Posterior Regret Γ-Minimax Estimation and Prediction with Applications on k-Records Data Under Entropy Loss Function

Robust Bayesian analysis is connected with the effect of changing a prior within a class Γ instead of being specified exactly. The multiplicity of prior leads to a collection or a range of Bayes actions. It is interesting not only to investigate the range of estimators but also to recommend the optimal procedures. In this article, we deal with posterior regret Γ-minimax (PRGM) estimation and prediction of an unknown parameter θ and a value of a random variable Y under entropy loss function. Applications for k-records such as estimation and prediction problems are discussed.     

A Bayesian Inference and Stochastic Dynamic Programming Approach to Determine the Best Binomial Distribution

In this research, we employ Bayesian inference and stochastic dynamic programming approaches to select the binomial population with the largest probability of success from n independent Bernoulli populations based upon the sample information. To do this, we first define a probability measure called belief for the event of selecting the best population. Second, we explain the way to model the selection problem using Bayesian inference. Third, we clarify the model by which we improve the beliefs and prove that it converges to select the best population. In this iterative approach, we update the beliefs by taking new observations on the populations under study. This is performed using Bayesian rule and prior beliefs. Fourth, we model the problem of making the decision in a predetermined number of decision stages using the stochastic dynamic programming approach. Finally, in order to understand and to evaluate the proposed methodology, we provide two numerical examples and a comparison study by simulation. The results of the comparison study show that the proposed method performs better than that of Levin and Robbins (1981 Levin , B. , Robbins , H. ( 1981 ). Selecting the highest probability in Binomial or multinomial trials . Proc. Nat. Acad. Sci. USA 78 : 4663 – 4666 .[Crossref], [PubMed], [Web of Science ®] , [Google Scholar]) for some values of estimated probability of making a correct selection.     

Comparison among non parametric prediction intervals of order statistics

Abstract

In this article, we are interested in conducting a comparison study between different non parametric prediction intervals of order statistics from a future sample based on an observed order statistics. Typically, coverage probabilities of well-known non parametric prediction intervals may not reach the preassigned probability levels. Moreover, prediction intervals for predicting future order statistics are no longer available in some cases. For this, we propose different methods involving random indices and fractional order statistics. In each case, we find the optimal prediction intervals. Numerical computations are presented to assess the performances of the so-obtained intervals. Finally, a real-life data set is presented and analyzed for illustrative purposes.     

A characterization of stationary renewal processes and of memoryless distributions

We prove first that a renewal process is stationary if and only if the distributions of the age and the residual waiting time coincide for every t>0, and for 0≦x相似文献   

Group Dynamics in Development of the Poor: Experience from BRAC

The groups deliberately formed by nongovernmental organizations to organize the poor for their development are often subgrouped for better performance. In this connection, the study investigates the extent subgroups contribute to group performance, the mechanisms that lead to the contribution of subgroups to group performance, and changes in the contribution of subgroups to the performance of a group. Altogether 239 Bangladesh Rural Advancement Committee groups, i.e., village organizations (VOs), with and without subgroups were investigated. The VOs with subgroups performed better than those without subgroups. The performance of the VOs with subgroups, however, declined over time. One of the reasons why effectiveness of VOs with subgroups declined was the belief that pursuing subgroup responsibilities would not bring any personal gain for members.     

A rich learning lesson using the Poisson distribution

In this note, we explore the rich information about inference that the Poisson distribution has. The source of this information is mainly the fact that the mean and variance of this distribution are equal.     

A 6.55 factor primal-dual approximation algorithm for the connected facility location problem

In the connected facility location (ConFL) problem, we are given a graph G=(V,E) with nonnegative edge cost c _e on the edges, a set of facilities ??V, a set of demands (i.e., clients) $\mathcal{D}\subseteq VIn the connected facility location (ConFL) problem, we are given a graph G=(V,E) with nonnegative edge cost c _e on the edges, a set of facilities ℱ⊆V, a set of demands (i.e., clients) D í V\mathcal{D}\subseteq V , and a parameter M≥1. Each facility i has a nonnegative opening cost f _i and each client j has d _j units of demand. Our objective is to open some facilities, say F⊆ℱ, assign each demand j to some open facility i(j)∈F and connect all open facilities using a Steiner tree T such that the total cost, which is ?_{i ? F}f_i+?_{j ? D}d_jc_i(j)j+M?_{e ? T}c_e\sum_{i\in F}f_{i}+\sum_{j\in \mathcal{D}}d_{j}c_{i(j)j}+M\sum_{e\in T}c_{e} , is minimized. We present a primal-dual 6.55-approximation algorithm for the ConFL problem which improves the previous primal-dual 8.55-approximation algorithm given by Swamy and Kumar (Algorithmica 40:245–269, 2004).     

Women’s Strategic Responses to Intimate Partner Violence: A Study in a Rural Community of Bangladesh

The objective of this study was to explore women’s strategic responses to physical violence perpetrated by an intimate partner. Twenty women from a rural area of the Narshingdi district in the Dhaka division of Bangladesh who experienced physical violence at home participated in the study. Development of the interview protocol and data analysis were carried out by applying the consensual qualitative research (CQR) method. The results showed that several themes, such as women’s responses to intimate partner violence, arose from the data. First, coping strategies to pre‐violent events included three themes: (i) leaving the scene; (ii) trying to divert attention; and (iii) preparing to protest. Women’s strategic responses to violent events consisted of four themes: (i) leaving the scene; (ii) remaining silent or no giving response; (iii) seeking help from others; and (iv) protesting against the violence. Lastly, women’s strategic responses to post‐violent events consisted of three themes: (i) temporary abstinence; (ii) verbally abusive behavior to family members; and (iii) going to the parental home. Given the findings of this study, we conclude by suggesting that more work is needed to better understand effective strategies and to draw women to institutional services to prevent violence to a greater extent.