This article describes a new Metropolis-like transition rule, the multiple-try Metropolis, for Markov chain Monte Carlo (MCMC) simulations. By using this transition rule together with adaptive direction sampling. we p...
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This article describes a new Metropolis-like transition rule, the multiple-try Metropolis, for Markov chain Monte Carlo (MCMC) simulations. By using this transition rule together with adaptive direction sampling. we propose a novel method for incorporating local optimization steps into a MCMC sampler in continuous state-space. Numerical studies show that the new method performs significantly better than the traditional Metropolis-Hastings (M-H) sampler. With minor tailoring in using the rule, the multiple-try method can also be exploited to achieve the effect of a griddy Gibbs sampler without having to bear with griddy approximations, and the effect of a hit-and-run algorithm without having to figure out the required conditional distribution in a random direction.
Gibbs sampler is widely used in Bayesian analysis. But it is often difficult to sample from the full conditional distribution, and this hardly weakens the efficiency of Gibbs sampler. In this paper, we propose to use ...
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ISBN:
(纸本)9783037854303
Gibbs sampler is widely used in Bayesian analysis. But it is often difficult to sample from the full conditional distribution, and this hardly weakens the efficiency of Gibbs sampler. In this paper, we propose to use mixture normal distribution for Gibbs sampler. The mixture normal distribution can approximate the target distribution. So carrying more information from target distribution, the mixture normal distribution tremendously improves the efficiency of Gibbs sampler. Further more, combining with mixture normal method, hit-and-run algorithm can also get more efficient sampling results. Simulation results show that Gibbs sampler with mixture normal distribution outperforms other sampling algorithms. The Gibbs sampler with mixture normal distribution can also be applied to explorer the surface of single crystal.
We formulate a mean-variance portfolio selection problem that accommodates qualitative input about expected returns anti provide an algorithm that solves the problem. This model and algorithm can be used, for example,...
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We formulate a mean-variance portfolio selection problem that accommodates qualitative input about expected returns anti provide an algorithm that solves the problem. This model and algorithm can be used, for example, when a portfolio manager determines that one industry will benefit more from a regulatory change than another but is unable to quantify the degree of difference. Qualitative views are expressed in terms of linear inequalities among expected returns. Our formulation builds on the Black-Litterman model for portfolio selection. The algorithm makes use of an adaptation of the hit-and-run method for Markov chain Monte Carlo simulation. We also present computational results that illustrate advantages of our approach over alternative heuristic methods for incorporating qualitative input. (C) 2011 Elsevier B.V. All rights reserved.
Although the block Gibbs sampler for the Bayesian graphical LASSO proposed by Wang (2012) has been widely applied and extended to various shrinkage priors in recent years, it has a less noticeable but possibly severe ...
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Although the block Gibbs sampler for the Bayesian graphical LASSO proposed by Wang (2012) has been widely applied and extended to various shrinkage priors in recent years, it has a less noticeable but possibly severe disadvantage that the positive definiteness of a precision matrix in the Gaussian graphical model is not guaranteed in each cycle of the Gibbs sampler. Specifically, if the dimension of the precision matrix exceeds the sample size, the positive definiteness of the precision matrix will be barely satisfied and the Gibbs sampler will almost surely fail. In this paper, we propose modifying the original block Gibbs sampler so that the precision matrix never fails to be positive definite by sampling it exactly from the domain of the positive definiteness. As we have shown in the Monte Carlo experiments, this modification not only stabilizes the sampling procedure but also significantly improves the performance of the parameter estimation and graphical structure learning. We also apply our proposed algorithm to a graphical model of the monthly return data in which the number of stocks exceeds the sample period, demonstrating its stability and scalability.
hit-and-run, a class of MCMC samplers that converges to general multivariate distributions, is known to be unique in its ability to mix fast for uniform distributions over convex bodies. In particular, its rate of con...
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hit-and-run, a class of MCMC samplers that converges to general multivariate distributions, is known to be unique in its ability to mix fast for uniform distributions over convex bodies. In particular, its rate of convergence to a uniform distribution is of a low order polynomial in the dimension. However, when the body of interest is difficult to sample from, typically a hyperrectangle is introduced that encloses the original body, and a one-dimensional acceptance/rejection is performed. The fast mixing analysis of hit-and-run does not account for this one-dimensional sampling that is often needed for implementation of the algorithm. Here we show that the effect of the size of the hyperrectangle on the efficiency of the algorithm is only a linear scaling effect. We also introduce a variation of hit-and-run that accelerates the sampler and demonstrate its capability through a computational study.
Sampling the fibre comprising the solutions of a linear inverse problem for count data is an important practical problem. Connectivity of the sampler is guaranteed only if a Markov basis, defining a sufficiently rich ...
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Sampling the fibre comprising the solutions of a linear inverse problem for count data is an important practical problem. Connectivity of the sampler is guaranteed only if a Markov basis, defining a sufficiently rich variety of sampling directions, is available. Computation of a Markov basis is typically challenging, and the mixing properties of the resulting sampler can be poor. However, for some problems a suitably chosen lattice basis will be a Markov basis. We provide an easily checkable condition for the existence of such a lattice Markov basis, and demonstrate that associated hit-and-run samplers will mix rapidly for uniform target distributions.
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