Understanding the Metropolis-Hastings Algorithm

Chib, Siddhartha; Greenberg, Edward

doi:10.1080/00031305.1995.10476177

Cited by 2,363 publications

(766 citation statements)

References 18 publications

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“…(28) are nonstandard we use a MetropolisHasting sampler (see Chib and Greenberg (1995)). Candidate draws of h (t,τ ) are made with a l t -variate Student-t distribution with mean vector m, covariance matrix, S, and ξ degrees of freedom where m is the argument maximizing π(…”

Section: Latent Volatility Samplermentioning

confidence: 99%

Estimating a Semiparametric Asymmetric Stochastic Volatility Model with a Dirichlet Process Mixture

Jensen

Maheu

2012

SSRN Journal

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In this paper, we extend the parametric, asymmetric, stochastic volatility model (ASV), where returns are correlated with volatility, by flexibly modeling the bivariate distribution of the return and volatility innovations nonparametrically. Its novelty is in modeling the joint, conditional, return-volatility distribution with an infinite mixture of bivariate Normal distributions with mean zero vectors, but having unknown mixture weights and covariance matrices. This semiparametric ASV model nests stochastic volatility models whose innovations are distributed as either Normal or Student-t distributions, plus the response in volatility to unexpected return shocks is more general than the fixed asymmetric response with the ASV model. The unknown mixture parameters are modeled with a Dirichlet process prior. This prior ensures a parsimonious, finite, posterior mixture that best represents the distribution of the innovations and a straightforward sampler of the conditional posteriors. We develop a Bayesian Markov chain Monte Carlo sampler to fully characterize the parametric and distributional uncertainty. Nested model comparisons and out-ofsample predictions with the cumulative marginal-likelihoods, and one-day-ahead, predictive logBayes factors between the semiparametric and parametric versions of the ASV model shows the semiparametric model projecting more accurate empirical market returns. A major reason is how volatility responds to an unexpected market movement. When the market is tranquil, expected volatility reacts to a negative (positive) price shock by rising (initially declining, but then rising when the positive shock is large). However, when the market is volatile, the degree of asymmetry and the size of the response in expected volatility is muted. In other words, when times are good, no news is good news, but when times are bad, neither good nor bad news matters with regards to volatility. JEL classification: C11, C14, C53, C58

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Section: Latent Volatility Samplermentioning

confidence: 99%

Estimating a Semiparametric Asymmetric Stochastic Volatility Model with a Dirichlet Process Mixture

Jensen

Maheu

2012

SSRN Journal

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“…Instead, we implemented a MCMC algorithm for our model within the C language. A Metropolis-Hasting algorithm [15] is used. The details of the Metropolis-Hasting algorithm used in this study are given in the Appendix.…”

Section: Joint Posterior Distributionmentioning

confidence: 99%

“…It generates correlated draws from the joint posterior distribution of model parameters. For our MRDD data analysis, a Metropolis-Hastings algorithm [15,29] was employed to sample for all the parameters. This Metropolis-Hasting algorithm can draw samples from any probability distribution and does not involve knowledge of the conditional posteriors to update the parameters.…”

Section: Appendixmentioning

confidence: 99%

Bayesian spatial modeling of disease risk in relation to multivariate environmental risk fields

Kim

Lawson

McDermott

et al. 2009

Statistics in Medicine

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The relationship between exposure to environmental chemicals during pregnancy and early childhood development is an important issue which has a spatial risk component. In this context, we have examined mental retardation and developmental delay (MRDD) outcome measures for children in a Medicaid population in South Carolina and sampled measures of soil chemistry (e.g. As, Hg, etc.) on a network of sites which are misaligned to the outcome residential addresses during pregnancy. The true chemical concentration at the residential addresses is not observed directly and must be interpolated from soil samples. In this study, we have developed a Bayesian joint model which interpolates soil chemical fields and estimates the associated MRDD risk simultaneously. Having multiple spatial fields to interpolate, we have considered a low-rank Kriging method for the interpolation which requires less computation than Bayesian Kriging. We performed a sensitivity analysis for a bivariate smoothing, changing the number of knots and the smoothing parameter. These analyses show that a low-rank Kriging method can be used as an alternative to a full-rank Kriging, reducing computational burden. However, the number of knots for the low-rank Kriging model need to be selected with caution as a bivariate surface estimation can be sensitive to the choice of the number of knots.

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“…In this study we use the random walk approach (Chib & Greenberg, 1995) to sample candidates, i.e. a uniform proposal density centred on the current value d i .…”

Section: (Ii) a Bayesian Hierarchical Modelmentioning

confidence: 99%

“…a uniform proposal density centred on the current value d i . The length of this uniform is determined empirically and should result in average acceptance rates between 0n20 and 0n50 (Chib & Greenberg, 1995) to ensure proper mixing through the parameter space. Note that for a discrete prior on d, i.e.…”

Section: (Ii) a Bayesian Hierarchical Modelmentioning

confidence: 99%

Markov chain Monte Carlo for mapping a quantitative trait locus in outbred populations

Bink

Janss²,

Quaas

2000

Genet. Res.

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SummaryA Bayesian approach is presented for mapping a quantitative trait locus (QTL) using the ' Fernando and Grossman ' multivariate Normal approximation to QTL inheritance. For this model, a Bayesian implementation that includes QTL position is problematic because standard Markov chain Monte Carlo (MCMC) algorithms do not mix, i.e. the QTL position gets stuck in one marker interval. This is because of the dependence of the covariance structure for the QTL effects on the adjacent markers and may be typical of the ' Fernando and Grossman ' model. A relatively new MCMC technique, simulated tempering, allows mixing and so makes possible inferences about QTL position based on marginal posterior probabilities. The model was implemented for estimating variance ratios and QTL position using a continuous grid of allowed positions and was applied to simulated data of a standard granddaughter design. The results showed a smooth mixing of QTL position after implementation of the simulated tempering sampler. In this implementation, map distance between QTL and its flanking markers was artificially stretched to reduce the dependence of markers and covariance. The method generalizes easily to more complicated applications and can ultimately contribute to QTL mapping in complex, heterogeneous, human, animal or plant populations.

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Understanding the Metropolis-Hastings Algorithm

Cited by 2,363 publications

References 18 publications

Estimating a Semiparametric Asymmetric Stochastic Volatility Model with a Dirichlet Process Mixture

Estimating a Semiparametric Asymmetric Stochastic Volatility Model with a Dirichlet Process Mixture

Bayesian spatial modeling of disease risk in relation to multivariate environmental risk fields

Markov chain Monte Carlo for mapping a quantitative trait locus in outbred populations

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