An empirical bayes approach to a variables acceptance sampling plan problem

An empirical Bayes approach to a variables acceptance sampling plan problem is presented and an empirical Bayes rule is developed which is shown to be asymptotically optimal under general conditions. The problem considered is one in which the ratio of the costs of accepting defective items and rejecting non-defective items is specified. Sampling costs are not considered and the size of the sample taken from each lot is fixed and constant. The empirical Bayes estimation of the Bayes rule is shown to require the estimation of a conditional probability. An estimator for conditional probabilities of the form needed is derived and shown to have good asymptotic properties.     

An optimization model for economic design of sampling plans based on conforming run length considering outgoing quality

In this article, a new economical acceptance sampling model is proposed based on Taguchi loss function. The objective function of the model consists of inspection cost, scrap cost, and Taguchi loss function including producer loss and consumer loss. The expected total cost includes the loss for an inspected item plus the loss for an accepted item which has not been inspected. Decision-making is based on conforming run length. It is assumed that the quality characteristics follow normal distribution. A numerical example is solved for illustrating application of this model. Sensitivity analysis is proposed for illustrating the effect of some important parameters on the objective function. Finally, we compared the results of the proposed method with classical Dodge–Romig sampling plans tables based on average outgoing quality limit. The results confirmed the superiority of proposed model.     

Bayesian design in queues: An application to aeronautic maintenance

We exploit Bayesian criteria for designing M/M/c//r$M/M/c//r$ queueing systems with spares. For illustration of our approach we use a real problem from aeronautic maintenance, where the numbers of repair crews and spare planes must be sufficiently large to meet the necessary operational capacity. Bayesian guarantees for this to happen can be given using predictive or posterior distributions.     

An application of robust Bayesian analysis to a medical experiment

This paper reviews a design for a clinical trail that uses expert opinion to guide the selection of treatments for patients in a way intended to be more favorable than random selection. The problems of analyzing data from the design are discussed. Using real data from a trial of two agents for treating hypertension after open heart surgery, issues of how to display the data are considered, and the extent to which the design and analysis may be robust to elicitation error is discussed.     

Inference under pivotal sampling: Properties,variance estimation,and application to tesselation for spatial sampling

Unequal probability sampling is commonly used for sample selection. In the context of spatial sampling, the variables of interest often present a positive spatial correlation, so that it is intuitively relevant to select spatially balanced samples. In this article, we study the properties of pivotal sampling and propose an application to tesselation for spatial sampling. We also propose a simple conservative variance estimator. We show that the proposed sampling design is spatially well balanced, with good statistical properties and is computationally very efficient.     

Bayesian and DEA efficiency modelling: an application to hospital foodservice operations

The significant impact of health foodservice operations on the total operational cost of the hospital sector has increased the need to improve the efficiency of these operations. Although important studies on the performance of foodservice operations have been published in various academic journals and industrial reports, the findings and implications remain simple and limited in scope and methodology. This paper investigates two popular methodologies in the efficiency literature: Bayesian “stochastic frontier analysis” (SFA) and “data envelopment analysis” (DEA). The paper discusses the statistical advantages of the Bayesian SFA and compares it with an extended DEA model. The results from a sample of 101 hospital foodservice operations show the existence of inefficiency in the sample, and indicate significant differences between the average efficiency generated by the Bayesian SFA and DEA models. The ranking of efficiency is, however, statistically independent of the methodologies.     

An adaptive sampling scheme guided by BART—with an application to predict processor performance

The evaluation of new processor designs is an important issue in electrical and computer engineering. Architects use simulations to evaluate designs and to understand trade‐offs and interactions among design parameters. However, due to the lengthy simulation time and limited resources, it is often practically impossible to simulate a full factorial design space. Effective sampling methods and predictive models are required. In this paper, the authors propose an automated performance predictive approach which employs an adaptive sampling scheme that interactively works with the predictive model to select samples for simulation. These samples are then used to build Bayesian additive regression trees, which in turn are used to predict the whole design space. Both real data analysis and simulation studies show that the method is effective in that, though sampling at very few design points, it generates highly accurate predictions on the unsampled points. Furthermore, the proposed model provides quantitative interpretation tools with which investigators can efficiently tune design parameters in order to improve processor performance. The Canadian Journal of Statistics 38: 136–152; 2010 © 2010 Statistical Society of Canada     

Bayesian hierarchical duration model for repeated events: an application to behavioral observations

This article presents a continuous-time Bayesian model for analyzing durations of behavior displays in social interactions. Duration data of social interactions are often complex because of repeated behaviors (events) at individual or group (e.g. dyad) level, multiple behaviors (multistates), and several choices of exit from a current event (competing risks). A multilevel, multistate model is proposed to adequately characterize the behavioral processes. The model incorporates dyad-specific and transition-specific random effects to account for heterogeneity among dyads and interdependence among competing risks. The proposed method is applied to child–parent observational data derived from the School Transitions Project to assess the relation of emotional expression in child–parent interaction to risk for early and persisting child conduct problems.     

Bayesian age-stratified joinpoint regression model: an application to lung and brain cancer mortality

Joinpoint regression model identifies significant changes in the trends of the incidence, mortality, and survival of a specific disease in a given population. The purpose of the present study is to develop an age-stratified Bayesian joinpoint regression model to describe mortality trend assuming that the observed counts are probabilistically characterized by the Poisson distribution. The proposed model is based on Bayesian model selection criteria with the smallest number of joinpoints that are sufficient to explain the Annual Percentage Change. The prior probability distributions are chosen in such a way that they are automatically derived from the model index contained in the model space. The proposed model and methodology estimates the age-adjusted mortality rates in different epidemiological studies to compare the trends by accounting the confounding effects of age. In developing the subject methods, we use the cancer mortality counts of adult lung and bronchus cancer, and brain and other Central Nervous System cancer patients obtained from the Surveillance Epidemiology and End Results data base of the National Cancer Institute.     

Bayesian spatial models with repeated measurements: with application to the herbaceous data analysis

This paper proposes a new statistical spatial model to analyze and predict the coverage percentage of the upland ground flora in the Missouri Ozark Forest Ecosystem Project (MOFEP). The flora coverage percentages are collected from clustered locations, which requires a new spatial model other than the traditional kriging method. The proposed model handles this special data structure by treating the flora coverage percentages collected from the clustered locations as repeated measurements in a Bayesian hierarchical setting. The correlation among the observations from the clustered locations are considered as well. The total vegetation coverage data in MOFEP is analyzed in this study. An Markov chain Monte Carlo algorithm based on the shrinkage slice sampler is developed for simulation from the posterior densities. The total vegetation coverage is modeled by three components, including the covariates, random spatial effect and correlated random errors. Prediction of the total vegetation coverage at unmeasured locations is developed.     

Bayesian inference over ICA models: application to multibiometric score fusion with quality estimates

Bayesian networks are not well-formulated for continuous variables. The majority of recent works dealing with Bayesian inference are restricted only to special types of continuous variables such as the conditional linear Gaussian model for Gaussian variables. In this context, an exact Bayesian inference algorithm for clusters of continuous variables which may be approximated by independent component analysis models is proposed. The complexity in memory space is linear and the overfitting problem is attenuated, while the inference time is still exponential. Experiments for multibiometric score fusion with quality estimates are conducted, and it is observed that the performances are satisfactory compared to some known fusion techniques.     

An application of ranked set sampling when observations from several distributions are to be included in the sample

ABSTRACT

In this article, we propose a method to estimate the common location and common scale parameters of several distributions using suitably defined ranked set sampling. Efficiency comparison of the obtained estimators with some of the standard estimators is made. Illustration of the results to real life data sets is also described.     

An application of a minimax Bayes rule and shrinkage estimators to the portofolio selection problem under the Bayesian approach

This paper shows that a minimax Bayes rule and shrinkage estimators can be effectively applied to portfolio selection under the Bayesian approach. Specifically, it is shown that the portfolio selection problem can result in a statistical decision problem in some situations. Following that, we present a method for solving a problem involved in portfolio selection under the Bayesian approach.     

Bayesian factor analysis for spatially correlated data: application to cancer incidence data in Scotland

A hierarchical Bayesian factor model for multivariate spatially correlated data is proposed. Multiple cancer incidence data in Scotland are jointly analyzed, looking for common components, able to detect etiological factors of diseases hidden behind the data. The proposed method searches factor scores incorporating a dependence within observations due to a geographical structure. The great flexibility of the Bayesian approach allows the inclusion of prior opinions about adjacent regions having highly correlated observable and latent variables. The proposed model is an extension of a model proposed by Rowe (2003a) and starts from the introduction of separable covariance matrix for the observations. A Gibbs sampling algorithm is implemented to sample from the posterior distributions.     

Discrete-time survival analysis under ranked set sampling: an application to Turkish motor insurance data

Survival models with continuous-time data are still superior methods of survival analysis. However when the survival data is discrete, taking it as continuous leads the researchers to incorrect results and interpretations. The discrete-time survival model has some advantages in applications such as it can be used for non-proportional hazards, time-varying covariates and tied observations. However, it has a disadvantage about the reconstruction of the survival data and working with big data sets. Actuaries are often rely on complex and big data whereas they have to be quick and efficient for short period analysis. Using the mass always creates inefficient processes and consumes time. Therefore sampling design becomes more and more important in order to get reliable results. In this study, we take into account sampling methods in discrete-time survival model using a real data set on motor insurance. To see the efficiency of the proposed methodology we conducted a simulation study.     

Bayesian Inference in Dynamic Disequilibrium Models: An Application to the Polish Credit Market

We propose a Bayesian approach for inference in a dynamic disequilibrium model. To circumvent the difficulties raised by the Maddala and Nelson (1974) specification in the dynamic case, we analyze a dynamic extended version of the disequilibrium model of Ginsburgh et al. (1980). We develop a Gibbs sampler based on the simulation of the missing observations. The feasibility of the approach is illustrated by an empirical analysis of the Polish credit market, for which we conduct a specification search using the posterior deviance criterion of Spiegelhalter et al. (2002).     

Bayesian Inference in Dynamic Disequilibrium Models: An Application to the Polish Credit Market

We propose a Bayesian approach for inference in a dynamic disequilibrium model. To circumvent the difficulties raised by the Maddala and Nelson (1974 Maddala , G. , Nelson , F. ( 1974 ). Maximum likelihood methods for models of markets in disequilibrium . Econometrica 42 ( 6 ): 1013 – 1030 .[Crossref], [Web of Science ®] , [Google Scholar]) specification in the dynamic case, we analyze a dynamic extended version of the disequilibrium model of Ginsburgh et al. (1980 Ginsburgh , V. , Tishler , A. , Zang , I. ( 1980 ). Alternative estimation methods for two regime models . European Economic Review 13 : 207 – 228 .[Crossref], [Web of Science ®] , [Google Scholar]). We develop a Gibbs sampler based on the simulation of the missing observations. The feasibility of the approach is illustrated by an empirical analysis of the Polish credit market, for which we conduct a specification search using the posterior deviance criterion of Spiegelhalter et al. (2002 Spiegelhalter , D. J. , Best , N. G. , Carlin , B. P. , Van Der Linde , A. ( 2002 ). Bayesian measures of complexity and fit . Journal of the Royal Statistical Society, Ser. B 64 : 583 – 639 .[Crossref] , [Google Scholar]).     

Empirical bayesInterval estimates: An application to geographical epidemiology

Summary Empirical Bayes estimates have been advocated as an improvement for mapping rare diseases or health events aggregated in small areas. In particular different parametric approaches have been proposed for dealing with non-normal data, assuming that disease occurrencies follow non-homogeneous Poisson law, whose parameters are treated as random variables. This paper shows how to conduct a complete Empirical Bayes analysis under an exchangeable model in the context of Geographical Epidemiology. Three different approaches for defining confidence limits obtained using a parametric bootstrap are compared: method 1 relies only on the first and second moment of the bootstrapped posterior distributions; method 2 computes the centiles of the bootstrapped posteriors; method 3 equates to α the average of the probabilities derived from the estimated bootstrapped cumulative posterior distributions. The simple Poisson-Gamma formulation was used to model mortality data on Larynx Cancer in the Local Health Units of Tuscany (1980–82 males). Two areas of significant elevated risk are identified.     

A Bayesian approach to Markov modelling in cost-effectiveness analyses: application to taxane use in advanced breast cancer

Summary. The paper demonstrates how cost-effectiveness decision analysis may be implemented from a Bayesian perspective, using Markov chain Monte Carlo simulation methods for both the synthesis of relevant evidence input into the model and the evaluation of the model itself. The desirable aspects of a Bayesian approach for this type of analysis include the incorporation of full parameter uncertainty, the ability to perform all the analysis, including each meta-analysis, in a single coherent model and the incorporation of expert opinion either directly or regarding the relative credibility of different data sources. The method is described, and its ease of implementation demonstrated, through a practical example to evaluate the cost-effectiveness of using taxanes for the second-line treatment of advanced breast cancer compared with conventional treatment. For completeness, the results from the Markov chain Monte Carlo simulation model are compared and contrasted with those from a classical Monte Carlo simulation model.