6533b7d3fe1ef96bd126138b
RESEARCH PRODUCT
On the stability and ergodicity of adaptive scaling Metropolis algorithms
Matti Viholasubject
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 - Probabilitydescription
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.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2011-12-01 | Stochastic Processes and their Applications |