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Recently, Kundu and Gupta (Metrika, 48: 83 C 97, 1998) established the asymptotic normality of the least squares estimators in the two dimensional cosine model. In this paper, we give the approximation to the general least squares estimators by using random weights which is called the Bayesian bootstrap or the random weighting method by Rubin (Annals of Statistics, 9: 130 C 134, 1981) and Zheng (Acta Math. Appl. Sinica (in Chinese), 10 (2): 247 C 253, 1987). A simulation study shows that this approximation works very well. [ABSTRACT FROM AUTHOR]

A procedure for estimating potential damage to buildings induced by accidental explosions on the railway is developed. By the damage failures of nearby structures due to actions generated by the accidental explosions are meant. This damage is measured in terms of probabilities of potential failures caused by explosions. The estimation of the damage probabilities is based on stochastic simulation of railway accidents involving an explosion. The proposed simulationâ€based procedure quantifies epistemic (stateâ€ofâ€knowledge) uncertainties in the damage probabilities. These uncertainties are expressed in terms of Bayesian prior and posterior distributions. The foundation of the procedure is a computer intensive method known as the Bayesian bootstrap. It is used for approximating the posterior distributions of damage probabilities. The application of the Bayesian bootstrap makes the proposed procedure highly automatic and convenient for assessing structures subjected to the hazard of the accidental actions. In addition, it can be used for specifying safe distances between the railway and nearby buildings. Structures of these buildings can be designed for tolerable probabilities of failures induced by accidental explosions. First Published Online: 27 Oct 2010

Business organizations are generating growing volumes of data about their employees, customers, and suppliers. Much of these data cannot be exploited for business value due to privacy and confidentiality concerns. National statistical agencies share sensitive data collected from individuals and businesses by modifying the data so individuals and firms cannot be identified but statistical utility is preserved. We build on this literature to develop a hybrid approach to data masking for business organizations. We demonstrate the validity of the hybrid approach, which we call multiple imputation with multimodal perturbation (MIMP), using Monte Carlo simulation and illustrate its application in a specific business context. Results of our analysis open new areas of research for information systems scholarship and new potential revenue sources for business organizations. [ABSTRACT FROM AUTHOR]

We propose a Bayesian approach for estimating the hazard functions under the constraint of a monotone hazard ratio. We construct a model for the monotone hazard ratio utilizing the Cox's proportional hazards model with a monotone time-dependent coefficient. To reduce computational complexity, we use a signed gamma process prior for the time-dependent coefficient and the Bayesian bootstrap prior for the baseline hazard function. We develope an efficient MCMC algorithm and illustrate the proposed method on simulated and real data sets. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, bootstrap prediction is adapted to resolve some problems in small sample datasets. The bootstrap predictive distribution is obtained by applying Breiman''s bagging to the plug-in distribution with the maximum likelihood estimator. The effectiveness of bootstrap prediction has previously been shown, but some problems may arise when bootstrap prediction is constructed in small sample datasets. In this paper, Bayesian bootstrap is used to resolve the problems. The effectiveness of Bayesian bootstrap prediction is confirmed by some examples. These days, analysis of small sample data is quite important in various fields. In this paper, some datasets are analyzed in such a situation. For real datasets, it is shown that plug-in prediction and bootstrap prediction provide very poor prediction when the sample size is close to the dimension of parameter while Bayesian bootstrap prediction provides stable prediction. [Copyright &y& Elsevier]

Traffic intensity is an important measure for assessing performance of a queueing system. In this paper, we propose a consistent and asymptotically normal estimator (CAN) of intensity for a queueing system with distribution-free interarrival and service times. Using this estimator and its estimated variance, a 100(1 − α)% asymptotic confidence interval of the intensity is constructed. Also, four bootstrap approaches—standard bootstrap, Bayesian bootstrap, percentile bootstrap, and bias-corrected and accelerated bootstrap are also applied to develop the confidence intervals of the intensity. A comparative analysis is conducted to demonstrate performances of the five confidence intervals of the intensity for a queueing system with short run data. [ABSTRACT FROM AUTHOR]

Process capability indices have been widely used in the manufacturing industry. While most studies consider estimation of capability indices for normal processes, comparatively little is known about their behavior in non-normal settings. Greenwich and Jahr-Schaffrath (Int. J. Qual. Reliab. Manage. 1995; 12:58–71) introduced the incapability index Cpp to evaluate processes. In this paper, we explore the interval estimation of the incapability index Cpp for non-normally distributed processes by utilizing seven feasible methods. We further develop an efficient criterion, which is relative coverage, to evaluate the performance of the seven methods. Detailed discussion of simulation results for six non-normally distributed processes is presented. The results display that the bootstrap pivotal method developed by Wasserman (All of Statistics: A Concise Course in Statistical Inference. Springer Science, Business Media, Inc., 2004) is the best feasible method to estimate Cpp. An example is also demonstrated to illustrate how the method may be used in practice. Copyright © 2008 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

Process capability indices have been widely used in the manufacturing industry. While most studies consider estimation of capability indices for normal processes, comparatively little is known about their behavior in non-normal settings. Greenwich and Jahr-Schaffrath (Int. J. Qual. Reliab. Manage. 1995; 12:58–71) introduced the incapability index Cpp to evaluate processes. In this paper, we explore the interval estimation of the incapability index Cpp for non-normally distributed processes by utilizing seven feasible methods. We further develop an efficient criterion, which is relative coverage, to evaluate the performance of the seven methods. Detailed discussion of simulation results for six non-normally distributed processes is presented. The results display that the bootstrap pivotal method developed by Wasserman (All of Statistics: A Concise Course in Statistical Inference. Springer Science, Business Media, Inc., 2004) is the best feasible method to estimate Cpp. An example is also demonstrated to illustrate how the method may be used in practice. Copyright © 2008 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

Abstract: It is well known that Efron''s bootstrap can fail in settings where the data are heavy tailed and when regularity conditions do not hold. Naturally this applies to weighted bootstrap schemes such as the Bayesian bootstrap. To deal with this, we introduce a Bayesian bootstrap analogue of the out of bootstrap. This bootstrap differs from traditional out of bootstraps in that all observations are used in the bootstrap test statistic. Moreover, the method is relatively robust to the selection of . We establish consistency for the new bootstrap and examine its other useful properties including a connection to the Dirichlet process. Several examples illustrating consistency in settings where the Efron bootstrap fails are given. Further generalizations are suggested. [Copyright &y& Elsevier]

This article proposes a weighted bootstrap procedure, which is an efficient bootstrap technique for neural model selection. Our primary interest in reducing computer effort is to not resample (in the original bootstrap procedure) uniformly from the original sample, but to modify this distribution in order to obtain variance reduction. The performance of the weighted bootstrap is demonstrated on two artificial data sets and one real dataset. Experimental results show that the weighted bootstrap procedure permits an approximately 2 to 1 reduction in replication size. [ABSTRACT FROM AUTHOR]

Abstract: Process incapability index Cpp has been proposed in the manufacturing industry to assess process incapability. In industries it is sometimes unable to get large samples, and, hence, the CAN (consistent and asymptotically normal) property of the unbiased estimator for Cpp is missing. In this paper, six bootstrap methods are applied to construct upper confidence bounds (UCBs) of Cpp for short-urn production processes where sample size is small; standard bootstrap (SB), Bayesian bootstrap (BB), bootstrap pivotal (BP), percentile bootstrap (PB), bias-corrected percentile bootstrap (BCPB), and bias-corrected and accelerated bootstrap (BCa). A numerical simulation study is conducted in order to demonstrate the performance of the six various estimation methods. We further investigate the accuracy of the six methods by calculating the relative coverage (defined as the ratio of coverage percentage to average length of UCB). Detailed discussions of simulation results for seven short-run processes are presented. Finally, one real example from Ford Company’s Windsor Casting Plant is used to illustrate the six interval estimation methods. [Copyright &y& Elsevier]

The receiver operating characteristic (ROC) curve is defined as true positive rate versus false positive rate obtained by varying a decision threshold criterion. It has been widely used in medical sciences for its ability to measure the accuracy of diagnostic or prognostic tests. Mathematically speaking, ROC curve is the composition of survival function of one population with the quantile function of another population. In this paper, we study strong approximation for the quantile processes of the Bayesian bootstrap (BB) resampling distributions, and use this result to study strong approximations for the BB version of the ROC process in terms of two independent Kiefer processes. The results imply asymptotically accurate coverage probabilities for the confidence bands for the ROC curve and confidence intervals for the area under the curve functional of the ROC constructed using the BB method. Similar results follow for the bootstrap resampling distribution. [ABSTRACT FROM AUTHOR]

A procedure for estimating potential damage to buildings induced by accidental explosions on the railway is developed. By the damage failures of nearby structures due to actions generated by the accidental explosions are meant. This damage is measured in terms of probabilities of potential failures caused by explosions. The estimation of the damage probabilities is based on stochastic simulation of railway accidents involving an explosion. The proposed simulation-based procedure quantifies epistemic (state-of-knowledge) uncertainties in the damage probabilities. These uncertainties are expressed in terms of Bayesian prior and posterior distributions. The foundation of the procedure is a computer intensive method known as the Bayesian bootstrap. It is used for approximating the posterior distributions of damage probabilities. The application of the Bayesian bootstrap makes the proposed procedure highly automatic and convenient for assessing structures subjected to the hazard of the accidental actions. In addition, it can be used for specifying safe distances between the railway and nearby buildings. Structures of these buildings can be designed for tolerable probabilities of failures induced by accidental explosions. [ABSTRACT FROM AUTHOR]

The present paper establishes conditional and unconditional central limit theorems for various resampling procedures for the t-statistic. The results work under fairly general conditions and the underlying random variables need not to be independent. Specific examples are then the m(n) (double) bootstrap out of k(n) observations, the Bayesian bootstrap and two-sample t-type permutation statistics. In case when m(n)/k(n) is bounded away from zero and infinity necessary and sufficient conditions for the conditional central limit law of the bootstrap t-statistics are established. For high resampling intensity when m(n)/k(n) tends to infinity the following general result is obtained. Without further other assumptions the bootstrap makes the resampled t-statistic automatically normal. The results are based on a general conditional limit theorem for weighted resampling statistics which is of own interest. [ABSTRACT FROM AUTHOR]

Estimates of mean response for a developmental toxicity study are developed using the techniques of Bayesian bootstrap. Using this method, a joint posterior distribution of mean response is simulated, providing a means for determining estimated variance and confidence statements. The approach allows for effects on litter size to be taken into consideration in the estimation of mean response. In addition a method is given for the incorporation of prior information into the analysis. The prior information may be information about mean response and about the litter size distribution as well. Results are compared with likelihood based estimates. [ABSTRACT FROM AUTHOR]

In this paper we consider a Bayesian nonparametric approach to the analysis of discrete-time queueing models. The main motivation consists in applications to telecommunications, and in particular to asynchronous transfer mode (ATM) systems. Attention is focused on the posterior distribution of the overflow rate. Since the exact distribution of such a quantity is not available in a closed form, an approximation based on “proper” Bayesian bootstrap is proposed, and its properties are studied. Some possible alternatives to proper Bayesian bootstrap are also discussed. Finally, an application to real data is provided. [Copyright &y& Elsevier]

Missing data refers to a class of problems made difficult by the absence of some portions of a familiar data structure For example, a regression problem might have some missing values in the predictor vectors This article concerns nonparametric approaches to assessing the accuracy of an estimator in a missing data situation. Three main topics are discussed: bootstrap methods for missing data, these methods' relationship to the theory of multiple imputation, and computationally efficient ways of executing them The simplest form of nonparametric bootstrap confidence interval turns out to give convenient and accurate answers There are interesting practical and theoretical differences between bootstrap methods and the multiple imputation approach, as well as some useful similarities [ABSTRACT FROM AUTHOR]

Confidence intervals for the mean function of the true proportion score ( μ), where ζ and x respectively denote the true proportion and observed test scores, can be approximated by the Efron, Bayesian, and parametric empirical Bayes (PEB) bootstrap procedures. The similarity of results yielded by all the bootstrap methods suggests the following: the unidentifiability problem of the prior distribution g(ζ) can be bypassed with respect to the construction of confidence intervals for the mean function, and a beta distribution for g(ζ) is a reasonable assumption for the test scores in compliance with a negative hypergeometric distribution. The PEB bootstrap, which reflects the construction of Morris intervals, is introduced for computing predictive confidence bands for ζ| x. It is noted that the effect of test reliability on the precision of interval estimates varies with the two types of confidence statements concerned. [ABSTRACT FROM AUTHOR]

The uniform distance between the distribution functions of the von Mises ω2-statistic for sampling from a continuous distribution and of the "generalized Bayesian ω2-statistic" for sampling from the uniform distribution on a finite number of points is estimated. Application to the generalized Bayesian bootstraps is discussed. [ABSTRACT FROM AUTHOR]

In the field of cognitive science, much research has been conducted on the diverse applications of artificial intelligence (AI). One important area of study is machines imitating human thinking. Although there are various approaches to development of thinking machines, we assume that human thinking is not always optimal in this paper. Sometimes, humans are driven by emotions to make decisions that are not optimal. Recently, deep learning has been dominating most machine learning tasks in AI. In the area of optimal decisions involving AI, many traditional machine learning methods are rapidly being replaced by deep learning. Therefore, because of deep learning, we can expect the faster growth of AI technology such as AlphaGo in optimal decision-making. However, humans sometimes think and act not optimally but emotionally. In this paper, we propose a method for building thinking machines imitating humans using Bayesian decision theory and learning. Bayesian statistics involves a learning process based on prior and posterior aspects. The prior represents an initial belief in a specific domain. This is updated to posterior through the likelihood of observed data. The posterior refers to the updated belief based on observations. When the observed data are newly added, the current posterior is used as a new prior for the updated posterior. Bayesian learning such as this also provides an optimal decision; thus, this is not well-suited to the modeling of thinking machines. Therefore, we study a new Bayesian approach to developing thinking machines using Bayesian decision theory. In our research, we do not use a single optimal value expected by the posterior; instead, we generate random values from the last updated posterior to be used for thinking machines that imitate human thinking. [ABSTRACT FROM AUTHOR]

Photovoltaic (PV) systems are widely spread across MV and LV distribution systems and the penetration of PV generation is solidly growing. Because of the uncertain nature of the solar energy resource, PV power forecasting models are crucial in any energy management system for smart distribution networks. Although point forecasts can suit many scopes, probabilistic forecasts add further flexibility to an energy management system and are recommended to enable a wider range of decision making and optimization strategies. This paper proposes methodology towards probabilistic PV power forecasting based on a Bayesian bootstrap quantile regression model, in which a Bayesian bootstrap is applied to estimate the parameters of a quantile regression model. A novel procedure is presented to optimize the extraction of the predictive quantiles from the bootstrapped estimation of the related coefficients, raising the predictive ability of the final forecasts. Numerical experiments based on actual data quantify an enhancement of the performance of up to 2.2% when compared to relevant benchmarks. [ABSTRACT FROM AUTHOR]

Although linear regression models are fundamental tools in statistical science, the estimation results can be sensitive to outliers. While several robust methods have been proposed in frequentist frameworks, statistical inference is not necessarily straightforward. We here propose a Bayesian approach to robust inference on linear regression models using synthetic posterior distributions based on γ-divergence, which enables us to naturally assess the uncertainty of the estimation through the posterior distribution. We also consider the use of shrinkage priors for the regression coefficients to carry out robust Bayesian variable selection and estimation simultaneously. We develop an efficient posterior computation algorithm by adopting the Bayesian bootstrap within Gibbs sampling. The performance of the proposed method is illustrated through simulation studies and applications to famous datasets. [ABSTRACT FROM AUTHOR]

Background: Partial factorial trials compare two or more pairs of treatments on overlapping patient groups, randomising some (but not all) patients to more than one comparison. The aims of this research were to compare different methods for conducting and analysing economic evaluations on partial factorial trials and assess the implications of considering factors simultaneously rather than drawing independent conclusions about each comparison.Methods: We estimated total costs and quality-adjusted life years (QALYs) within 10 years of surgery for 2252 patients in the Knee Arthroplasty Trial who were randomised to one or more comparisons of different surgical types. We compared three analytical methods: an "at-the-margins" analysis including all patients randomised to each comparison (assuming no interaction); an "inside-the-table" analysis that included interactions but focused on those patients randomised to two comparisons; and a Bayesian vetted bootstrap, which used results from patients randomised to one comparison as priors when estimating outcomes for patients randomised to two comparisons. Outcomes comprised incremental costs, QALYs and net benefits.Results: Qualitative interactions were observed for costs, QALYs and net benefits. Bayesian bootstrapping generally produced smaller standard errors than inside-the-table analysis and gave conclusions that were consistent with at-the-margins analysis, while allowing for these interactions. By contrast, inside-the-table gave different conclusions about which intervention had the highest net benefits compared with other analyses.Conclusions: All analyses of partial factorial trials should explore interactions and assess whether results are sensitive to assumptions about interactions, either as a primary analysis or as a sensitivity analysis. For partial factorial trials closely mirroring routine clinical practice, at-the-margins analysis may provide a reasonable estimate of average costs and benefits for the whole trial population, even in the presence of interactions. However, such conclusions will be misleading if there are large interactions or if the proportion of patients allocated to different treatments differs markedly from what occurs in clinical practice. The Bayesian bootstrap provides an alternative to at-the-margins analysis for analysing clinical or economic endpoints from partial factorial trials, which allows for interactions while making use of the whole sample. The same techniques could be applied to analyses of clinical endpoints.Trial Registration: ISRCTN, ISRCTN45837371 . Registered on 25 April 2003. [ABSTRACT FROM AUTHOR]