Bayesian analysis of categorical data informatively censored

This article presents a general Bayesian analysis of incomplete categorical data considered as generated by a statistical model involving the categorical sampling process and the observable censoring process. The novelty is that we allow dependence of the censoring process paramenters on the sampling categories; i.e., an informative censoring process. In this way, we relax the assumptions under which both classical and Bayesian solutions have been de-veloped. The proposed solution is outlined for the relevant case of the censoring pattern based on partitions. It is completely developed for a simple but typical examples. Several possible extensions of our procedure are discussed in the final remarks.     

A class of statistics based on the information concept

The methodic use of Shannon's entropy as a basic concept, complementing probability, leads to a new class of statistics which provides, inter alia, a measure of mutual dissimilarity y between several frequency distributions. Application to contin-gency tables with any number of dimensions yields a dimension-less, standardised contingency coefficient which depends on the direction of inference and will combine multiplicatively with the number of observed events. This class of statistics further in-cludes a continuous modification W of the number of degrees of freedom in a table, and a measure Q of its overall information content. Numerical illustrations and comparisons with former re-sults are worked out. Direct applications include the optimal partition of a quasicontinuum into cells by maximizing Q, the ordering of unordered tables by minimising local values of y, and a tentative absolute weighting of inductive inference based on the minimal necessary shift, required by an hypothesis, between the actually observed data and a set of assumed future events.     

Efficient posterior integration in stable paretian models

The paper proposes a Markov Chain Monte Carlo method for Bayesian analysis of general regression models with disturbances from the family of stable distributions with arbitrary characteristic exponent and skewness parameter. The method does not require data augmentation and is based on combining fast Fourier transforms of the characteristic function to get the likelihood function and a Metropolis random walk chain to perform posterior analysis. Both a validation nonlinear regression and a nonlinear model for the Standard and Poor’s composite price index illustrate the method.     

Time series analysis of non-Gaussian observations based on state space models from both classical and Bayesian perspectives

The analysis of non-Gaussian time series by using state space models is considered from both classical and Bayesian perspectives. The treatment in both cases is based on simulation using importance sampling and antithetic variables; Markov chain Monte Carlo methods are not employed. Non-Gaussian disturbances for the state equation as well as for the observation equation are considered. Methods for estimating conditional and posterior means of functions of the state vector given the observations, and the mean-square errors of their estimates, are developed. These methods are extended to cover the estimation of conditional and posterior densities and distribution functions. The choice of importance sampling densities and antithetic variables is discussed. The techniques work well in practice and are computationally efficient. Their use is illustrated by applying them to a univariate discrete time series, a series with outliers and a volatility series.     

Nonparametric Bayes estimation in repair models

Consider a sequence of dependent random variables _X1,_X2,…,_Xn$X_1,X_2,\dots ,X_n$, where _X1$X_1$ has distribution F (or probability measure P  ), and the distribution of _Xi+1$X_{i+1}$ given _X1,…,_Xi$X_1,\dots ,X_i$ and other covariates and environmental factors depends on F   and the previous data, i=1,…,n-1$i=1,\dots ,n-1$. General repair models give rise to such random variables as the failure times of an item subject to repair. There exist nonparametric non-Bayes methods of estimating F in the literature, for instance, Whitaker and Samaniego [1989. Estimating the reliability of systems subject to imperfect repair. J. Amer. Statist. Assoc. 84, 301–309], Hollander et al. [1992. Nonparametric methods for imperfect repair models. Ann. Statist. 20, 879–896] and Dorado et al. [1997. Nonparametric estimation for a general repair model. Ann. Statist. 25, 1140–1160], etc. Typically these methods apply only to special repair models and also require repair data on N independent items until exactly only one item is left awaiting a “perfect repair”.     

Model-based clustering with non-elliptically contoured distributions

The majority of the existing literature on model-based clustering deals with symmetric components. In some cases, especially when dealing with skewed subpopulations, the estimate of the number of groups can be misleading; if symmetric components are assumed we need more than one component to describe an asymmetric group. Existing mixture models, based on multivariate normal distributions and multivariate t distributions, try to fit symmetric distributions, i.e. they fit symmetric clusters. In the present paper, we propose the use of finite mixtures of the normal inverse Gaussian distribution (and its multivariate extensions). Such finite mixture models start from a density that allows for skewness and fat tails, generalize the existing models, are tractable and have desirable properties. We examine both the univariate case, to gain insight, and the multivariate case, which is more useful in real applications. EM type algorithms are described for fitting the models. Real data examples are used to demonstrate the potential of the new model in comparison with existing ones.     

长江三角洲城市旅游资源空间一体化分析

由上海、南京、杭州、苏州等15座旅游城市组成的长江三角洲城市旅游空间一体化发展区域,在我国的区域旅游发展中占有极其重要的地位。对该区域城市旅游空间一体化发展加以研究具有深刻的意义。文章对长江三角洲城市旅游资源的类型结构、强度效应、聚集效应、城际差异、绝对丰度、相对丰度、总丰度、空间结构及其主题功能进行了系统分析与比较。     

A bivariate generalized geometric distribution with applications

This paper proposes a bivariate version of the univariate discrete generalized geometric distribution considered by Gómez–Déniz (2010 Gómez–Déniz, E. (2010). Another generalization of the geometric distribution. Test 19:399–415.[Crossref], [Web of Science ®] , [Google Scholar]). The proposed bivariate distribution can have a positive or negative correlation coefficient which can be used for modeling bivariate-dependent count data. After discussing some of its properties, maximum likelihood estimation is discussed. Two illustrative examples are given for fitting and demonstrating the usefulness of the new bivariate distribution proposed here.     

A new class of bivariate lifetime distributions

This paper introduces a new class of bivariate lifetime distributions. Let {X_i}_{i ? 1} and {Y_i}_{i ? 1} be two independent sequences of independent and identically distributed positive valued random variables. Define T₁ = min?(X₁, …, X_M) and T₂ = min?(Y₁, …, Y_N), where (M, N) has a discrete bivariate phase-type distribution, independent of {X_i}_{i ? 1} and {Y_i}_{i ? 1}. The joint survival function of (T₁, T₂) is studied.