Which Wald statistic? Choosing a parameterization of the Wald statistic to maximize power in k-sample generalized estimating equations

The Wald statistic is known to vary under reparameterization. This raises the question: which parameterization should be chosen, in order to optimize power of the Wald statistic? We specifically consider k-sample tests of generalized linear models (GLMs) and generalized estimating equations (GEEs) in which the alternative hypothesis contains only two parameters. An example is presented in which such an alternative hypothesis is of interest. Amongst a general class of parameterizations, we find the parameterization that maximizes power via analysis of the non-centrality parameter, and show how the effect on power of reparameterization depends on sampling design and the differences in variance across samples. There is no single parameterization with optimal power across all alternatives. The Wald statistic commonly used under the canonical parameterization is optimal in some instances but it performs very poorly in others. We demonstrate results by example and by simulation, and describe their implications for likelihood ratio statistics and score statistics. We conclude that due to poor power properties, the routine use of score statistics and Wald statistics under the canonical parameterization for GEEs is a questionable practice.     

A framework for the comparison of maximum pseudo-likelihood and maximum likelihood estimation of exponential family random graph models

The statistical modeling of social network data is difficult due to the complex dependence structure of the tie variables. Statistical exponential families of distributions provide a flexible way to model such dependence. They enable the statistical characteristics of the network to be encapsulated within an exponential family random graph (ERG) model. For a long time, however, likelihood-based estimation was only feasible for ERG models assuming dyad independence. For more realistic and complex models inference has been based on the pseudo-likelihood. Recent advances in computational methods have made likelihood-based inference practical, and comparison of the different estimators possible.     

Two-stage approaches to the analysis of occupancy data I: the homogeneous case (analysis of occupancy data)

Abstract

Occupancy models are used in statistical ecology to estimate species dispersion. The two components of an occupancy model are the detection and occupancy probabilities, with the main interest being in the occupancy probabilities. We show that for the homogeneous occupancy model there is an orthogonal transformation of the parameters that gives a natural two-stage inference procedure based on a conditional likelihood. We then extend this to a partial likelihood that gives explicit estimators of the model parameters. By allowing the separate modeling of the detection and occupancy probabilities, the extension of the two-stage approach to more general models has the potential to simplify the computational routines used there.     

Interspecies Extrapolation of Physiological Pharmacokinetic Parameter Distributions

Three methods (multiplicative, additive, and allometric) were developed to extrapolate physiological model parameter distributions across species, specifically from rats to humans. In the multiplicative approach, the rat model parameters are multiplied by the ratio of the mean values between humans and rats. Additive scaling of the distributions is denned by adding the difference between the average human value and the average rat value to each rat value. Finally, allometric scaling relies on established extrapolation relationships using power functions of body weight. A physiologically-based pharmacokinetic model was fitted independently to rat and human benzene disposition data. Human model parameters obtained by extrapolation and by fitting were used to predict the total bone marrow exposure to benzene and the quantity of metabolites produced in bone marrow. We found that extrapolations poorly predict the human data relative to the human model. In addition, the prediction performance depends largely on the quantity of interest. The extrapolated models underpredict bone marrow exposure to benzene relative to the human model. Yet, predictions of the quantity of metabolite produced in bone marrow are closer to the human model predictions. These results indicate that the multiplicative and allometric techniques were able to extrapolate the model parameter distributions, but also that rats do not provide a good kinetic model of benzene disposition in humans.     

Generating autocorrelated pseudo-random numbers with specific distributions

An easily implemented and computationally efficient procedure is presented for the generation of autocorrelated pseudo-random numbers with specific probability distributions. A plot illustrates the relationship among the autocorrelations of the uniform, Rayleigh, and exponential distributions corresponding to a given autocorrelation in the normal generating distribution.     

Laplace Approximations for Natural Exponential Families with Cuts

Standard and fully exponential form Laplace approximations to marginal densities are described and conditions under which these give exact answers are investigated. A general result is obtained and is subsequently applied in the case of natural exponential families with cuts, in order to derive the marginal posterior density of the mean parameter corresponding to the cut, the canonical parameter corresponding to the complement of the cut and transformations of these. Important cases of families for which a cut exists and the approximations are exact are presented as examples     

On Efron's Parameterization

This paper discusses a curved exponential family of distributions which is defined by a differential equation with respect to the expectation parameters in the two–dimensional exponential family. The differential equation considered here is the same as the one given by Efron (1975) for the trinomial distribution. This equation is extended here to a general exponential family, and called Efron's parameterization in the two–dimensional exponential family. The solution of Efron's parameterization is obtained explicitly in an exponential family, although Kumagai & Inagaki (1996) showed that there exists no proper solution of Efron's equation for the trinomial distribution, in line with the counterexample given by Efron (1975 p. 1206). The paper gives some characterizations of Efron's parameterization with special reference to Fisher's circle model. The implications of these characterizations are the two–dimensional normal distribution and a spiral curve in the plane.     

Impact of Uncertainty Parameter Distribution on Robust Decision Making Outcomes for Climate Change Adaptation under Deep Uncertainty

Deep uncertainty in future climatic and economic conditions complicates developing infrastructure designed to last several generations, such as water reservoirs. In response, analysts have developed multiple robust decision frameworks to help identify investments and policies that can withstand a wide range of future states. Although these frameworks are adept at supporting decisions where uncertainty cannot be represented probabilistically, analysts necessarily choose probabilistic bounds and distributions for uncertain variables to support exploratory modeling. The implications of these assumptions on the analytical outcomes of robust decision frameworks are rarely evaluated, and little guidance exists in terms of how to select uncertain variable distributions. Here, we evaluate the impact of these choices by following the robust decision-making procedure, using four different assumptions about the probabilistic distribution of exogenous uncertainties in future climatic and economic states. We take a water reservoir system in Ethiopia as our case study, and sample climatic parameters from uniform, normal, extended uniform, and extended normal distributions; we similarly sample two economic parameters. We compute regret and satisficing robustness decision criteria for two performance measures, agricultural water demand coverage and net present value, and perform scenario discovery on the most robust reservoir alternative. We find lower robustness scores resulting from extended parameter distributions and demonstrate that parameter distributions can impact vulnerabilities identified through scenario discovery. Our results suggest that exploratory modeling within robust decision frameworks should sample from extended, uniform parameters distributions.     

CAXA在化工设备设计中的应用

随着化工设备设计过程中对零部件标准化、系列化程度的要求不断提高,应用计算机辅助技术进行优化设计和快速绘制化工设备图成为必然的发展趋势.应用国产计算机辅助技术软件-CAXA电子图板可实现化工设备零部件标准化、系列化设计,快速进行化工设备优化设计,降低设计人员劳动强度,提高化工设备制图速度.     

CP型单螺杆压缩机的计算机辅助设计

基于CP型单螺杆压缩机工作原理和主要零部件设计计算方法，利用三维建模、工程数据库、三维动画和可视界面等先进技术，完成了集实体建模、参数化设计和绘图、动画演示等功能于一体的计算机辅助设计系统。