On Reproducing Linear Estimators within the Gauss–Markov Model with Stochastic Constraints

In a Gauss–Markov Model (GMM) with fixed constraints, all the relevant estimators perfectly satisfy these constraints. As soon as they become stochastic, most estimators are allowed to satisfy them only approximately, thereby leaving room for nonvanishing residuals to describe the deviation from the prior information.

Sometimes, however, linear estimators may be preferred that are able to perfectly reproduce the prior information in form of stochastic constraints, including their variances and covariances. As typical example may be considered the case where a geodetic network ought to be densified without changing the higher-order point coordinates that are usually introduced together with their variances and (some) covariances. Traditional estimators are based on the “Helmert” or “S-transformation,” respectively an adaptation of the fixed-constraints Least-Squares estimator.

Here we show that neither approach generates the optimal reproducing estimator, which will be presented in detail and compared with the other reproducing estimators in terms of their MSE-risks.     

Two-sided Bayesian and frequentist tolerance intervals: general asymptotic results with applications

It is well known that that the construction of two-sided tolerance intervals is far more challenging than that of their one-sided counterparts. In a general framework of parametric models, we derive asymptotic results leading to explicit formulae for two-sided Bayesian and frequentist tolerance intervals. In the process, probability matching priors for such intervals are characterized and their role in finding frequentist tolerance intervals via a Bayesian route is indicated. Furthermore, in situations where matching priors are hard to obtain, we develop purely frequentist tolerance intervals as well. The findings are applied to real data. Simulation studies are seen to lend support to the asymptotic results in finite samples.     

Preschool-Age Adopted Chinese Girls’ Behaviors That Were Most Concerning to Their Mothers

Children's behavioral difficulties are a major source of parental concern. The goals of the current study were to (1) describe preschool-age adopted Chinese girls’ behaviors that were most concerning to their adoptive mothers and (2) examine the relation between children's concerning behaviors and parent/child demographics. Qualitative data from 422 mothers on 480 adopted Chinese girls (M = 44.2 months, SD = 15.2) were collected using three sequenced methods (i.e., open-ended question, follow-ups, and a focus group discussion). These girls were adopted at 3 to 60 months of age (M = 13.8, SD = 8.0) and had lived in the adoptive homes for at least 6 months (M = 30.2, SD = 14.4). Data analysis showed that 242 (57.3%) mothers (representing 274 girls) reported one to three concerning behaviors per child (total = 323 concerns), including behaviors that indicated attachment problems (107 or 33.1%), poor social skills (46 or 14.2%), language/speech problems (42 or 13%), sleep problems (29 or 9%), health/physical problems (24 or 7.4%), and problems in other areas (e.g., potty training) (75 or 23.2%). Further analysis showed that the mothers with prior experience of raising adopted children, but not biological children, were more likely to report concerning attachment behaviors than first-time mothers.     

Bayes sequential estimation in a life test and asymptotic properties

For a life test without replacement on M machines, assuming an exponential distribution for failure times, the Bayes sequential procedure for estimating the failure rate is studied. Estimation error is assumed to be measured by one of a family of loss functions, and the cost of sampling consists of a cost per machine failure c, >, 0 and a cost per unit time c > 0. Assuming a conjugate prior on 9, the Bayes sequential procedure and its asymptotic Bayesian and sampling theory properties are obtained as c1, z9 - 0 and M + jointly.     

Expert knowledge elicitation using item response theory

In an expert knowledge elicitation exercise, experts face a carefully constructed list of questions that they answer according to their knowledge. The elicitation process concludes when a probability distribution is found that adequately captures the experts' beliefs in the light of those answers. In many situations, it is very difficult to create a set of questions that will efficiently capture the experts' knowledge, since experts might not be able to make precise probabilistic statements about the parameter of interest. We present an approach for capturing expert knowledge based on item response theory, in which a set of binary response questions is proposed to the expert, trying to capture responses directly related to the quantity of interest. As a result, the posterior distribution of the parameter of interest will represent the elicited prior distribution that does not assume any particular parametric form. The method is illustrated by a simulated example and by an application involving the elicitation of rain prophets' predictions for the rainy season in the north-east of Brazil.     

Bayesian Analysis of Masked Data in Step-stress Accelerated Life Testing

This article considers a k level step-stress accelerated life testing (ALT) on series system products, where independent Weibull-distributed lifetimes are assumed for the components. Due to cost considerations or environmental restrictions, causes of system failures are masked and type-I censored observations might occur in the collected data. Bayesian approach combined with auxiliary variables is developed for estimating the parameters of the model. Further, the reliability and hazard rate functions of the system and components are estimated at a specified time at use stress level. The proposed method is illustrated through a numerical example based on two priors and various masking probabilities.     

Sensitivity of a bayesian inference to prior assumptions

The sensitivity of-a Bayesian inference to prior assumptions is examined by Monte Carlo simulation for the beta-binomial conjugate family of distributions. Results for the effect on a Bayesian probability interval of the binomial parameter indicate that the Bayesian inference is for the most part quite sensitive to misspecification of the prior distribution. The magnitude of the sensitivity depends primarily on the difference of assigned means and variances from the respective means and variances of the actually-sampled prior distributions. The effect of a disparity in form between the assigned prior and actually-sampled distributions was less important for the cases tested.     

Adaptive wavelet empirical Bayes estimation of a location or a scale parameter

Assume that in independent two-dimensional random vectors (X₁,θ₁),…,(X_n,θ_n), each θ_i is distributed according to some unknown prior density function g. Also, given θ_i=θ, X_i has the conditional density function q(x−θ), x,θ(−∞,∞) (a location parameter case), or θ⁻¹q(x/θ), x,θ(0,∞) (a scale parameter case). In each pair the first component is observable, but the second is not. After the (n+1)th pair (X_n+1,θ_n+1) is obtained, the objective is to construct an empirical Bayes (EB) estimator of θ. In this paper we derive the EB estimators of θ based on a wavelet approximation with Meyer-type wavelets. We show that these estimators provide adaptation not only in the case when g belongs to the Sobolev space H with an unknown , but also when g is supersmooth.     

教育现象学研究的程序和方法

现象学在其本质上是一种方法，一种让事物按照其本来面目显现出来的方法。这在教育现象学研究中具体表现为以下四道程序与方法：其一，将研究的对象转向师生所体验到的教育生活世界；其二，通过调查研究来观看个别的示例———个别师生所体验到的教育生活世界；其三，在个别示例的基础上对教育生活世界进行现象学还原，从而直观到教育的纯粹本质———教育生活世界的稳定结构；其四，将自己的研究成果与其他现象学者和其他方法的相关研究成果进行比较，以分析其中的异同和各自的利弊，从而使自己的研究变得更加完善。