Monte Carlo simulation (MCS) on the thermal properties in Gd-Mg alloy becomes essential as there axe only limited experiments available. A realistic Johnson potential is used to workout the specific heats for various ...
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Monte Carlo simulation (MCS) on the thermal properties in Gd-Mg alloy becomes essential as there axe only limited experiments available. A realistic Johnson potential is used to workout the specific heats for various temperatures and hence the Debye temperature. The results from the present simulation technique axe very well compared with our shell model calculation. The need of better X-ray measurements for Debye-Waller factor and Debye temperature other than the measurements of Subadhra and Sirdeshmukh, is discussed in detail.
Markov chain Monte Carlo (MCMC;the metropolis-Hastings algorithm) has been used for many statistical problems, including Bayesian inference, likelihood inference, and tests of significance. Though the method generally...
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Markov chain Monte Carlo (MCMC;the metropolis-Hastings algorithm) has been used for many statistical problems, including Bayesian inference, likelihood inference, and tests of significance. Though the method generally works well, doubts about convergence often remain. Here we propose MCMC methods distantly related to simulated annealing. Our samplers mix rapidly enough to be usable for problems in which other methods would require eons of computing time. They simulate realizations from a sequence of distributions, allowing the distribution being simulated to vary randomly over time. If the sequence of distributions is well chosen, then the sampler will mix well and produce accurate answers for all the distributions. Even when there is only one distribution of interest, these annealing-like samplers may be the only known way to get a rapidly mixing sampler. These methods are essential for attacking very hard problems, which arise in areas such as statistical genetics. We illustrate the methods with an application that is much harder than any problem previously done by MCMC, involving ancestral inference on a very large genealogy (7 generations, 2,024 individuals). The problem is to find, conditional on data on living individuals, the probabilities of each individual having been a carrier of cystic fibrosis. Exact calculation of these conditional probabilities is infeasible. Moreover, a Gibbs sampler for the problem would not mix in a reasonable time, even on the fastest imaginable computers. Our annealing-like samplers have mixing times of a few hours. We also give examples of samplers for the ''witch's hat'' distribution and the conditional Strauss process.
The development of sophisticated experimental means to control nanoscale systems has motivated efforts to design driving protocols that minimize the energy dissipated to the environment. Computational models are a cru...
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The development of sophisticated experimental means to control nanoscale systems has motivated efforts to design driving protocols that minimize the energy dissipated to the environment. Computational models are a crucial tool in this practical challenge. We describe a general method for sampling an ensemble of finite-time, nonequilibrium protocols biased toward a low average dissipation. We show that this scheme can be carried out very efficiently in several limiting cases. As an application, we sample the ensemble of low-dissipation protocols that invert the magnetization of a 2D Ising model and explore how the diversity of the protocols varies in response to constraints on the average dissipation. In this example, we find that there is a large set of protocols with average dissipation close to the optimal value, which we argue is a general phenomenon.
In biomedical and epidemiological studies, often outcomes obtained are of mixed discrete and continuous in nature. Furthermore, due to some technical inconvenience or else, continuous responses are censored and also a...
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In biomedical and epidemiological studies, often outcomes obtained are of mixed discrete and continuous in nature. Furthermore, due to some technical inconvenience or else, continuous responses are censored and also a few covariates cease to be observed completely. In this paper, we develop a model to tackle these complex situations. Our methodology is developed in a more general framework and provides a full-scale robust analysis of such complex models. The proposed robust maximum likelihood estimators of the model parameters are resistant to potential outliers in the data. We discuss the asymptotic properties of the robust estimators. To avoid computational difficulties involving irreducibly high-dimensional integrals, we propose a Monte Carlo method based on the metropolis algorithm for approximating the robust maximum likelihood estimators. We study the empirical properties of these estimators in simulations. We also illustrate the proposed robust method using clustered data on blood sugar content from a clinical trial of individuals who were investigated for diabetes.
This paper studies the computational complexity of Markov chain Monte Carlo algorithms with finite-valued Markov random fields on a finite regular lattice as target distributions. We state conditions under which the c...
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This paper studies the computational complexity of Markov chain Monte Carlo algorithms with finite-valued Markov random fields on a finite regular lattice as target distributions. We state conditions under which the complexity for approximate convergence is polynomial in n, the number of variables. Approximate convergence takes time O(n log n) as n --> infinity if the target field satisfies certain spatial mixing conditions. Otherwise, if the held has a potential with finite interaction range independent of n, the complexity is exponential in n(gamma), with gamma < 1, which is still more favourable than enumerating all the states. When the interaction range grows with n,the algorithms can converge exponentially in n. Analogous results are provided for an expectation approximated by an average along the chain.
Hierarchical classes models are models for N-way N-mode data that represent the association among the N modes and simultaneously yield, for each mode, a hierarchical classification of its elements. In this paper we pr...
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Hierarchical classes models are models for N-way N-mode data that represent the association among the N modes and simultaneously yield, for each mode, a hierarchical classification of its elements. In this paper we present a stochastic extension of the hierarchical classes model for two-way two-mode binary data. In line with the original model, the new probabilistic extension still represents both the association among the two modes and the hierarchical classifications. A fully Bayesian method for fitting the new model is presented and evaluated in a simulation study. Furthermore, we propose tools for model selection and model checking based on Bayes factors and posterior predictive checks. We illustrate the advantages of the new approach with applications in the domain of the psychology of choice and psychiatric diagnosis.
metropolis algorithms along with Gibbs steps are proposed to perform a Bayesian analysis for the Block and Basu (ACBVE) bivariate exponential distribution. We also consider the use of Gibbs sampling to develop Bayesia...
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metropolis algorithms along with Gibbs steps are proposed to perform a Bayesian analysis for the Block and Basu (ACBVE) bivariate exponential distribution. We also consider the use of Gibbs sampling to develop Bayesian inference for accelerated life tests assuming a power rule model and the ACBVE distribution. The methodology developed in this paper is exemplified with two examples.
Maximum pseudo-likelihood estimation has hitherto been viewed as a practical but flawed alternative to maximum likelihood estimation, necessary because the maximum likelihood estimator is too hard to compute, but flaw...
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Maximum pseudo-likelihood estimation has hitherto been viewed as a practical but flawed alternative to maximum likelihood estimation, necessary because the maximum likelihood estimator is too hard to compute, but flawed because of its inefficiency when the spatial interactions are strong. We demonstrate that a single Newton-Raphson step starting from the maximum pseudo-likelihood estimator produces an estimator which is close to the maximum likelihood estimator in terms of its actual value, attained likelihood, and efficiency, even in the presence of strong interactions. This hybrid technique greatly increases the practical applicability of pseudo-likelihood-based estimation. Additionally, in the case of the spatial point processes, we propose a proper maximum pseudo-likelihood estimator which is different from the conventional one. The proper maximum pseudo-likelihood estimator clearly shows better performance than the conventional one does when the spatial interactions are strong.
We construct arbitrarily sparse locally-jammed packings of non-overlapping congruent disks in various finite area regions-in particular, we give constructions for the square, hexagon, and for certain flat tori.
We construct arbitrarily sparse locally-jammed packings of non-overlapping congruent disks in various finite area regions-in particular, we give constructions for the square, hexagon, and for certain flat tori.
The threshold autoregressive (TAR) model is generalized which results in more flexibility in applications. We construct a Bayesian framework to show that Markov chain Monte Carlo method can be applied to estimating pa...
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The threshold autoregressive (TAR) model is generalized which results in more flexibility in applications. We construct a Bayesian framework to show that Markov chain Monte Carlo method can be applied to estimating parameters with success. (C) 1998 Elsevier Science B.V. All rights reserved.
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