Informed reversible jump algorithms

Gagnon, Philippe

doi:10.1214/21-ejs1877

Cited by 6 publications

(3 citation statements)

References 34 publications

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“…This innovative approach has been shown to have a dimension-free mixing time limit under conditions similar to those in Yang et al (2016). For further advances related to locally informed proposals, see work such as that of Livingstone and Zanella (2022); Gagnon (2021) and Power and Goldman (2019). Another proposal is the Hamming ball sampler, proposed in Titsias and Yau (2017), which introduced a method for sampling models based on their locally-truncated posterior probability within a neighbourhood defined by a Hamming ball 3 Contaminated experiments…”

Section: Notation Basic Formulas and A Brief Review Of Search Methodsmentioning

confidence: 99%

Searching in ultra high dimensional sparse model spaces: New performance tests and boosting Gibbs sampling algorithms

García-Donato,

Castellanos

2024

Preprint

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In the context of variable selection in sparse settings, we present a novel class of experiments. These are based on the notion of contaminating real data sets with artificial spurious covariates in such a way that exact solutions can be easily computed. Such exact responses provide a direct and compelling way to evaluate the performance of search methods on model spaces of arbitrary cardinality. We apply this tool to Gaussian regression models, an important statistical problem that has benefited from the emergence of many new search methods in recent years. We also contribute to this catalog by revisiting classical Gibbs sampling algorithms proposing new implementations that take advantage of sparsity. Despite their simplicity, the resulting methods are very competitive and fully automatic. We use a real genetic dataset to illustrate and motivate the various procedures presented in this research.

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Section: Notation Basic Formulas and A Brief Review Of Search Methodsmentioning

confidence: 99%

Searching in ultra high dimensional sparse model spaces: New performance tests and boosting Gibbs sampling algorithms

García-Donato,

Castellanos

2024

Preprint

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“…For other developments concerning locally informed proposals, see e.g. Livingstone and Zanella (2019); Gagnon (2021); Power and Goldman (2019).…”

Section: Introductionmentioning

confidence: 99%

Adaptive random neighbourhood informed Markov chain Monte Carlo for high-dimensional Bayesian variable selection

2022

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We introduce a framework for efficient Markov chain Monte Carlo algorithms targeting discrete-valued high-dimensional distributions, such as posterior distributions in Bayesian variable selection problems. We show that many recently introduced algorithms, such as the locally informed sampler of Zanella (J Am Stat Assoc 115(530):852–865, 2020), the locally informed with thresholded proposal of Zhou et al. (Dimension-free mixing for high-dimensional Bayesian variable selection, 2021) and the adaptively scaled individual adaptation sampler of Griffin et al. (Biometrika 108(1):53–69, 2021), can be viewed as particular cases within the framework. We then describe a novel algorithm, the adaptive random neighbourhood informed sampler, which combines ideas from these existing approaches. We show using several examples of both real and simulated data-sets that a computationally efficient point-wise implementation (PARNI) provides more reliable inferences on a range of variable selection problems, particularly in the very large p setting.

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“…While this asymptotic regime is ubiquitous in statistics, it is only recently that it was found useful in the analysis of MCMC algorithms (Deligiannidis et al. 2018 ; Gagnon 2021 ; Schmon et al. 2021a ).…”

Section: Introductionmentioning

confidence: 99%

Optimal scaling of random walk Metropolis algorithms using Bayesian large-sample asymptotics

Schmon

Gagnon

2022

Stat Comput

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High-dimensional limit theorems have been shown useful to derive tuning rules for finding the optimal scaling in random walk Metropolis algorithms. The assumptions under which weak convergence results are proved are, however, restrictive: the target density is typically assumed to be of a product form. Users may thus doubt the validity of such tuning rules in practical applications. In this paper, we shed some light on optimal scaling problems from a different perspective, namely a large-sample one. This allows to prove weak convergence results under realistic assumptions and to propose novel parameter-dimension-dependent tuning guidelines. The proposed guidelines are consistent with the previous ones when the target density is close to having a product form, and the results highlight that the correlation structure has to be accounted for to avoid performance deterioration if that is not the case, while justifying the use of a natural (asymptotically exact) approximation to the correlation matrix that can be employed for the very first algorithm run.

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Informed reversible jump algorithms

Cited by 6 publications

References 34 publications

Searching in ultra high dimensional sparse model spaces: New performance tests and boosting Gibbs sampling algorithms

Searching in ultra high dimensional sparse model spaces: New performance tests and boosting Gibbs sampling algorithms

Adaptive random neighbourhood informed Markov chain Monte Carlo for high-dimensional Bayesian variable selection

Optimal scaling of random walk Metropolis algorithms using Bayesian large-sample asymptotics

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