Journal ArticleDOI
Scaling analysis of delayed rejection MCMC methods
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TLDR
A modification of the delayed rejection algorithm is proposed, in which the direction of the different proposals is fixed once for all, and the Metropolis–Hastings accept-reject mechanism is used to select a proper scaling along the search direction.Abstract:
In this paper, we study the asymptotic efficiency of the delayed rejection strategy In particular, the efficiency of the delayed rejection Metropolis–Hastings algorithm is compared to that of the regular Metropolis algorithm To allow for a fair comparison, the study is carried under optimal mixing conditions for each of these algorithms After introducing optimal scaling results for the delayed rejection (DR) algorithm, we outline the fact that the second proposal after the first rejection is discarded, with a probability tending to 1 as the dimension of the target density increases To overcome this drawback, a modification of the delayed rejection algorithm is proposed, in which the direction of the different proposals is fixed once for all, and the Metropolis–Hastings accept-reject mechanism is used to select a proper scaling along the search direction It is shown that this strategy significantly outperforms the original DR and Metropolis algorithms, especially when the dimension becomes large We include numerical studies to validate these conclusionsread more
Citations
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Journal ArticleDOI
Convergence of Probability Measures
TL;DR: Convergence of Probability Measures as mentioned in this paper is a well-known convergence of probability measures. But it does not consider the relationship between probability measures and the probability distribution of probabilities.
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Bayesian computation: a summary of the current state, and samples backwards and forwards
TL;DR: The difficulties of modelling and then handling ever more complex datasets most likely call for a new type of tool for computational inference that dramatically reduces the dimension and size of the raw data while capturing its essential aspects.
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Scaling analysis of multiple-try MCMC methods
TL;DR: It is shown that the speed of the algorithm increases with the number of candidates in the proposal pool and that the increase in speed is favored by the introduction of dependence among the proposals.
Journal ArticleDOI
Are Health State Valuations from the General Public Biased? A Test of Health State Reference Dependency Using Self-assessed Health and an Efficient Discrete Choice Experiment.
TL;DR: In this article, the authors investigated the impact of reference dependency on health state valuations using an efficient discrete choice experiment administered to a Dutch nationally representative sample of 788 respondents and found that respondents with impaired health worse than or equal to the health state levels under evaluation have approximately 30% smaller health state decrements.
Journal ArticleDOI
Efficient computational strategies for doubly intractable problems with applications to Bayesian social networks
Alberto Caimo,Antonietta Mira +1 more
TL;DR: The delayed rejection (DR) strategy is modified in order to integrate it within the approximate exchange algorithm (AEA) to avoid the computation of intractable normalising constant that appears in exponential random graph models.
References
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Book
Convergence of Probability Measures
TL;DR: Weak Convergence in Metric Spaces as discussed by the authors is one of the most common modes of convergence in metric spaces, and it can be seen as a form of weak convergence in metric space.
Book
Monte Carlo Statistical Methods
TL;DR: This new edition contains five completely new chapters covering new developments and has sold 4300 copies worldwide of the first edition (1999).
Journal ArticleDOI
Convergence of Probability Measures
TL;DR: Convergence of Probability Measures as mentioned in this paper is a well-known convergence of probability measures. But it does not consider the relationship between probability measures and the probability distribution of probabilities.
Journal ArticleDOI
Weak convergence and optimal scaling of random walk Metropolis algorithms
TL;DR: In this paper, the authors consider scaling the proposal distribution of a multidimensional random walk Metropolis algorithm in order to maximize the efficiency of the algorithm and obtain a weak convergence result as the dimension of a sequence of target densities, n, converges to $\infty$.