Flexible Bayesian Modelling for Survival Data

The analysis of failure time data often involves two strong assumptions. The proportional hazards assumption postulates that hazard rates corresponding to different levels of explanatory variables are proportional. The additive effects assumption specifies that the effect associated with a particular explanatory variable does not depend on the levels of other explanatory variables. A hierarchical Bayes model is presented, under which both assumptions are relaxed. In particular, time-dependent covariate effects are explicitly modelled, and the additivity of effects is relaxed through the use of a modified neural network structure. The hierarchical nature of the model is useful in that it parsimoniously penalizes violations of the two assumptions, with the strength of the penalty being determined by the data.     

Numerical Method for Reliability Analysis of Phased-Mission System Using Markov Chains

This article presents a numerical method for solving continuous time Markov chain (CTMC) model for reliability evaluation of phased-mission system. The method generates infinitesimal matrix based on the statistical independence of subsystem failure and repair process. The infinitesimal generator matrix is stored by the use of sparse matrix-compressed storage schemes, and the transient solution of the CTMC model is obtained by using three methods including the uniformization method, forward Euler method, and Runge-Kutta method, which take advantage of the sparseness of the infinitesimal generator matrix. An example PMS is used to compare the preconditioning methods for sparse matrix and numerical methods. Experiment results show that compressed row storage scheme (CRS) saves more storage than other storage formats, and uniformization method combined with CRS achieves the best efficiency and accuracy.     

Near-optimal control policy for loss networks

In this paper, the phenomenon of the optimal management of requests of service in general networks is formulated as a control problem for a finite number of multiserver loss queues with Markovian routing. This type of problem may arise in a wide range of fields, e.g., manufacturing industries, storage facilities, computer networks, and communication systems. Using inductive approach of dynamic programming, the optimal admission control can be induced to be the functions of the number of requested service in progress. However, for large-scale network, the computational burden to find optimal control policy may be infeasible due to its involvement of the states for all stations in the networks. Hence, the idea of bottleneck modeling is borrowed to compute the near-optimal admission control policy. We reduced the scale of loss network and decreased the difference between the original and reduced models by making compensation for system parameters. A novel method is proposed in this paper to compute the compensation. Numerical results show that the near-optimal control policy demonstrates close performance to the optimal policy.     

灰色马尔可夫模型在房价指数预测中的应用

灰色马尔可夫模型预测兼有灰色预测和马尔可夫链预测的优点,并能对较短的时间序列数据进行建模计算。文章尝试将该模型应用于房价指数的预测分析,并对2003年7月到2005年7月间的中房上海住宅指数和办公楼指数进行了实证分析,结果表明模型的拟合精度较高,在房价指数的预测中有较强的适用性。     

A Note on Collapsibility in DAG Models of Contingency Tables

Abstract.  Necessary and sufficient conditions for collapsibility of a directed acyclic graph (DAG) model for a contingency table are derived. By applying the conditions, we can easily check collapsibility over any variable in a given model either by using the joint probability distribution or by using the graph of the model structure. It is shown that collapsibility over a set of variables can be checked in a sequential manner. Furthermore, a DAG is compared with its moral graph in the context of collapsibility.     

The random intrinsic fast initial response of one-sided CUSUM charts

This article analyses the performance of a one-sided cumulative sum (CUSUM) chart that is initialized using a random starting point following the natural or intrinsic probability distribution of the CUSUM statistic. By definition, this probability distribution remains stable as the chart is used. The probability that the chart starts at zero according to this intrinsic distribution is always smaller than one, which confers on the chart a fast initial response feature. The article provides a fast and accurate algorithm to compute the in-control and out-of-control average run lengths and run-length probability distributions for one-sided CUSUM charts initialized using this random intrinsic fast initial response (RIFIR) scheme. The algorithm also computes the intrinsic distribution of the CUSUM statistic and random samples extracted from this distribution. Most importantly, no matter how the chart was initialized, if no level shifts and no alarms have occurred before time τ?>?0, the distribution of the run length remaining after τ is provided by this algorithm very accurately, provided that τ is not too small.     

Bayesian inversion of geoelectrical resistivity data

Summary. Enormous quantities of geoelectrical data are produced daily and often used for large scale reservoir modelling. To interpret these data requires reliable and efficient inversion methods which adequately incorporate prior information and use realistically complex modelling structures. We use models based on random coloured polygonal graphs as a powerful and flexible modelling framework for the layered composition of the Earth and we contrast our approach with earlier methods based on smooth Gaussian fields. We demonstrate how the reconstruction algorithm may be efficiently implemented through the use of multigrid Metropolis–coupled Markov chain Monte Carlo methods and illustrate the method on a set of field data.     

政府监督下单群体行为的博弈分析

基于马尔可夫和博弈理论探讨一类群体的学习与行动过程。在政府监督下某类被监督个体行为是随机的 ,概率转移矩阵被使用描述个体行为的选择 ;又由于群体的行为是大量个体行为的聚集 ,马尔可夫—生灭过程理论被用来阐述群体行为的形成和学习过程。博弈论被应用解释个体行为的选择过程 ,确定出个体的转移概率。政府管理者应当关注和了解群体信息 ,为其制定政策提供有益的参考     

Bayesian inference for categorical data analysis

This article surveys Bayesian methods for categorical data analysis, with primary emphasis on contingency table analysis. Early innovations were proposed by Good (1953, 1956, 1965) for smoothing proportions in contingency tables and by Lindley (1964) for inference about odds ratios. These approaches primarily used conjugate beta and Dirichlet priors. Altham (1969, 1971) presented Bayesian analogs of small-sample frequentist tests for 2 x 2 tables using such priors. An alternative approach using normal priors for logits received considerable attention in the 1970s by Leonard and others (e.g., Leonard 1972). Adopted usually in a hierarchical form, the logit-normal approach allows greater flexibility and scope for generalization. The 1970s also saw considerable interest in loglinear modeling. The advent of modern computational methods since the mid-1980s has led to a growing literature on fully Bayesian analyses with models for categorical data, with main emphasis on generalized linear models such as logistic regression for binary and multi-category response variables.     

On the Markov Equivalence of Chain Graphs, Undirected Graphs, and Acyclic Digraphs

Graphical Markov models use undirected graphs (UDGs), acyclic directed graphs (ADGs), or (mixed) chain graphs to represent possible dependencies among random variables in a multivariate distribution. Whereas a UDG is uniquely determined by its associated Markov model, this is not true for ADGs or for general chain graphs (which include both UDGs and ADGs as special cases). This paper addresses three questions regarding the equivalence of graphical Markov models: when is a given chain graph Markov equivalent (1) to some UDG? (2) to some (at least one) ADG? (3) to some decomposable UDG? The answers are obtained by means of an extension of Frydenberg’s (1990) elegant graph-theoretic characterization of the Markov equivalence of chain graphs.