Adaptive Rejection Metropolis Sampling within Gibbs Sampling

Gilks, Walter R.; Best, Nicola; Tan, Keith

doi:10.2307/2986138

Cited by 552 publications

(414 citation statements)

References 24 publications

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“…If not, generic univariate simulation methods such as Adaptive Rejection Metropolis Sampling (Gilks et al 1995) can be employed. We now consider a couple of examples.…”

Section: Slice Samplermentioning

confidence: 99%

Slice sampling mixture models

2009

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We propose a more efficient version of the slice sampler for Dirichlet process mixture models described by Walker (2007). This sampler allows the fitting of infinite mixture models with a wide-range of prior specification. To illustrate this flexiblity we develop a new nonparametric prior for mixture models by normalizing an infinite sequence of independent positive random variables and show how the slice sampler can be applied to make inference in this model. Two submodels are studied in detail. The first one assumes that the positive random variables are Gamma distributed and the second assumes that they are inverseGaussian distributed. Both priors have two hyperparameters and we consider their effect on the prior distribution of the number of occupied clusters in a sample. Extensive computational comparisons with alternative "conditional" simulation techniques for mixture models using the standard Dirichlet process prior and our new prior are made. The properties of the new prior are illustrated on a density estimation problem.

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“…If not, generic univariate simulation methods such as Adaptive Rejection Metropolis Sampling (Gilks et al 1995) can be employed. We now consider a couple of examples.…”

Section: Slice Samplermentioning

confidence: 99%

Slice sampling mixture models

2009

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“…, N, independently draw a sample v (7) with sample size m i by a MCMC sample, e.g. via the Gibbs sampler with the adaptive rejection sampling algorithm (Gilks et al, 1995).…”

Section: M-stepmentioning

confidence: 99%

Mixed-Effects Models for Conditional Quantiles with Longitudinal Data

Liu¹,

Bottai²

2009

The International Journal of Biostatistics

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We propose a regression method for the estimation of conditional quantiles of a continuous response variable given a set of covariates when the data are dependent. Along with fixed regression coefficients, we introduce random coefficients which we assume to follow a form of multivariate Laplace distribution. In a simulation study, the proposed quantile mixed-effects regression is shown to model the dependence among longitudinal data correctly and estimate the fixed effects efficiently. It performs similarly to the linear mixed model at the central location when the regression errors are symmetrically distributed, but provides more efficient estimates when the errors are over-dispersed. At the same time, it allows the estimation at different locations of conditional distribution, which conveys a comprehensive understanding of data. We illustrate an application to clinical data where the outcome variable of interest is bounded within a closed interval.

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“…11 In particular, we employed the Adaptive Rejection Metropolis Sampling (ARMS) algorithm of Gilks, Best, and Tan (1995), and Gilks, Neal, Best, and Tan (1997). 12 In this case, we use independent beta priors on ψ 1 (= α + β) and ψ 2 (= β/(α + β)), with mean 3/4 and standard deviation .1443, which are centred around the typical values estimated by previous studies with monthly return data.…”

Section: Simulated Bayesian Inferencementioning

confidence: 99%

Likelihood-Based Estimation of Latent Generalized ARCH Structures

Fiorentini¹,

Sentana²,

Shephard³

2004

Econometrica

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GARCH models are commonly used as latent processes in econometrics, Þnancial economics and macroeconomics. Yet no exact likelihood analysis of these models has been provided so far. In this paper we outline the issues and suggest a Markov chain Monte Carlo algorithm which allows the calculation of a classical estimator via the simulated EM algorithm or a Bayesian solution in O(T ) computational operations, where T denotes the sample size. We assess the performance of our proposed algorithm in the context of both artiÞcial examples and an empirical application to 26 UK sectorial stock returns, and compare it to existing approximate solutions.

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Adaptive Rejection Metropolis Sampling within Gibbs Sampling

Cited by 552 publications

References 24 publications

Slice sampling mixture models

Slice sampling mixture models

Mixed-Effects Models for Conditional Quantiles with Longitudinal Data

Likelihood-Based Estimation of Latent Generalized ARCH Structures

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