Empirical Uncertain Bayes Methods in Area‐level Models

Random effects model can account for the lack of fitting a regression model and increase precision of estimating area‐level means. However, in case that the synthetic mean provides accurate estimates, the prior distribution may inflate an estimation error. Thus, it is desirable to consider the uncertain prior distribution, which is expressed as the mixture of a one‐point distribution and a proper prior distribution. In this paper, we develop an empirical Bayes approach for estimating area‐level means, using the uncertain prior distribution in the context of a natural exponential family, which we call the empirical uncertain Bayes (EUB) method. The regression model considered in this paper includes the Poisson‐gamma and the binomial‐beta, and the normal‐normal (Fay–Herriot) model, which are typically used in small area estimation. We obtain the estimators of hyperparameters based on the marginal likelihood by using a well‐known expectation‐maximization algorithm and propose the EUB estimators of area means. For risk evaluation of the EUB estimator, we derive a second‐order unbiased estimator of a conditional mean squared error by using some techniques of numerical calculation. Through simulation studies and real data applications, we evaluate a performance of the EUB estimator and compare it with the usual empirical Bayes estimator.     

Can Demographic Variables Predict Lottery and Pari-mutuel Losses? An Empirical Investigation

Using data from the 2004 and 2005 Consumer Expenditure Surveys (CES) comprising of 15,000 respondents, this study examines two research questions. The first of these considers the demographic differences between households whose members lose money playing the lottery and/or engaging in pari-mutuel betting and those whose members do not lose money participating in such activities. The second assesses demographic differences among households whose members lose money playing the lottery and/or engaging in pari-mutuel betting. It was found that respondents living in money-losing households are slightly older, better off financially, more likely to be married or divorced, more likely to live in a state with at least one legal casino and more likely to live in the Northeast than respondents living in non-money-losing households. Among those living in money-losing households, the least wealthy and African American respondents are more likely to lose a higher proportion of their respective incomes purchasing lottery tickets and engaging in pari-mutuel betting than wealthier respondents and whites.     

Estimating powers of the generalized variance under the Pitman closeness criterion

For estimating powers of the generalized variance under a multivariate normal distribution with an unknown mean, the inadmissibility of the closest affine equivariant estimator is shown for the Pitman closeness criterion.     

Akaike Information Criterion for Selecting Variables in the Nested Error Regression Model

The Akaike Information Criterion (AIC) is developed for selecting the variables of the nested error regression model where an unobservable random effect is present. Using the idea of decomposing the likelihood into two parts of “within” and “between” analysis of variance, we derive the AIC when the number of groups is large and the ratio of the variances of the random effects and the random errors is an unknown parameter. The proposed AIC is compared, using simulation, with Mallows' C _p , Akaike's AIC, and Sugiura's exact AIC. Based on the rates of selecting the true model, it is shown that the proposed AIC performs better.     

GIS‐Based Integration of Social Vulnerability and Level 3 Probabilistic Risk Assessment to Advance Emergency Preparedness,Planning, and Response for Severe Nuclear Power Plant Accidents

In the nuclear power industry, Level 3 probabilistic risk assessment (PRA) is used to estimate damage to public health and the environment if a severe accident leads to large radiological release. Current Level 3 PRA does not have an explicit inclusion of social factors and, therefore, it is not possible to perform importance ranking of social factors for risk‐informing emergency preparedness, planning, and response (EPPR). This article offers a methodology for adapting the concept of social vulnerability, commonly used in natural hazard research, in the context of a severe nuclear power plant accident. The methodology has four steps: (1) calculating a hazard‐independent social vulnerability index for the local population; (2) developing a location‐specific representation of the maximum radiological hazard estimated from current Level 3 PRA, in a geographic information system (GIS) environment; (3) developing a GIS‐based socio‐technical risk map by combining the social vulnerability index and the location‐specific radiological hazard; and (4) conducting a risk importance measure analysis to rank the criticality of social factors based on their contribution to the socio‐technical risk. The methodology is applied using results from the 2012 Surry Power Station state‐of‐the‐art reactor consequence analysis. A radiological hazard model is generated from MELCOR accident consequence code system, translated into a GIS environment, and combined with the Center for Disease Control social vulnerability index (SVI). This research creates an opportunity to explicitly consider and rank the criticality of location‐specific SVI themes based on their influence on risk, providing input for EPPR.     

Bayesian modeling of dynamic extreme values: extension of generalized extreme value distributions with latent stochastic processes

This paper develops Bayesian inference of extreme value models with a flexible time-dependent latent structure. The generalized extreme value distribution is utilized to incorporate state variables that follow an autoregressive moving average (ARMA) process with Gumbel-distributed innovations. The time-dependent extreme value distribution is combined with heavy-tailed error terms. An efficient Markov chain Monte Carlo algorithm is proposed using a state-space representation with a finite mixture of normal distributions to approximate the Gumbel distribution. The methodology is illustrated by simulated data and two different sets of real data. Monthly minima of daily returns of stock price index, and monthly maxima of hourly electricity demand are fit to the proposed model and used for model comparison. Estimation results show the usefulness of the proposed model and methodology, and provide evidence that the latent autoregressive process and heavy-tailed errors play an important role to describe the monthly series of minimum stock returns and maximum electricity demand.     

Bayesian Estimators for Small Area Models Shrinking Both Means and Variances

For small area estimation of area‐level data, the Fay–Herriot model is extensively used as a model‐based method. In the Fay–Herriot model, it is conventionally assumed that the sampling variances are known, whereas estimators of sampling variances are used in practice. Thus, the settings of knowing sampling variances are unrealistic, and several methods are proposed to overcome this problem. In this paper, we assume the situation where the direct estimators of the sampling variances are available as well as the sample means. Using this information, we propose a Bayesian yet objective method producing shrinkage estimation of both means and variances in the Fay–Herriot model. We consider the hierarchical structure for the sampling variances, and we set uniform prior on model parameters to keep objectivity of the proposed model. For validity of the posterior inference, we show under mild conditions that the posterior distribution is proper and has finite variances. We investigate the numerical performance through simulation and empirical studies.     

《文学杂志》、《文艺月报》与左联活动探赜——以北方左联克服“关门主义”的过程为中心

1933年间,北平相继出现了两种大型文学杂志《文学杂志》和《文艺月报》。体裁与内容相似的这两种公开杂志之间有何关系?关于《文学杂志》,据当时左联负责人员陆万美的证言,它被当做了北方左联的机关刊物。但朱正以王志之在其《鲁迅印象记》里所描写的该杂志发刊筹备的情况为证据,主张它不是左联机关刊物。我再三慎重斟酌两种杂志的内容以及两位论者的主张,最后得出了如下结论:与朱正的主张相反,我认为《文学杂志》的产生是北方左联在纠正"关门主义"的过程中所做的实践之一。但这个富有重要意义的尝试也被文总(即指导左联的上级机关)视为"右倾化"的产物而拒绝了。负责开展左联活动的潘漠华、陆万美等人受到批判,左联又改变了方向。《文艺月报》是在文总的指导下以北平社联的负责人员为中心创办的刊物,它是在推动北方左联全体走上"左倾"路线起了很大作用的一种杂志。     

Shrinkage and modification techniques in estimation of variance and the related problems: A review

One of the surprising decision-theoretic results Charles Stein discovered is the inadmissibility of the uniformly minimum variance unbiased estirnator(UMVUE) of the variance of a normal distribution with an unknown mean. Some methods for deriving estimators better than the UMVUE were given by Stein. Brown, Brewster and Zidek. Recently Kubokawa established a novel approach, called the IERD method, by use of which one gets a unified class of improved estimators including their previous procedures. This paper gives a review for a series of these decision-theoretical developments as well as surveys the study of the variance-estimation problem from various aspects. Related to this issue, the paper enumerates several topics with the situations where the usual plain estimators are required to be shrunken or modified, and gives reasonable procedures improving the usual ones through the IERD method.     

Efficient Semiparametric Bayesian Estimation of Multivariate Discrete Proportional Hazards Model with Random Effects

We incorporate a random effect into a multivariate discrete proportional hazards model and propose an efficient semiparametric Bayesian estimation method. By introducing a prior process for the parameters of baseline hazards, we consider a nonparametric estimation of baseline hazards function. Using a state space representation, we derive a dynamic modeling of baseline hazards function and propose an efficient block sampler for Markov chain Monte Carlo method. A numerical example using kidney patients data is given.