Adaptive Markov Chain Monte Carlo through Regeneration

Gilks, Walter R.; Roberts, Gareth O.; Sahu, Sujit K.

doi:10.1080/01621459.1998.10473766

Cited by 207 publications

(141 citation statements)

References 18 publications

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“…A variety of related algorithms collectively known as adaptive MCMC were developed for this reason (Gilks, Roberts, & George, 1994;Gelfand & Sahu, 1994;Gilks, Roberts, & Sahu, 1998). These algorithms work by using samples from the chain in order to adjust the proposal distribution to be more efficient.…”

Section: Cautions and Recommendationsmentioning

confidence: 99%

Uncovering mental representations with Markov chain Monte Carlo

Sanborn

Griffiths

Shiffrin

2010

Cognitive Psychology

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A note on versions:The version presented here may differ from the published version or, version of record, if you wish to cite this item you are advised to consult the publisher's version. Please see the 'permanent WRAP URL' above for details on accessing the published version and note that access may require a subscription. Richard M. Shiffrin Indiana University, Bloomington Abstract A key challenge for cognitive psychology is the investigation of mental representations, such as object categories, subjective probabilities, choice utilities, and memory traces. In many cases, these representations can be expressed as a non-negative function defined over a set of objects. We present a behavioral method for estimating these functions. Our approach uses people as components of a Markov chain Monte Carlo (MCMC) algorithm, a sophisticated sampling method originally developed in statistical physics. Experiments 1 and 2 verified the MCMC method by training participants on various category structures and then recovering those structures. Experiment 3 demonstrated that the MCMC method can be used estimate the structures of the real-world animal shape categories of giraffes, horses, dogs, and cats. Experiment 4 combined the MCMC method with multidimensional scaling to demonstrate how different accounts of the structure of categories, such as prototype and exemplar models, can be tested, producing samples from the categories of apples, oranges, and grapes.

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Section: Cautions and Recommendationsmentioning

confidence: 99%

Uncovering mental representations with Markov chain Monte Carlo

Sanborn

Griffiths

Shiffrin

2010

Cognitive Psychology

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“…is ergodic. In the second type of algorithms, the Robbins-Monro type, ergodicity properties must be assured by updating only at regeneration times [15]. In any case, as pointed out by Andrieu et al [17] the convergence to the target distribution is assured if optimization vanishes.…”

Section: Introductionmentioning

confidence: 99%

“…Two main approaches are known which take the Markov Chain history into account: Adaptive Metropo-lis (AM) algorithms [13] (implemented for example in PyMC [14]) and algorithms that use rules following Robbins-Monro update [12,15,16]. In the first case, parameter jumps are tuned using the covariance matrix at every step, so that once the adaptation is finished the algorithm should be wandering with a parameter jump close to the "error" of the parameter (defined as the variance of the posterior parameter PDF).…”

Section: Introductionmentioning

confidence: 99%

Fitting in a complexχ2landscape using an optimized hypersurface sampling

Pardo¹,

Rovira-Esteva²,

Büsch³

et al. 2011

Phys. Rev. E

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Fitting a data set with a parametrized model can be seen geometrically as finding the global minimum of the χ 2 hypersurface, depending on a set of parameters {Pi}. This is usually done using the Levenberg-Marquardt algorithm. The main drawback of this algorithm is that despite of its fast convergence, it can get stuck if the parameters are not initialized close to the final solution. We propose a modification of the Metropolis algorithm introducing a parameter step tuning that optimizes the sampling of parameter space. The ability of the parameter tuning algorithm together with simulated annealing to find the global χ 2 hypersurface minimum, jumping across χ 2 {Pi} barriers when necessary, is demonstrated with synthetic functions and with real data.

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“…Gilks, Roberts and Sahu [12] have shown that the transition kernel used in an MCMC algorithm can be updated without damaging the ergodicity at regeneration times. The self-regenerative algorithm by Sahu and Zhigljavsky [26] is based on constructing an auxiliary chain and picking elements of this chain a suitable number of times.…”

Section: Introductionmentioning

confidence: 99%

“…These are either based on regeneration or slowing down the adaptation as sampling proceeds (see [3,7,12,14,15,17,23,24,26]). …”

Section: Introductionmentioning

confidence: 99%

Adaptive independence samplers

2008

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Markov chain Monte Carlo (MCMC) is an important computational technique for generating samples from non-standard probability distributions. A major challenge in the design of practical MCMC samplers is to achieve efficient convergence and mixing properties. One way to accelerate convergence and mixing is to adapt the proposal distribution in light of previously sampled points, thus increasing the probability of acceptance. In this paper, we propose two new adaptive MCMC algorithms based on the Independent Metropolis-Hastings algorithm. In the first, we adjust the proposal to minimize an estimate of the cross-entropy between the target and proposal distributions, using the experience of pre-runs. This approach provides a general technique for deriving natural adaptive formulae. The second approach uses multiple parallel chains, and involves updating chains individually, then updating a proposal density by fitting a Bayesian model to the population. An important feature of this approach is that adapting the proposal does not change the limiting distributions of the chains. Consequently, the adaptive phase of the sampler can be continued indefinitely. We include results of numerical experiments indicating that the new algorithms compete well with traditional Metropolis-Hastings algorithms. We also demonstrate the method for a realistic problem arising in Comparative Genomics.

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Adaptive Markov Chain Monte Carlo through Regeneration

Cited by 207 publications

References 18 publications

Uncovering mental representations with Markov chain Monte Carlo

Uncovering mental representations with Markov chain Monte Carlo

Fitting in a complexχ2landscape using an optimized hypersurface sampling

Adaptive independence samplers

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