Adaptive Component-Wise Multiple-Try Metropolis Sampling

Yang, Jinyoung; Levi, Evgeny; Craiu, Radu V.; Rosenthal, Jeffrey S.

doi:10.1080/10618600.2018.1513365

Cited by 4 publications

(9 citation statements)

References 34 publications

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“…We will compare the adaptive Plateau proposal algorithm with the adaptive Gaussian MCMC algorithm [27] using multivariate Normal target distributions. As the target distribution is Normal, performance should favour the adaptive Gaussian MCMC method due to similarity between the target and proposal distribution shape.…”

Section: Adaptation Of Plateau Proposalsmentioning

confidence: 99%

“…We stress that a particular adaptation strategy is proposal-dependent, that is, here we compare the combined performance of the proposal and the adaptation procedure. We shall denote the adaptive Plateau proposal MCMC method as AP and the adaptive Gaussian proposal MCMC method proposed in [27] as AG2 (a variant of AG2, denoted as AG1, will be introduced later in Sect. 6).…”

Section: Adaptation Of Plateau Proposalsmentioning

confidence: 99%

“…6). Following [27], the Gaussian proposal distributions in AG2 are adapted as follows: If the proposal with the largest standard deviation is under(over)-selected, then it is halved (doubled). Conversely, if the proposal with the smallest standard deviation is under(over)-selected, then it is doubled (halved).…”

Section: Adaptation Of Plateau Proposalsmentioning

confidence: 99%

“…After either of these two updates, the other standard deviations are adjusted to be equidistant on a log-scale (base 2). For further algorithmic details on this adaptation scheme; see [27]. The adaptation interval for both methods was set to L = 50 and P n = −1 (in Step 4, Algorithm 2) to trigger adaptations every 50 iterations.…”

Section: Adaptation Of Plateau Proposalsmentioning

confidence: 99%

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Plateau proposal distributions for adaptive component-wise multiple-try metropolis

Lau

Krumscheid

2022

METRON

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Markov chain Monte Carlo (MCMC) methods are sampling methods that have become a commonly used tool in statistics, for example to perform Monte Carlo integration. As a consequence of the increase in computational power, many variations of MCMC methods exist for generating samples from arbitrary, possibly complex, target distributions. The performance of an MCMC method, in particular that of a Metropolis–Hastings MCMC method, is predominately governed by the choice of the so-called proposal distribution used. In this paper, we introduce a new type of proposal distribution for the use in Metropolis–Hastings MCMC methods that operates component-wise and with multiple trials per iteration. Specifically, the novel class of proposal distributions, called Plateau distributions, does not overlap, thus ensuring that the multiple trials are drawn from different regions of the state space. Furthermore, the Plateau proposal distributions allow for a bespoke adaptation procedure that lends itself to a Markov chain with efficient problem dependent state space exploration and favourable burn-in properties. Simulation studies show that our novel MCMC algorithm outperforms competitors when sampling from distributions with a complex shape, highly correlated components or multiple modes.

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Section: Adaptation Of Plateau Proposalsmentioning

confidence: 99%

Section: Adaptation Of Plateau Proposalsmentioning

confidence: 99%

Section: Adaptation Of Plateau Proposalsmentioning

confidence: 99%

Section: Adaptation Of Plateau Proposalsmentioning

confidence: 99%

See 2 more Smart Citations

Plateau proposal distributions for adaptive component-wise multiple-try metropolis

Lau

Krumscheid

2022

METRON

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“…Complementary, small-world sampling [( Guan and Krone, 2007 ; Yang et al , 2016 )] and delayed rejection AM ( Haario et al , 2006 ) has been introduced. These methods employ multi-component and multi-try proposals, respectively, and can be combined with the aforementioned approaches.…”

Section: Introductionmentioning

confidence: 99%

Bayesian parameter estimation for biochemical reaction networks using region-based adaptive parallel tempering

et al. 2018

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MotivationMathematical models have become standard tools for the investigation of cellular processes and the unraveling of signal processing mechanisms. The parameters of these models are usually derived from the available data using optimization and sampling methods. However, the efficiency of these methods is limited by the properties of the mathematical model, e.g. non-identifiabilities, and the resulting posterior distribution. In particular, multi-modal distributions with long valleys or pronounced tails are difficult to optimize and sample. Thus, the developement or improvement of optimization and sampling methods is subject to ongoing research.ResultsWe suggest a region-based adaptive parallel tempering algorithm which adapts to the problem-specific posterior distributions, i.e. modes and valleys. The algorithm combines several established algorithms to overcome their individual shortcomings and to improve sampling efficiency. We assessed its properties for established benchmark problems and two ordinary differential equation models of biochemical reaction networks. The proposed algorithm outperformed state-of-the-art methods in terms of calculation efficiency and mixing. Since the algorithm does not rely on a specific problem structure, but adapts to the posterior distribution, it is suitable for a variety of model classes.Availability and implementationThe code is available both as Supplementary Material and in a Git repository written in MATLAB.Supplementary information Supplementary data are available at Bioinformatics online.

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Approximate Methods for Bayesian Computation

Craiu

Levi

2023

Annu. Rev. Stat. Appl.

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Rich data generating mechanisms are ubiquitous in this age of information and require complex statistical models to draw meaningful inference. While Bayesian analysis has seen enormous development in the last 30 years, benefitting from the impetus given by the successful application of Markov chain Monte Carlo (MCMC) sampling, the combination of big data and complex models conspire to produce significant challenges for the traditional MCMC algorithms. We review modern algorithmic developments addressing the latter and compare their performance using numerical experiments. Expected final online publication date for the Annual Review of Statistics and Its Application, Volume 10 is March 2023. Please see http://www.annualreviews.org/page/journal/pubdates for revised estimates.

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Adaptive Component-Wise Multiple-Try Metropolis Sampling

Cited by 4 publications

References 34 publications

Plateau proposal distributions for adaptive component-wise multiple-try metropolis

Plateau proposal distributions for adaptive component-wise multiple-try metropolis

Bayesian parameter estimation for biochemical reaction networks using region-based adaptive parallel tempering

Approximate Methods for Bayesian Computation

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