Bayesian Stopping Rules for Greedy Randomized Procedures

A greedy randomized adaptive search procedure (GRASP) is proposed for the approximate solution of general mixed binary programming problems (MBP). Examples are provided of practical applications that can be formulated as MBP requiring the solution of a large number of problem instances. This justifies, from both a practical and a theoretical perspective, the development of stopping rules aimed at controlling the number of iterations in a GRASP. To this end, a bayesian framework is laid down, two different prior distributions are proposed and stopping conditions are explicitly derived in analytical form. Numerical evidence shows that the stopping rules lead to an optimal trade-off between accuracy and computational effort, saving from unneeded iterations and still achieving good approximations.     

Structured additive regression for overdispersed and zero‐inflated count data

In count data regression there can be several problems that prevent the use of the standard Poisson log‐linear model: overdispersion, caused by unobserved heterogeneity or correlation, excess of zeros, non‐linear effects of continuous covariates or of time scales, and spatial effects. We develop Bayesian count data models that can deal with these issues simultaneously and within a unified inferential approach. Models for overdispersed or zero‐inflated data are combined with semiparametrically structured additive predictors, resulting in a rich class of count data regression models. Inference is fully Bayesian and is carried out by computationally efficient MCMC techniques. Simulation studies investigate performance, in particular how well different model components can be identified. Applications to patent data and to data from a car insurance illustrate the potential and, to some extent, limitations of our approach. Copyright © 2006 John Wiley & Sons, Ltd.     

A hierarchy machine: Learning to optimize from nature and humans

This article proposes a competent hierarchical optimization method called the hierarchical Bayesian optimization algorithm (hBOA). hBOA extends the Bayesian optimization algorithm (BOA) by incorporating three important features for robust and scalable optimization of hierarchical problems: proper decomposition, chunking, and preservation of alternative solutions. Additionally, the article proposes a class of difficult hierarchical problems called hierarchical traps. hBOA is shown to provide a scalable solution to the class of hierarchically decomposable problems and anything easier. Specifically, hBOA can solve hierarchical traps and other nearly decomposable problems in approximately O(n^1.55 log n) to O(n²) function evaluations, where n is the number of decision variables in the problem. © 2003 Wiley Periodicals, Inc.     

Process pathway inference via time series analysis

Motivated by recent experimental developments in functional genomics, we construct and test a numerical technique for inferring process pathways, in which one process calls another process, from time series data. We validate using a case in which data are readily available and we formulate an extension, appropriate for genetic regulatory networks, which exploits Bayesian inference and in which the present-day undersampling is compensated for by prior understanding of genetic regulation.     

Accounting for inspection errors and change in maintenance behaviour

We propose a way to account for inspection errors in a particularframework. We consider a situation where the lifetime of a systemdepends essentially of a particular part. A deterioration ofthis part is regarded as an unacceptable state for the safetyof the system and a major renewal is deemed necessary. Thusthe statistical analysis of the deterioration time distributionof this part is of primary interest for the preventive maintenanceof the system. In this context, we faced the following problem.In the early life of the system, unwarranted renewals of thepart are decided upon, caused by overly cautious behaviour.Such unnecessary renewals make the statistical analysis of deteriorationtime data difficult and can induce and underestimation of themean life of the part. To overcome this difficulty, we proposeto regard the problem as an incomplete data model. We presentits estimation under the maximum likelihood methodology. Numericalexperiments show that this approach eliminates the pessimisticbias in the estimation of the mean life of the part. We alsopresent a Bayesian analysis of the problem which can be usefulin a small sample setting.     

Robust Bayesian analysis in partially ordered plausibility calculi

In Robust Bayesian analysis one attempts to avoid the ‘Dogma of Precision’ in Bayesian analysis by entertaining a set of probability distributions instead of exactly one. The algebraic approach to plausibility calculi is inspired by Cox's and Jaynes' analyses of plausibility assessment as a logic of uncertainty. In the algebraic approach one is not so much interested in different ways to prove that precise Bayesian probability is inevitable but rather in how different sets of assumptions are reflected in the resulting plausibility calculus. It has repeatedly been pointed out that a partially ordered plausibility domain is more appropriate than a totally ordered one, but it has not yet been completely resolved exactly what such domains can look like. One such domain is the natural robust Bayesian representation, an indexed family of probabilities.We show that every plausibility calculus embeddable in a partially ordered ring is equivalent to a subring of a product of ordered fields, i.e., the robust Bayesian representation is universal under our assumptions, if extended rather than standard probability is used.We also show that this representation has at least the same expressiveness as coherent sets of desirable gambles with real valued payoffs, for a finite universe.     

不完全信息下三度价格歧视的有效性研究

基于不完全信息静态博弈模型,讨论了相互竞争的两厂商在双方都掌握的线性需求函数和一方随机选取的线性成本函数这样的不完全信息情况下实施三度价格歧视的有效性问题,且给出了双方实施三度价格歧视的最优产量,最优价格以及最大利润公式,并把相关结论与基于完全信息静态博弈的三度歧视定价和不完全信息静态博弈的统一定价进行对比,得出了许多重要的结论.     

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??Kundu and Gupta proposed to use the importance sampling method to compute the Bayesian estimation of the unknown parameters of the Marshall-Olkin bivariate Weibull distribution. However, we find that the performance of the importance sampling method becomes worse as the sample size gets larger. In this paper, we introduce latent variables to simplify the likelihood function, and use MCMC algorithm to estimate the unknown parameters. Numerical simulations are carried out to assess the performance of the proposed method by comparing with the maximum likelihood estimation, and we find that the Bayesian estimates perform better even for the case of small sample size. A real data is also analyzed for illustrative purpose.     

Bayesian Ensemble Trees (BET) for Clustering and Prediction in Heterogeneous Data

We propose a novel “tree-averaging” model that uses the ensemble of classification and regression trees (CART). Each constituent tree is estimated with a subset of similar data. We treat this grouping of subsets as Bayesian ensemble trees (BET) and model them as a Dirichlet process. We show that BET determines the optimal number of trees by adapting to the data heterogeneity. Compared with the other ensemble methods, BET requires much fewer trees and shows equivalent prediction accuracy using weighted averaging. Moreover, each tree in BET provides variable selection criterion and interpretation for each subset. We developed an efficient estimating procedure with improved estimation strategies in both CART and mixture models. We demonstrate these advantages of BET with simulations and illustrate the approach with a real-world data example involving regression of lung function measurements obtained from patients with cystic fibrosis. Supplementary materials for this article are available online.     

对称损失下二项分布参数的E-Bayes估计及其性质

在已有的文献中提出了一种新的参数估计方法——E-Bayes估计法.在对称损失函数下,对二项分布的参数给出了E-Bayes估计和多层Bayes估计,并给出了E-Bayes估计的性质.最后,给出了数值算例,结果表明提出的方法可行且便于应用.