. The both algorithms adjust the scaling of the proposal distribution continuously based on the observed acceptance probability. Unlike the previously proposed forms of the algorithms, the adapted scaling parameter is not constrained within a predefined compact interval. The first algorithm is based on scale adaptation only, while the second one incorporates also covariance adaptation. A strong law of large numbers is shown to hold assuming that the target density is smooth enough and has either compact support or super-exponentially decaying tails.

Statistics and ProbabilityStochastic approximationMathematics - Statistics TheoryStatistics Theory (math.ST)Law of large numbersMultiple-try Metropolis01 natural sciencesStability (probability)010104 statistics & probabilityModelling and Simulation65C40 60J27 93E15 93E35Adaptive Markov chain Monte CarloFOS: Mathematics0101 mathematicsScalingMetropolis algorithmMathematicsta112Applied Mathematics010102 general mathematicsRejection samplingErgodicityProbability (math.PR)ta111CovarianceRandom walkMetropolis–Hastings algorithmModeling and SimulationAlgorithmStabilityMathematics - ProbabilityStochastic Processes and their Applications
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Multi-label Classification Using Stacked Hierarchical Dirichlet Processes with Reduced Sampling Complexity

2018

Nonparametric topic models based on hierarchical Dirichlet processes (HDPs) allow for the number of topics to be automatically discovered from the data. The computational complexity of standard Gibbs sampling techniques for model training is linear in the number of topics. Recently, it was reduced to be linear in the number of topics per word using a technique called alias sampling combined with Metropolis Hastings (MH) sampling. We propose a different proposal distribution for the MH step based on the observation that distributions on the upper hierarchy level change slower than the document-specific distributions at the lower level. This reduces the sampling complexity, making it linear i…

Topic modelComputational complexity theoryComputer science02 engineering and technologyLatent Dirichlet allocationDirichlet distributionsymbols.namesakeArtificial Intelligence020204 information systems0202 electrical engineering electronic engineering information engineeringMathematicsMulti-label classificationbusiness.industrySampling (statistics)Pattern recognitionHuman-Computer InteractionDirichlet processMetropolis–Hastings algorithmHardware and ArchitectureTest setsymbols020201 artificial intelligence & image processingArtificial intelligencebusinessAlgorithmSoftwareInformation SystemsGibbs sampling2017 IEEE International Conference on Big Knowledge (ICBK)
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