A Bayesian Approach to Selecting Covariates for Prediction

We consider the problem of selecting a regression model from a large class of possible models in the case where no true model is believed to exist. In practice few statisticians, or scientists who employ statistical methods, believe that a true model exists, but nonetheless they seek to select a model as a proxy from which they want to predict. Unlike much of the recent work in this area we address this problem explicitly. We develop Bayesian predictive model selection techniques when proper conjugate priors are used and obtain an easily computed expression for the model selection criterion. We also derive expressions for updating the value of the statistic when a predictor is dropped from the model and apply this approach to a large well-known data set.     

Cross validation of ridge regression estimator in autocorrelated linear regression models

ABSTRACT

In this paper, we investigated the cross validation measures, namely OCV, GCV and Cp under the linear regression models when the error structure is autocorrelated and regressor data are correlated. The best performed ridge regression estimator is obtained by getting the optimal ridge parameter so as to minimize these measures. A Monte Carlo simulation study is given to see how the optimal ridge parameter is affected by autocorrelation and the strength of multicollinearity.     

Uniformity of Node Level Conflict Measures in Bayesian Hierarchical Models Based on Directed Acyclic Graphs

Hierarchical models defined by means of directed, acyclic graphs are a powerful and widely used tool for Bayesian analysis of problems of varying degrees of complexity. A simulation‐based method for model criticism in such models has been suggested by O'Hagan in the form of a conflict measure based on contrasting separate local information sources about each node in the graph. This measure is however not well calibrated. In order to rectify this, alternative mutually similar tail probability‐based measures have been proposed independently and have been proved to be uniformly distributed under the assumed model in quite general normal models with known covariance matrices. In the present paper, we extend this result to a variety of models. An advantage of this is that computationally costly pre‐calibration schemes needed for some other suggested methods can be avoided. Another advantage is that non‐informative prior distributions can be used when performing model criticism.     

A review of some adaptive statistical techniques

We present several methods for full, partial, and practical adaptation. Selector statistics that are measures of skewness, peakedness, and tailweight are used, primarily in estimating loca-tion in some single-sample situations. We note several practical adaptive techniques in current use, including illustrations in-volving stepwise regression, analysis of variance, ridge regres-sion, and splines. We suggest some areas in which future develop-ment of adaptive methods is needed:density estimation; M, R, and L estimation in regression; and dependent data. There is also a need to develop better selector statistics.     

Measuring what matters and guiding policy: An evaluation of the Genuine Progress Indicator

This article examines the Genuine Progress Indicator (GPI), which seeks to respond to the shortcomings of GDP and the main contemporary challenges to welfare. As a monetary indicator, the GPI is uniquely suited to evaluate the impact of policy proposals and its dashboard-like features are able to track changes in contributing variables. While the GPI is currently not available for use in cross-country analyses, it will be measurable using a standard methodology once certain data issues have been resolved and a consensus is reached on GPI 2.0. Currently, the main obstacles to its widespread use are lack of political leadership and institutional support.     

中立型两阶段交叉效率评价方法

在数据包络分析中,已有的两阶段交叉效率评价方法,不仅只能用于基本两阶段网络结构,而且没有中立地分解子阶段效率。文章提出了一个既适用于基本两阶段网络结构,又适用于具有共享输入的两阶段网络结构的,中立型交叉效率评价方法。该方法定义自评时整体效率等于子阶段效率的加权和,在自评整体效率最大的前提下,从使各子阶段效率都尽可能大的角度为每个决策单元分别确定一组最优权重,进而通过互评计算决策单元整体和子阶段的最终效率得分。最后,通过两个实例验证了方法的实用、合理、有效。     

Perspective‐taking and gift‐giving in Chinese preschool children

This study explored Chinese preschool children's perspective‐taking via a gift‐giving paradigm. Unlike findings with North American children (Atance et al. in, Dev Psychol 46:1505–1513, 2010), the results from two experiments (N_{Exp. 1} = 329; N_{Exp. 2} = 112) showed that allowing Chinese children to first choose a desired object for themselves did not enhance their subsequent perspective‐taking performance in gift selection or gift justifications. This was true regardless of gift type (consumable or recreational items) or of recipient (mom, teacher, experimenter, or friend). In addition, children's perspective‐taking did not correlate with their performances in behavioral inhibition and delay of gratification tasks. These results suggest the possibility that the prior desire fulfillment effect varies with children's socio‐cultural experiences. Finally, Chinese children showed better perspective‐taking in choosing consumable gifts (e.g., drinks, snacks) than recreational gifts (e.g., toys, magazines), although this effect was not found for gift selection in Experiment 2. One interpretation of these results is that children's capacity for prosocial perspective‐taking is influenced by socio‐cultural experiences and social knowledge about individuals' preferences for different kinds of objects.     

Partial order relations for classification comparisons

The Bayes classification rule offers the optimal classifier, minimizing the classification error rate, whereas the Neyman–Pearson lemma offers the optimal family of classifiers to maximize the detection rate for any given false alarm rate. These motivate studies on comparing classifiers based on similarities between the classifiers and the optimal. In this article, we define partial order relations on classifiers and families of classifiers, based on rankings of rate function values and rankings of test function values, respectively. Each partial order relation provides a sufficient condition, which yields better classification error rates or better performance on the receiver operating characteristic analysis. Various examples and applications of the partial order theorems are discussed to provide comparisons of classifiers and families of classifiers, including the comparison of cross-validation methods, training data that contains outliers, and labelling errors in training data. The Canadian Journal of Statistics 48: 152–166; 2020 © 2019 Statistical Society of Canada     

Parallel, AA/BB, AB/BA and Balaam's design: efficient and maximin choices when testing the treatment effect in a mixed effects linear regression

When examining the effect of treatment A versus B, there may be a choice between a parallel group design, an AA/BB design, an AB/BA cross‐over and Balaam's design. In case of a linear mixed effects regression, it is examined, starting from a flexible function of the costs involved and allowing for subject dropout, which design is most efficient in estimating this effect. For no carry‐over, the AB/BA cross‐over design is most efficient as long as the dropout rate at the second measurement does not exceed 2ρ/(1 + ρ), ρ being the intraclass correlation. For steady‐state carry‐over, depending on the costs involved, the dropout rate and ρ, either a parallel design or an AA/BB design is most efficient. For types of carry‐over that allow for self carry‐over, interest is in the direct treatment effect plus the self carry‐over effect, with either an AA/BB or Balaam's design being most efficient. In case of insufficient knowledge on the dropout rate or ρ, a maximin strategy is devised: choose the design that minimizes the maximum variance of the treatment estimator. Such maximin designs are derived for each type of carry‐over. Copyright © 2012 John Wiley & Sons, Ltd.     

Iterative Bias Correction of the Cross‐Validation Criterion

Abstract. The cross‐validation (CV) criterion is known to be asecond‐order unbiased estimator of the risk function measuring the discrepancy between the candidate model and the true model, as well as the generalized information criterion (GIC) and the extended information criterion (EIC). In the present article, we show that the 2kth‐order unbiased estimator can be obtained using a linear combination from the leave‐one‐out CV criterion to the leave‐k‐out CV criterion. The proposed scheme is unique in that a bias smaller than that of a jackknife method can be obtained without any analytic calculation, that is, it is not necessary to obtain the explicit form of several terms in an asymptotic expansion of the bias. Furthermore, the proposed criterion can be regarded as a finite correction of a bias‐corrected CV criterion by using scalar coefficients in a bias‐corrected EIC obtained by the bootstrap iteration.