Article

# Adaptive rejection Metropolis sampling using Lagrange interpolation polynomials of degree 2

Department of Statistics, University of Auckland, Private Bag 92019, Auckland, New Zealand; Department of Epidemiology and Biostatistics, University of South Carolina, Columbia, SC 29208, United States; Department of Mathematics and Statistics, University of Montreal, Montreal, Quebec, Canada H3C 3J7

Computational Statistics & Data Analysis (Impact Factor: 1.15). 03/2008; DOI: 10.1016/j.csda.2008.01.005 Source: DBLP

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**ABSTRACT:**To obtain the probability density functions and the cumulative distribution functions of static responses of stochastic structures, a hybrid stochastic method named as the transformed perturbation stochastic finite element method (TPSFEM) is proposed. In TPSFEM, the static responses of stochastic structures are approximated as the linear functions of random variables by using the first order perturbation technique. According to the approximated linear relationships between static responses and random variables, the probability density functions of static responses are obtained by the change-of-variable technique. The cumulative distribution functions of static responses are calculated by the numerical integration method. The numerical examples on a thin plate, a six-bar truss structure, a Mindlin plate and a shell structure verify the effectiveness and accuracy of the proposed method. Hence, the proposed method can be considered as an alternative engineering method for the static response analysis of stochastic structures.Finite Elements in Analysis and Design 02/2014; 79:9–21. · 1.60 Impact Factor - [Show abstract] [Hide abstract]

**ABSTRACT:**We introduce a new class of adaptive Metropolis algorithms called adaptive sticky algorithms for efficient general-purpose simulation from a target probability distribution. The transition of the Metropolis chain is based on a multiple-try scheme and the different proposals are generated by adaptive nonparametric distributions. Our adaptation strategy uses the interpolation of support points from the past history of the chain as in the adaptive rejection Metropolis. The algorithm efficiency is strengthened by a step that controls the evolution of the set of support points. This extra stage improves the computational cost and accelerates the convergence of the proposal distribution to the target. Despite the algorithms are presented for univariate target distributions, we show that they can be easily extended to the multivariate context by a Gibbs sampling strategy. We show the ergodicity of the proposed algorithms and illustrate their efficiency and effectiveness through some simulated examples involving target distributions with complex structures.SSRN Electronic Journal 08/2013; -
##### Conference Paper: INDEPENDENT DOUBLY ADAPTIVE REJECTION METROPOLIS SAMPLING

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**ABSTRACT:**Adaptive Rejection Metropolis Sampling (ARMS) is a well-known MCMC scheme for generating samples from one-dimensional target distributions. ARMS is widely used within Gibbs sampling, where automatic and fast samplers are of-ten needed to draw from univariate full-conditional densities. In this work, we propose an alternative adaptive algorithm (IA 2 RMS) that overcomes the main drawback of ARMS (an uncomplete adaptation of the proposal in some cases), speed-ing up the convergence of the chain to the target. Numerical results show that IA 2 RMS outperforms the standard ARMS, providing a correlation among samples close to zero. Index Terms— Monte Carlo methods, Gibbs sampler, adaptive rejection Metropolis sampling (ARMS).IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP); 01/2014

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