We attempt to trace the history and development of Markov chain Monte Carlo (MCMC) from its early inception in the late 1940s through its use today. We see how the earlier stages of Monte Carlo (MC, not MCMC) research...
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We attempt to trace the history and development of Markov chain Monte Carlo (MCMC) from its early inception in the late 1940s through its use today. We see how the earlier stages of Monte Carlo (MC, not MCMC) research have led to the algorithms currently in use. More importantly, we see how the development of this methodology has not only changed our solutions to problems, but has changed the way we think about problems.
In many applications of wireless sensor network(WSN), it is essential to ensure that sensors can determine their location, even in the presence of malicious adversaries. However, almost all the localization algorithms...
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In many applications of wireless sensor network(WSN), it is essential to ensure that sensors can determine their location, even in the presence of malicious adversaries. However, almost all the localization algorithms need the location information of reference nodes to locate the unknown nodes. When the location information is tempered by the attacks, the accuracy of these algorithms will degrade badly. We present a novel mechanism for secure localization. The mechanism aims to filter out malicious reference signals on the basis of the normal distribution trait among multiple reference signals. This will ensure each node to obtain correct information about its position in the presence of attackers. In this paper, a simulation circumstance which might be attacked is constructed to compare the improved algorithm with original one. The experiment results demonstrate that the proposed mechanism can effectively survive malicious attacks.
We perform Markov chain Monte Carlo simulations for a Bayesian inference of the GJR-GARCH model which is one of asymmetric LARCH, models. The adaptive construction scheme is used for the construction of the proposal d...
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ISBN:
(纸本)9783642040696
We perform Markov chain Monte Carlo simulations for a Bayesian inference of the GJR-GARCH model which is one of asymmetric LARCH, models. The adaptive construction scheme is used for the construction of the proposal density in the metropolis-hastings algorithm and the parameters of the proposal density are determined adaptively by using the data sampled by the Markov chain Monte Carlo simulation. We study the performance of the scheme with the artificial GJR-GARCH data. We: find that the adaptive construction scheme samples GJR-GARCH parameters effectively and conclude that the metropolis-hastings algorithm with the adaptive construction scheme is art efficient method to the Bayesian inference of the GJR-GARCH model.
Customer losing problems are concerned by telecom operators as market becoming more competitive. Based on data mining technology, Bayesian networks classifier is used in the analysis of the problems. During the proces...
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Customer losing problems are concerned by telecom operators as market becoming more competitive. Based on data mining technology, Bayesian networks classifier is used in the analysis of the problems. During the process of Bayesian networks modeling, K2 and MCMC algorithms are utilized together. Effective variables are distilled through topology of networks, and churn rules are drawn based on CPT (condition probability table), then high probability churn customer groups are obtained. Considering loss function in classifier, different criterions and their class effects are provided. In contrast with other algorithm, such as decision tree and ANN (artificial neural networks), Bayesian networks can be modeled without over-sampling, when churn rate is relatively low.
Computing marginal probabilities is an important and fundamental issue in Bayesian inference. We present a simple method which arises from a likelihood identity for computation. The likelihood identity, called Candida...
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Computing marginal probabilities is an important and fundamental issue in Bayesian inference. We present a simple method which arises from a likelihood identity for computation. The likelihood identity, called Candidate's formula, sets the marginal probability as a ratio of the prior likelihood to the posterior density. Based on Markov chain Monte Carlo output simulated from the posterior distribution, a nonparametric kernel estimate is used to estimate the posterior density contained in that ratio. This derived nonparametric Candidate's estimate requires only one evaluation of the posterior density estimate at a point. The optimal point for such evaluation can be chosen to minimize the expected mean square relative error. The results show that the best point is not necessarily the posterior mode, but rather a point compromising between high density and low Hessian. For high dimensional problems, we introduce a variance reduction approach to ease the tension caused by data sparseness. A simulation study is presented.
作者：
Przytycka, TNIH
Natl Ctr Biotechnol Informat Natl Lib Med Bethesda MD 20894 USA
Despite significant effort, the problem of predicting a protein's three-dimensional fold from its amino-acid sequence remains unsolved. An important strategy involves treating folding as a statistical process, usi...
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Despite significant effort, the problem of predicting a protein's three-dimensional fold from its amino-acid sequence remains unsolved. An important strategy involves treating folding as a statistical process, using the Markov chain formalism, implemented as a metropolis Monte Carlo algorithm. A formal prerequisite of this approach is the condition of detailed balance, the plausible requirement that at equilibrium, the transition from state i to state j is traversed with the same probability as the reverse transition from state j to state i. Surprisingly, some relatively successful methods that use biased sampling fail to satisfy this requirement. Is this compromise merely a convenient heuristic that results in faster convergence? Or, is it instead a cryptic energy term that compensates for an incomplete potential function? I explore this question using metropolis-hasting Monte Carlo simulations. Results from these simulations suggest the latter answer is more likely. (C) 2004 Wiley-Liss, Inc.
A model is presented for the interpretation of magnetometer data in terms of archeological features beneath the ground. it describes the detector's response to the assemblage of buried features, incorporating both...
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A model is presented for the interpretation of magnetometer data in terms of archeological features beneath the ground. it describes the detector's response to the assemblage of buried features, incorporating both a spread function and a statistical error process as well as appropriate prior beliefs about the nature of archeological features. The problem is to estimate the magnetic susceptibility of the buried features at each horizontal location. A Monte Carlo Markov chain approach is used to estimate magnetic susceptibilities and all prior parameters. This requires estimation of the normalization constant of the Gibbs prior distribution. The approach is illustrated with both simulated data and measurements from an archeological rite. In the latter case, the reconstruction of the buried features corresponds well with the archeologist's observations during subsequent excavation.
作者：
Chen, SXNYU
Stern Sch Business New York NY 10012 USA
This paper outlines a theoretical framework for finite population models with unequal sample probabilities, along with sampling schemes for drawing random samples from these models. We first present four exact weighte...
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This paper outlines a theoretical framework for finite population models with unequal sample probabilities, along with sampling schemes for drawing random samples from these models. We first present four exact weighted sampling schemes that can be used for any finite population model to satisfy such requirements as ordered/unordered samples, with/without replacement, and fixed/nonfixed sample size. We then introduce a new class of finite population models called weighted polynomial models or, in short, WPM. The probability density of a WPM is defined through a symmetric polynomial of the weights of the units in the sample. The WPM is shown to have been applied in many statistical analyses including survey sampling, logistic regression, case-control studies, lottery, DNA sequence alignment and MCMC simulations. We provide general strategies that can help improve the efficiency of the exact weighted sampling schemes for any given WPM. We show that under a mild condition, sampling from any WPM can be implemented within polynomial time. A metropolis-hasting-type scheme is proposed for approximate weighted sampling when the exact sampling schemes become intractable for moderate population and sample sizes. We show that under a mild condition, the average acceptance rate of the approximate sampling scheme for any WPM can be expressed in closed form using only the inclusion probabilities.
I describe a simple procedure for investigating the convergence properties of Markov chain Monte Carlo sampling schemes. The procedure uses coupled chains from the same sampler, obtained by using the same sequence of ...
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I describe a simple procedure for investigating the convergence properties of Markov chain Monte Carlo sampling schemes. The procedure uses coupled chains from the same sampler, obtained by using the same sequence of random deviates for each run. By examining the distribution of the iteration at which all sample paths couple, convergence properties for the system can be established. The procedure also provides a simple diagnostic for detecting modes in multimodal posteriors. Several examples of the procedure are provided. In Ising models, the relation between the correlation parameter and the convergence rate of rudimentary Gibbs samplers is investigated. In another example, the effects of multiple modes on the convergence of coupled paths are explored using mixtures of bivariate normal distributions. The technique is also used to evaluate the convergence properties of a Gibbs sampling scheme applied to a model for rat growth rates.
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