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Both philosophically and in practice, statistics is dominated by frequentist and Bayesian thinking. Under those paradigms, our courses and textbooks talk about the accuracy with which true model parameters are estimated or the posterior probability that they lie in a given set. In nonparametric problems, they talk about convergence to the true function (density, regression, etc.) or the probability that the true function lies in a given set. But the usual paradigms' focus on learning the true model and parameters can distract the analyst from another important task: discovering whether there are many sets of models and parameters that describe the data reasonably well. When we discover many good models we can see in what ways they agree. Points of agreement give us more confidence in our inferences, but points of disagreement give us less. Further, the usual paradigms' focus seduces us into judging and adopting procedures according to how well they learn the true values. An alternative is to judge models and parameter values, not procedures, and judge them by how well they describe data, not how close they come to the truth. The latter is especially appealing in problems without a true model. [ABSTRACT FROM AUTHOR]

Both philosophically and in practice, statistics is dominated by frequentist and Bayesian thinking. Under those paradigms, our courses and textbooks talk about the accuracy with which true model parameters are estimated or the posterior probability that they lie in a given set. In nonparametric problems, they talk about convergence to the true function (density, regression, etc.) or the probability that the true function lies in a given set. But the usual paradigms' focus on learning the true model and parameters can distract the analyst from another important task: discovering whether there are many sets of models and parameters that describe the data reasonably well. When we discover many good models we can see in what ways they agree. Points of agreement give us more confidence in our inferences, but points of disagreement give us less. Further, the usual paradigms' focus seduces us into judging and adopting procedures according to how well they learn the true values. An alternative is to judge models and parameter values, not procedures, and judge them by how well they describe data, not how close they come to the truth. The latter is especially appealing in problems without a true model. [ABSTRACT FROM AUTHOR]

The article presents comment on the stud regarding the methods used in topic modeling in document analysis. It recognizes the use of formally Bayesian approach to modeling and estimation and complexity-penalized regularization, as an alternative lens to the process. It discusses the result of the study and commends the researchers for making a significant contribution to future directions in document analysis.

In the past 20 years, there has been a staggering increase in the use of Bayesian statistical inference, based on Markov chain Monte Carlo (MCMC)methods, to estimate model parameters and other quantities of interest. This trend exists in virtually all areas of engineering and science. In a typical application, researcherswill report estimates of parametric functions (e.g., quantiles, probabilities, or predictions of future outcomes) and corresponding intervals from MCMC methods. One difficulty with the use of inferentialmethods based on Monte Carlo (MC) is that reported results may be inaccurate due to MC error. MC error, however, can be made arbitrarily small by increasing the number of MC draws. Most users of MCMC methods seem to use indirect diagnostics, trial-and-error, or guess-work to decide how long to run a MCMC algorithm and accuracy of MCMC output results is rarely reported. Unless careful analysis is done, reported numerical results may contain digits that are completely meaningless. In this article, we describe an algorithm to provide direct guidance on the number of MCMC draws needed to achieve a desired amount of precision (i.e., a specified number of accurate significant digits) for Bayesian credible interval endpoints. [ABSTRACT FROM AUTHOR]

Bayesian credible interval (CI) estimation is a statistical procedure that has been well addressed in both the theoretical and applied literature. Parametric assumptions regarding baseline data distributions are critical for the implementation of this method. We provide a nonparametric technique for incorporating prior information into the equal-tailed (ET) and highest posterior density (HPD) CI estimators in the Bayesianmanner. We propose to use a data-driven likelihood function, replacing the parametric likelihood function to create a distribution-free posterior. Higher order asymptotic propositions are derived to show the efficiency and consistency of the proposed method. We demonstrate that the proposed approach may correct confidence regions with respect to skewness of the data distribution. An extensive Monte Carlo (MC) study confirms the proposed method significantly outperforms the classical CI estimation in a frequentist context. A real data example related to a study of myocardial infarction illustrates the excellent applicability of the proposed technique. Supplementary material, including the R code used to implement the developed method, is available online. [ABSTRACT FROM AUTHOR]

The article discusses issues related to spatial structure, accounting for complex survey design, and Bayesian computation. The need for more complicated model to validate and assess the simpler model to assess the simpler model in isolation is tackled. The approach to accounting for complex survey design and the design effects for the aggregated data sources are also outlined.

Rank aggregation, that is, combining several ranking functions (called base rankers) to get aggregated, usually stronger rankings of a given set of items, is encountered in many disciplines. Most methods in the literature assume that base rankers of interest are equally reliable. It is very common in practice, however, that some rankers are more informative and reliable than others. It is desirable to distinguish high quality base rankers from low quality ones and treat them differently. Some methods achieve this by assigning prespecified weights to base rankers. But there are no systematic and principled strategies for designing a proper weighting scheme for a practical problem. In this article, we propose a Bayesian approach, called Bayesian aggregation of rank data (BARD), to overcome this limitation. By attaching a quality parameter to each base ranker and estimating these parameters along with the aggregation process, BARD measures reliabilities of base rankers in a quantitative way and makes use of this information to improve the aggregated ranking. In addition, we design a method to detect highly correlated rankers and to account for their information redundancy appropriately. Both simulation studies and real data applications show that BARD significantly outperforms existing methods when equality of base rankers varies greatly. [ABSTRACT FROM AUTHOR]

The article presents comment on the study regarding ways to improve interpretability of statistical language models. It discusses the difficulties involved in model interpretation in analyzing topics which could result to frustration when goals are unclear. It discusses the result of the study and commends the researchers for proving the usefulness of the unsupervised topic modeling in the interpretation and labeling of topics.

The missionary zeal of many Bayesians of old has been matched, in the other direction, by an attitude among some theoreticians that Bayesian methods were absurd—not merely misguided but obviously wrong in principle. We consider several examples, beginning with Feller's classic text on probability theory and continuing with more recent cases such as the perceived Bayesian nature of the so-called doomsday argument. We analyze in this note the intellectual background behind various misconceptions about Bayesian statistics, without aiming at a complete historical coverage of the reasons for this dismissal. [ABSTRACT FROM AUTHOR]

The article discusses the insights of the authors on the comments of other authors regarding their article on the analysis of reliability growth. It says that the authors did not develop a maximum likelihood estimation (MLE) for the variable k since limiting metrics provide finite k estimates. It tells that the authors agree to use the Bayesian strategy to deal with the fix effectiveness factors. The authors concede that the analysis of n and x as pseudo trials and failures was needless.

Modeling recurrent event data is of current interest in statistics and engineering. This article proposes a framework for incorporating covariates in flowgraph models, with application to recurrent event data in systems reliability settings. A flowgraph is a generalized transition graph (GTG) originally developed to model total system waiting times for semi-Markov processes. The focus of flowgraph models is expanded by linking covariates into branch transition models, enriching the toolkit of available data analysis methods for complex stochastic systems. This article takes a Bayesian approach to the analysis of flowgraph models. Potential applications are not limited to engineering systems, but also extend to survival analysis. [ABSTRACT FROM AUTHOR]

We present a tractable class of nonregular continuous statistical models where 1) likelihoods have multiple singularities and ordinary maximum likelihood is intrinsically unavailable, but 2) Bayes procedures achieve convergence rates better than n-1 across the whole parameter space. In fact, for every p > 1, there is a member of the class for which the posterior distribution is consistent at rate n-p uniformly in the parameter. [ABSTRACT FROM AUTHOR]

In many branches of modern science, researchers first study or mine large datasets, and then select the parameters they estimate and the data they use and publish. Such data-based selection complicates formal statistical inference. An example discussed here for the purpose of illustration, is that of pharmaceutical companies that typically conduct many experiments but may publish only selected data. The selection often depends on the outcomes of the experiments since naturally there is interest in potentially useful drugs, and it is in general unclear how it should affect inference. Is this effect the same for the company and the public? Does it matter if they are Bayesian or frequentist? Should the company reveal all experiments it conducts and, if so, how should this change the conclusions? This note discusses these questions in terms of a simple example of a sequence of binomial experiments conducted by a pharmaceutical company, where results are published only if the number of "failures" is small. We do not suggest that this example corresponds to reality in the pharmaceutical industry, nor in science in general; our goal is to elaborate on the importance and difficulties of taking selection into account when performing statistical analysis. [ABSTRACT FROM AUTHOR]

Since the U.S. Environmental Protection Agency began widespread monitoring of PM2.5 (particulate matter <2.5 p in diameter) concentration levels in the late 1990s, the epidemiological community has performed several observational studies directly relating PM2.5 concentration to various health endpoints including mortality and morbidity. However, recent research suggests that human exposure to the constituents of PM2.5 may differ significantly from ambient (or outdoor) PM2.5 concentration measured by monitors because people spend a great deal of time in environments, such as various indoor environments, where they are partially shielded from ambient sources of PM and are exposed to nonambient sources of PM. Recent research has provided some ways to include exposure information, but little has been done to determine the impact of including such information in a statistical model. To address this concern, we develop a three-stage Bayesian hierarchical model based on the Poisson regression model that is traditionally used to characterize the relationship between PM2.5 concentration and health endpoints. Our approach includes a spatial model relating monitor readings to average county PM2.5 concentration and an exposure simulator that links average ambient PM2.5 concentration to average personal exposure using activity pattern data. We apply our model to a study population in North Carolina and explore the impact of various exposure modeling assumptions on the conclusions that can be drawn about the link between PM2.5 exposure and cardiovascular mortality. [ABSTRACT FROM AUTHOR]

The problem of marginal density estimation for a multivariate density function f (x) can be generally stated as a problem of density function estimation for a random vector λ(x) of dimension lower than that of x. In this article, we propose a technique, the so-called continuous Contour Monte Carlo (CCMC) algorithm, for solving this problem. CCMC can be viewed as a continuous version of the contour Monte Carlo (CMC) algorithm recently proposed in the literature. CCMC abandons the use of sample space partitioning and incorporates the techniques of kernel density estimation into its simulations. CCMC is more general than other marginal density estimation algorithms. First, it works for any density functions, even for those having a rugged or unbalanced energy landscape. Second, it works for any transformation λ(x) regardless of the availability of the analytical form of the inverse transformation. In this article, CCMC is applied to estimate the unknown normalizing constant function for a spatial autologistic model, and the estimate is then used in a Bayesian analysis for the spatial autologistic model in place of the true normalizing constant function. Numerical results on the U.S. cancer mortality data indicate that the Bayesian method can produce much more accurate estimates than the MPLE and MCMLE methods for the parameters of the spatial autologistic model. [ABSTRACT FROM AUTHOR]

We propose classification models for binary and multicategory data where the predictor is a random function. We use Bayesian modeling with wavelet basis functions that have nice approximation properties over a large class of functional spaces and can accommodate a wide variety of functional forms observed in real life applications. We develop an unified hierarchical model to encompass both the adaptive wavelet-based function estimation model and the logistic classification model. We couple together these two models are to borrow strengths from each other in a unified hierarchical framework. The use of Gibbs sampling with conjugate priors for posterior inference makes the method computationally feasible. We compare the performance of the proposed model with other classification methods, such as the existing naive plug-in methods, by analyzing simulated and real data sets. [ABSTRACT FROM AUTHOR]

In the applications of finite mixture of regression (FMR) models, often many covariates are used, and their contributions to the response variable vary from one component to another of the mixture model. This creates a complex variable selection problem. Existing methods, such as the Akaike information criterion and the Bayes information criterion, are computationally expensive as the number of covariates and components in the mixture model increases. In this article we introduce a penalized likelihood approach for variable selection in FMR models. The new method introduces penalties that depend on the size of the regression coefficients and the mixture structure. The new method is shown to be consistent for variable selection. A data-adaptive method for selecting tuning parameters and an EM algorithm for efficient numerical computations are developed. Simulations show that the method performs very well and requires much less computing power than existing methods. The new method is illustrated by analyzing two real data sets. [ABSTRACT FROM AUTHOR]

We propose Bayesian parametric and semiparametric partially linear regression methods to analyze the outcome-dependent follow-up data when the random time of a follow-up measurement of an individual depends on the history of both observed longitudinal Outcomes and previous measurement times. We begin with the investigation of the simplifying assumptions of Lipsitz, Fitzmaurice, Ibrahim, Gelber, and Lipshultz, and present a new model for analyzing such data by allowing subject-specific correlations for the longitudinal response and by introducing a subject-specific latent variable to accommodate the association between the longitudinal measurements and the follow-up times. An extensive simulation study shows that our Bayesian partially linear regression method facilitates accurate estimation of the true regression line and the regression parameters. We illustrate our new methodology using data from a longitudinal observational study. [ABSTRACT FROM AUTHOR]

This article introduces the problem of determining the probability that a rotating and bouncing cylinder (i.e.. flipped coin) will land and conic to rest on its edge. We present this problem and analysis as a practical, nontrivial example to introduce the reader to Bayesian model comparison. Several models are presented. each of which take into consideration different physical aspects of the problem and the relative effects on the edge landing probability. The Bayesian formulation of model comparison is then used to compare the models and their predictive agreement with data from hand-flipped cylinders of several sizes. [ABSTRACT FROM AUTHOR]

An important use of experimental designs is in screening, in which experimenters seek to identify significant effects (both main effects and potentially interactions) from a large set of candidate effects. This article goes further than identification of effects, introducing a design criterion that seeks to maximize the ability to discriminate between models. Motivated by the work of Meyer, Steinberg, and Box, the Bayesian criterion is based on the Hellinger distance between predictive distributions under competing models. A bound for the criterion is obtained, greatly improving interpretability. The set of all possible models to compare is huge, and not all models are equally plausible. This challenge is addressed through prior distributions on the space of models that indicate preference for intuitively appealing models, such as those with few effects, more low-order than high-order effects, and inheritance structure between active main effects and interactions. Techniques for evaluating the criterion and searching for optimal designs are presented. The effectiveness of the criterion is illustrated with a number of examples that consider regular and nonregular designs, robust designs, and scenarios with partial prior knowledge of which effects are significant. [ABSTRACT FROM AUTHOR]

We present a framework that enables computer model evaluation oriented toward answering the question: Does the computer model adequately represent reality? The proposed validation framework is a six-step procedure based on Bayesian and likelihood methodology. The Bayesian methodology is particularly well suited to treating the major issues associated with the validation process: quantifying multiple sources of error and uncertainty in computer models, combining multiple sources of information, and updating validation assessments as new information is acquired. Moreover, it allows inferential statements to be made about predictive error associated with model predictions in untested situations. The framework is implemented in a test bed example of resistance spot welding, to provide context for each of the six steps in the proposed validation process. [ABSTRACT FROM AUTHOR]

The rapid development of biological technology in recent years has generated an overwhelming quantity of highly complex genetical data. In retrospect it is perhaps now obvious that standard stochastic sampling algorithms were destined to fail when applied to the type of models that these data require. During this period, both the genetics and statistics research communities have developed a range of new algorithms that have endeavored to avoid these failures. This article presents a brief journey through the development of some of these algorithms. I hope to demonstrate that continued collaborative research and education in both genetics and statistics disciplines is crucial for the advancement of future sampling frameworks, and call on researchers in both fields to take up this challenge. [ABSTRACT FROM AUTHOR]

The problem considered involves forecasting the future costs of hard drives of various capacities and speeds of revolution or, more generally, forecasting the future costs of various quantifiably different versions of a commodity that is subject to technological advance. In the primary development, it is supposed that the data consist of past and present costs. A model is proposed in which the past. present, and future costs of each version are related with each other and also with the costs of the other versions. The model encompasses a stochastic version of an empirical relationship known as Moore's law. A forecasting methodology was developed by adopting a Bayesian approach and taking the prior distribution to be of a relatively tractable them. An implementation of the Gibbs sampler was devised top making draws from the posterior distribution of the future costs: the forecasts are based on those draws. The proposed methodology was used to obtain forecasts retrospectively from data accumulated (over a 5-year period) on the quarterly costs of hard drives. The accuracy of the longer-term forecasts compared favorably with those of certain benchmark forecasts, whereas the accuracy of the shorter-term forecasts compared less favorably. Greater accuracy can be achieved through enhancements to the proposed methodology that provide for the use of supplementary information (i.e., information that is relevant but not fully reflected in the past and present costs). [ABSTRACT FROM AUTHOR]

The article presents a discussion on the previous article entitled "Hidden Markov Models for Microarray Time Course Data in Multiple Biological Conditions. " The article presented a new approach in researching and analyzing microarray expression data, utilizing the empirical Bayes method. This practice helped to share information across a range of time. By using the authors' technique, gene expression can be monitored in each of its states and across varying conditions. Several other options were suggested, such as the ANOVA approach, but were weary of using it due to a potential for low power.

This article addresses issues of model criticism and model comparison in Bayesian contexts, and focuses on the use of the so-called posterior predictive p values (ppp). These involve a general discrepancy or conflict measure and depend on the prior, the model, and the data. They are used in statistical practice to quantify the degree of surprise or conflict in data and to compare different combinations of prior and model. The distribution of such ppp values is far from uniform however, as we demonstrate for different models, making their interpretation and comparison a difficult matter. We propose a natural calibration of the ppp values, where the resulting cppp values are uniform on the unit interval under model conditions. The cppp values, which in general rely on a double-simulation scheme for their computation, may then be used to assess and compare different priors and models. Our methods also make it possible to compare parametric and nonparametric model specifications, in that genuine "measures of surprise" are put on the same canonical uniform scale. We illustrate our techniques for some applications to real data. We also present supplementing theoretical results on various properties of the ppp and cppp. [ABSTRACT FROM AUTHOR]

The lack of an agreed inferential basis for statistics makes life "interesting" for academic statisticians, but at the price of negative implications for the status of statistics in industry, science, and government. The practice of our discipline will mature only when we can come to a basic agreement about how to apply statistics to real problems. Simple and more general illustrations are given of the negative consequences of the existing schism between frequentists and Bayesians. An assessment of strengths and weaknesses of the frequentist and Bayes systems of inference suggests that calibrated Bayes—a compromise based on the works of Box, Rubin, and others—captures the strengths of both approaches and provides a roadmap for future advances. The approach asserts that inferences under a particular model should be Bayesian, but model assessment can and should involve frequentist ideas. This article also discusses some implications of this proposed compromise for the teaching and practice of statistics. [ABSTRACT FROM AUTHOR]

Case-control studies are among the most commonly used means of assessing association between exposure and outcome. Sample size determination and the optimal control-to-case ratio are vital to the design of such studies. In this article we investigate Bayesian sample size determination and the control-to-case ratio for case-control studies, when interval estimation is the goal of the eventual statistical analysis. In certain cases we are able to derive approximate closed-form sample size formulas. We also describe two Monte Carlo methods, each of which provides a unified approach to the sample size problem, because they may be applied to a wide range of interval-based criteria. We compare the accuracy of the different methods. We also extend our methods to include cross-sectional designs and designs for gene-environment interaction studies. [ABSTRACT FROM AUTHOR]

We introduce a general perspective on the introduction of skewness into symmetric distributions. Through inverse probability integral transformations we provide a constructive representation of skewed distributions, where the skewing mechanism and the original symmetric distributions are specified separately. We study the effects of the skewing mechanism on, e.g., modality, tail behavior and the amount of skewness generated. The representation is used to introduce novel classes of skewed distributions, where we induce certain prespecified characteristics through particular choices of the skewing mechanism. Finally, we use a Bayesian linear regression framework to compare the new classes with some existing distributions in the context of two empirical examples. [ABSTRACT FROM AUTHOR]

Modern Bayesian statistical methods, such as Gibbs and Metropolis-Hastings sampling, were developed to liberate statisticians from the necessity of making large-sample assumptions and to facilitate the numerical approximation of problems that had previously been analytically intractable. Counter to this trend, we develop a method for constructing asymptotic joint posterior approximations based on models with k blocks of parameters and where the corresponding properly normalized full conditionals are themselves asymptotically normal. We illustrate these techniques by applying them to particular linear and generalized linear mixed models (GLMMs). We also consider the relevance of different parameterizations with regard to our asymptotics. Recent work has indicated that Gibbs samplers based on so-called "centering parameterizations" result in better convergence properties for the resulting Markov chains. Our results for the one-way random-effects model shed some light on this issue. For this example, we also consider the distinction between letting the within-group sample size, n, tend to infinity versus letting the number of groups K (as defined by the random-effects part of the model) tend to infinity. Letting n grow results in a proper limiting normal distribution only when the weight on the prior for the variance component grows at a rate comparable to n. With large K, on the other hand, proper limits are obtained without this assumption, and thus it is seen that the information in the data will ultimately swamp standard prior information. We compare results based on simulated data when n and K are large. A dataset involving the effect of smoking on hormone function is analyzed using our asymptotics and compared with results based on Gibbs sampling. [ABSTRACT FROM AUTHOR]

We propose a new stochastic algorithm for Bayesian-optimal design in nonlinear and high-dimensional contexts. Following Peter Muller, we solve an optimization problem by exploring the expected utility surface through Markov chain Monte Carlo simulations. The optimal design is the mode of this surface considered a probability distribution. Our algorithm relies on a "particle" method to efficiently explore high-dimensional multimodal surfaces, with simulated annealing to concentrate the samples near the modes. We first test the method on an optimal allocation problem for which the explicit solution is available, to compare its efficiency with a simpler algorithm. We then apply our method to a challenging medical case study in which an optimal protocol treatment needs to be determined. For this case, we propose a formalization of the problem in the framework of Bayesian decision theory, taking into account physicians' knowledge and motivations. We also briefly review further improvements and alternatives. [ABSTRACT FROM AUTHOR]

Randomized comparisons among several treatments give rise to an incomplete-blocks structure known as mixed treatment comparisons (MTCs). To analyze such data structures, it is crucial to assess whether the disparate evidence sources provide consistent information about the treatment contrasts. In this article we propose a general method for assessing evidence inconsistency in the framework of Bayesian hierarchical models. We begin with the distinction between basic parameters, which have prior distributions, and functional parameters, which are defined in terms of basic parameters. Based on a graphical analysis of MTC structures, evidence inconsistency is defined as a relation between a functional parameter and at least two basic parameters, supported by at least three evidence sources. The inconsistency degrees of freedom (ICDF) is the number of such inconsistencies. We represent evidence consistency as a set of linear relations between effect parameters on the log odds ratio scale, then relax these relations to allow for inconsistency by adding to the model random inconsistency factors (ICFs). The number of ICFs is determined by the ICDF. The overall consistency between evidence sources can be assessed by comparing models with and without ICFs, whereas their posterior distribution reflects the extent of inconsistency in particular evidence cycles. The methods are elucidated using two published datasets, implemented with standard Markov chain Monte Carlo software. [ABSTRACT FROM AUTHOR]

This article proposes a two-stage statistical method for the analysis of multivariate computer experiments when at least one of the output dimensions is large. The stage-one data are modeled by a multivariate extension of a widely used scalar statistical model for computer output. Conditioned on stage-one data, a simple statistical model is then proposed for the stage-two data. The method is demonstrated in a geophysical application involving an ocean model. [ABSTRACT FROM AUTHOR]

This article considers a robust Bayesian approach to the sample size determination problem. We focus on global Bayesian robustness that studies lower bound (Ln), upper bound (Un), and range (Rn) of posterior quantities of interest, obtained as the prior varies in a class of distributions. Specifically, we are interested in the selection of an appropriate sample size that gives guarantees to the researcher of observing a small value of the range and, depending on the problems, either a sufficiently large lower bound or a sufficiently small upper bound. Toward this end, we approach the problem as a design issue and provide new sample size determination criteria based on summaries of the predictive distributions of Ln, Un, and Rn, such as expectations and tail probabilities. Relationships and comparison to standard classical and (nonrobust) Bayesian methods are discussed. The proposed methods are studied for the normal model with conjugate priors and used for choosing the size of a clinical trial. [ABSTRACT FROM AUTHOR]

We consider the problem of variable or feature selection for model-based clustering. The problem of comparing two nested subsets of variables is recast as a model comparison problem and addressed using approximate Bayes factors. A greedy search algorithm is proposed for finding a local optimum in model space. The resulting method selects variables (or features), the number of clusters, and the clustering model simultaneously. We applied the method to several simulated and real examples and found that removing irrelevant variables often improved performance. Compared with methods based on all of the variables, our variable selection method consistently yielded more accurate estimates of the number of groups and lower classification error rates, as well as more parsimonious clustering models and easier visualization of results. [ABSTRACT FROM AUTHOR]

A novel fully automatic Bayesian procedure for variable selection in normal regression models is proposed. The procedure uses the posterior probabilities of the models to drive a stochastic search. The posterior probabilities are computed using intrinsic priors, which can be considered default priors for model selection problems; that is, they are derived from the model structure and are free from tuning parameters. Thus they can be seen as objective priors for variable selection. The stochastic search is based on a Metropolis-Hastings algorithm with a stationary distribution proportional to the model posterior probabilities. The procedure is illustrated on both simulated and real examples. [ABSTRACT FROM AUTHOR]

The article presents abstracts of articles related to computational and graphical statistics. They include "The R Commander: A Basic-Statistics Graphical User Interface to R," "Bivariate Poisson and Diagonal Inflated Bivariate Poisson Regression Models in R," "Monkeying With the Goodness-of-Fit Test," "A CLUE for CLUster Ensembles," "BayesX: Analyzing Bayesian Structured Additive Regression Models," "Bayesian Analysis for Penalized Spline Regression Using WinBUGS," and "Introducing BACCO: An R Bundle for Bayesian Analysis of Computer Code Output."

This article introduces a simple Bayesian method for ranking college football teams. The parameter space is the set of all possible rankings, and individual game results are modeled by taking the odds that the lower ranked team wins to be β : 1, where β < 1. As a result, the likelihood for a given ranking is a function solely of the number of in-sample errors, and by choosing the parameter β to be very close to zero, we may effectively minimize the number of in-sample errors. We propose both a modified Gibbs sampler algorithm for exploring the posterior distribution and an associated importance sampling scheme for examining the impact of individual games on the posterior mean ranks. We rank teams according to their posterior mean ranks, and we use simulations to compare the performance of this ranking to that of rankings produced by standard methods that use the same (win/loss only) information. We find that the new method is almost as good as standard methods in predicting unknown game results, while far outdoing standard methods in matching known game results. An outlier-resistance property of the ranking method is illustrated using the importance sampling scheme. [ABSTRACT FROM AUTHOR]

The support vector machine (SVM) is known for its good performance in two-class classification, but its extension to multiclass classification is still an ongoing research is- sue. In this article, we propose a new approach for classification, called the import vector machine (IVM), which is built on kernel logistic regression (KLR). We show that the IVM not only performs as well as the SVM in two-class classification, but also can naturally be generalized to the multiclass case. Furthermore, the IVM provides an estimate of the underlying probability. Similar to the support points of the SVM, the IVM model uses only a fraction of the training data to index kernel basis functions, typically a much smaller fraction than the SVM. This gives the IVM a potential computational advantage over the SVM. [ABSTRACT FROM AUTHOR]

Describing the structure in a two-way contingency table in terms of an RC(m) association model, we are concerned with the computation of posterior distributions of the model parameters using prior distributions which take into account the nonlinear restrictions of the model. We are further involved with the determination of the order of association in, based on Bayesian arguments. Using projection methods, a prior distribution over the parameters of the simpler RC(m) model is induced from a prior of the parameters of the saturated model. The fit of the assumed RC(m) model is evaluated using the posterior distribution of its distance from the full model. Our methods are illustrated with a popular dataset. [ABSTRACT FROM AUTHOR]

Causal effects are defined as comparisons of potential outcomes under different treatments on a common set of units. Observed values of the potential outcomes are revealed by the assignment mechanism-a probabilistic model for the treatment each unit receives as a function of covariates and potential outcomes. Fisher made tremendous contributions to causal inference through his work on the design of randomized experiments, but the potential outcomes perspective applies to other complex experiments and nonrandomized studies as well. As noted by Kempthorne in his 1976 discussion of Savage's Fisher lecture, Fisher never bridged his work on experimental design and his work on parametric modeling, a bridge that appears nearly automatic with an appropriate view of the potential outcomes framework, where the potential outcomes and covariates are given a Bayesian distribution to complete the model specification. Also, this framework crisply separates scientific inference for causal effects and decisions based on such inference, a distinction evident in Fisher's discussion of tests of significance versus tests in an accept/reject framework. But Fisher never used the potential outcomes framework, originally proposed by Neyman in the context of randomized experiments, and as a result he provided generally flawed advice concerning the use of the analysis of covariance to adjust for posttreatment concomitants in randomized trials. [ABSTRACT FROM AUTHOR]

A Bayesian model for off-line signature verification involving the representation of a signature through its curvature is developed. The prior model makes use of a spatial point process for specifying the knots in an approximation restricted to a buffer region close to a template curvature, along with an independent time-warping mechanism. In this way, prior shape information about the signature can be built into the analysis. The observation model is based on additive white noise superimposed on the underlying curvature. The approach is implemented using Markov chain Monte Carlo and applied to a collection of documented instances of William Shakespeare's signature. [ABSTRACT FROM AUTHOR]

Broadly speaking, nineteenth century statistics was Bayesian, while the twentieth century was frequentist, at least from the point of view of most scientific practitioners. Here in the twenty-first century scientists are bringing statisticians much bigger problems to solve, often comprising millions of data points and thousands of parameters. Which statistical philosophy will dominate practice? My guess, backed up with some recent examples, is that a combination of Bayesian and frequentist ideas will be needed to deal with our increasingly intense scientific environment. This will be a challenging period for statisticians, both applied and theoretical, but it also opens the opportunity for a new golden age, rivaling that of Fisher, Neyman, and the other giants of the early 1900s. What follows is the text of the 164th ASA presidential address, delivered at the awards ceremony in Toronto on August 10, 2004. [ABSTRACT FROM AUTHOR]

This article compares three methods for computing the posterior probabilities of the possible orders in polynomial regression models. These posterior probabilities are used for forecasting using Bayesian model averaging. It is shown that Bayesian model averaging provides a closer relationship between the theoretical coverage of the high-density predictive interval (HDPI) and the observed coverage than those corresponding to selecting the best model. The performance of the different procedures is illustrated with simulations and some known engineering data. [ABSTRACT FROM AUTHOR]

Sample size determination is among the most commonly en- countered tasks in statistical practice. A broad range of frequentist and Bayesian methods for sample size determination can be described as choosing the smallest sample that is sufficient to achieve some set of goals. An example for the frequentist is seeking the smallest sample size that is sufficient to achieve a desired power at a specified significance level. An example for the Bayesian is seeking the smallest sample size necessary to obtain, in expectation, a desired rate of correct classification of the hypothesis as true or false. This article explores parallels between Bayesian and frequentist methods for determining sample size. We provide a simple but general and pragmatic framework for investigating the relationship between the two approaches, based on identifying mappings to connect the Bayesian and frequentist inputs necessary to obtain the same sample size. We illustrate this mapping with examples, highlighting a somewhat surprising "approximate functional correspondence" between power-based and information-based optimal sample sizes. [ABSTRACT FROM AUTHOR]

Almost all of the current nonparametric regression methods, such as smoothing splines, generalized additive models. and varying-coefficients models, assume a linear relationship when nonparametric functions are regarded as parameters. In this article we propose a general class of smoothing spline nonlinear nonparametric models that allow nonparametric functions to act nonlinearly. They arise in many fields as either theoretical or empirical models. Our new estimation methods are based on an extension of the Gauss-Newton method to infinite-dimensional spaces and the backfitting procedure. We extend the generalized cross-validation and generalized maximum likelihood methods to estimate smoothing parameters. We establish connections between some nonlinear nonparametric models and nonlinear mixed-effects models. We derive approximate Bayesian confidence intervals for inference. We illustrate the methods with an application to term structure of interest rates and conduct simulations to evaluate the finite-sample performance of our methods. [ABSTRACT FROM AUTHOR]

This article describes a Bayesian approach to estimating the spectral density of a stationary time series. A nonparametric prior on the spectral density is described through Bernstein polynomials. Because the actual likelihood is very complicated, a pseudoposterior distribution is obtained by updating the prior using the Whittle likelihood. A Markov chain Monte Carlo algorithm for sampling from this, posterior distribution is described that is used for computing the posterior mean, variance, and other statistics. A consistency result is established for this pseudoposterior distribution that holds for a short-memory Gaussian time series and under some conditions on the prior. To prove this asymptotic result, a general consistency theorem of Schwartz is extended for a triangular array of independent, nonidentically distributed observations. This extension is also of independent interest. A simulation study is conducted to compare the proposed method with some existing methods. The method is illustrated with the well-studied sunspot dataset. [ABSTRACT FROM AUTHOR]

Analytical or coding errors in posterior simulators can produce reasonable but incorrect approximations of posterior moments. This article develops simple tests of posterior simulators that detect both kinds of errors, and uses them to detect and correct errors in two previously published articles. The tests exploit the fact that a Bayesian model specifies the joint distribution of observables (data) and unobservables (parameters). There are two joint distribution simulators. The marginal-conditional simulator draws unobservables from the prior and then observables conditional on unobservables. The successive-conditional simulator alternates between the posterior simulator and an observables simulator. Formal comparison of moment approximations of the two simulators reveals existing analytical or coding errors in the posterior simulator. [ABSTRACT FROM AUTHOR]

Prostate cancer is one of the most common cancers in American men. Management depends on the staging of prostate cancer. Only cancers that are confined to organs of origin are potentially curable. The article considers a hierarchical Bayesian neural network approach for posterior prediction probabilities of certain features indicative of non-organ-confined prostate cancer. The Bayesian procedure is implemented by an application of the Markov chain Monte Carlo numerical integration technique. For the problem at hand, the hierarchical Bayesian neural network approach is shown to be superior to the approach based on hierarchical Bayesian logistic regression model as well as the classical feed forward neural networks. [ABSTRACT FROM AUTHOR]

In this paper, we highlight properties of Bayesian models in which the prior puts positive mass on all Kullback-Leibler neighborhoods of all densities. These properties are concerned with model choice via the Bayes factor, density estimation and the maximization of expected utility for decision problems. In four illustrations we focus on the Bayes factor and show that whatever models are being compared, the [log(Bayes factor)]/[sample size] converges to a non-random number which has a nice interpretation. A parametric versus semiparametric model comparison provides a fifth illustration. [ABSTRACT FROM AUTHOR]

Model selection is an important part of any statistical analysis and, indeed, is central to the pursuit of science in general. Many authors have examined the question of model selection from both frequentist and Bayesian perspectives, and many tools for selecting the "best model" have been suggested in the literature. This paper considers the various proposals from a Bayesian decision-theoretic perspective. [ABSTRACT FROM AUTHOR]