Exact Bayesian Inference and Model Selection for Stochastic Models of Epidemics Among a Community of Households

Abstract.  Much recent methodological progress in the analysis of infectious disease data has been due to Markov chain Monte Carlo (MCMC) methodology. In this paper, it is illustrated that rejection sampling can also be applied to a family of inference problems in the context of epidemic models, avoiding the issues of convergence associated with MCMC methods. Specifically, we consider models for epidemic data arising from a population divided into households. The models allow individuals to be potentially infected both from outside and from within the household. We develop methodology for selection between competing models via the computation of Bayes factors. We also demonstrate how an initial sample can be used to adjust the algorithm and improve efficiency. The data are assumed to consist of the final numbers ultimately infected within a sample of households in some community. The methods are applied to data taken from outbreaks of influenza.     

On Confounding, Prediction and Efficiency in the Analysis of Longitudinal and Cross-sectional Clustered Data

Abstract.  In the analysis of clustered and/or longitudinal data, it is usually desirable to ignore covariate information for other cluster members as well as future covariate information when predicting outcome for a given subject at a given time. This can be accomplished through con-ditional mean models which merely condition on the considered subject's covariate history at each time. Pepe & Anderson (Commun. Stat. Simul. Comput. 23, 1994 , 939) have shown that ordinary generalized estimating equations may yield biased estimates for the parameters in such models, but that valid inferences can be guaranteed by using a diagonal working covariance matrix in the equations. In this paper, we provide insight into the nature of this problem by uncovering substantive data-generating mechanisms under which such biases will result. We then propose a class of asymptotically unbiased estimators for the parameters indexing the suggested conditional mean models. In addition, we provide a representation for the efficient estimator in our class, which attains the semi-parametric efficiency bound under the model, along with an efficient algorithm for calculating it. This algorithm is easy to apply and may realize major efficiency improvements as demonstrated through simulation studies. The results suggest ways to improve the efficiency of inverse-probability-of-treatment estimators which adjust for time-varying confounding, and are used to estimate the effect of discontinuing highly active anti-retroviral therapy (HAART) on viral load in HIV-infected patients.     

Functionally Compatible Local Characteristics for the Local Specification of Priors in Graphical Models

Abstract.  The local specification of priors in non-decomposable graphical models does not necessarily yield a proper joint prior for all the parameters of the model. Using results concerning general exponential families with cuts, we derive specific results for the multivariate Gamma distribution (conjugate prior for Poisson counts) and the Wishart distribution (conjugate prior for Gaussian models). These results link the existence of a locally specified joint prior to the solvability of a related marginal problem over the cliques of the graph.     

‘q-Pareto-Scalar’ Two-Stage Extremization Model and its Reducibility to One-Stage Model

A two-stage sequential choice model is studied, the first stage being defined by q-Pareto multicriterial choice rule, and the second stage being defined by scalar extremization model. In this model, at the first stage the q-Pareto rule choses alternatives which are not only undominated in terms of Pareto comparison, but also includes into choice the alternatives which are dominated by no more than q alternatives. Since the choice set of the first-stage usually contains too many elements, obtained set is used as a presentation for the second stage constructed by a scalar extremization model. The properties of the model are studied as well as its representability to one-stage scalar extremization model.     

Avoiding 'data snooping' in multilevel and mixed effects models

Summary.  Multilevel or mixed effects models are commonly applied to hierarchical data. The level 2 residuals, which are otherwise known as random effects, are often of both substantive and diagnostic interest. Substantively, they are frequently used for institutional comparisons or rankings. Diagnostically, they are used to assess the model assumptions at the group level. Inference on the level 2 residuals, however, typically does not account for 'data snooping', i.e. for the harmful effects of carrying out a multitude of hypothesis tests at the same time. We provide a very general framework that encompasses both of the following inference problems: inference on the 'absolute' level 2 residuals to determine which are significantly different from 0, and inference on any prespecified number of pairwise comparisons. Thus, the user has the choice of testing the comparisons of interest. As our methods are flexible with respect to the estimation method that is invoked, the user may choose the desired estimation method accordingly. We demonstrate the methods with the London education authority data, the wafer data and the National Educational Longitudinal Study data.     

Likelihood-based estimation for Gaussian MRFs

Markov random fields (MRFs) express spatial dependence through conditional distributions, although their stochastic behavior is defined by their joint distribution. These joint distributions are typically difficult to obtain in closed form, the problem being a normalizing constant that is a function of unknown parameters. The Gaussian MRF (or conditional autoregressive model) is one case where the normalizing constant is available in closed form; however, when sample sizes are moderate to large (thousands to tens of thousands), and beyond, its computation can be problematic. Because the conditional autoregressive (CAR) model is often used for spatial-data modeling, we develop likelihood-inference methodology for this model in situations where the sample size is too large for its normalizing constant to be computed directly. In particular, we use simulation methodology to obtain maximum likelihood estimators of mean, variance, and spatial-depencence parameters (including their asymptotic variances and covariances) of CAR models.     

大学英语"多元互补型"课堂教学模式

为更好地探究"多元互补型"课堂教学模式在西部地区地方性工科院校大学英语教学中的运用,首先指出"多元互补型"课堂教学模式是建立在一定的理论基础之上,接着阐述"多元互补型"课堂教学模式的具体构成,最后强调对大学英语"多元互补型"课堂教学模式的研究,旨在探索出适合于西部地区地方性工科院校大学英语教学的有效的教学模式,最终促进大学英语的教学改革.     

What can Statistics Contribute to a Causal Understanding?

Abstract.  We discuss the concept of causality in a broad manner. The traditional attitude in statistics has been to shy away from the causality concept. In recent years, however, a more proactive attitude to the causality concept has developed among statisticians. On the one hand, there is the school of counterfactual causality directed towards forming a better basis for clinical trials and epidemiology. On the other hand, there is the mechanistic view of causality. These developments are discussed and set into a larger context, where the often ignored role of time is emphasized. An extension of path analysis to stochastic processes is briefly presented. Causality is furthermore discussed in relation to genetic studies and to the emerging field of systems biology. Statisticians should also relate to the philosophical content of causality, especially that found in the foundations of physics.     

The impact of trade liberalisation on poverty and inequality: Evidence from CGE models

In this paper we carry out a systematic review of the evidence from CGE models regarding the effect of trade liberalisation on income inequality and poverty in developing countries. The evidence suggests quite strongly that trade liberalisation tends to reduce poverty, but is more likely to increase inequality than reduce it; however, the predicted effects are relatively small. Variation in the size and direction of effects can be explained by the choice of outcome measure, the fiscal response to liberalisation, the type of CGE model, and certain country characteristics – but not the method used to link the CGE model to the distribution of income.     

Determining the mean-variance relationship in generalized linear models—A parametric robust way

This article introduces a parametric robust way of determining the mean-variance relationship in the setting of generalized linear models. More specifically, the normal likelihood is properly amended to become asymptotically valid even if normality fails. Consequently, legitimate inference for the parametric relationship between mean and variance could be derived under model misspecification. More details are given to the scenario when the variance is proportional to an unknown power of the mean function. The efficacy of the novel technique is demonstrated via simulations and the analysis of two real data sets.