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In statistical genetics, the sequentially Markov coalescent (SMC) is an important family of models for approximating the distribution of genetic variation data under complex evolutionary models. Methods based on SMC are widely used in genetics and evolutionary biology, with significant applications to genotype phasing and imputation, recombination rate estimation, and inferring population history. SMC allows for likelihood-based inference using hidden Markov models (HMMs), where the latent variable represents a genealogy. Because genealogies are continuous, while HMMs are discrete, SMC requires discretizing the space of trees in a way that is awkward and creates bias. In this work, we propose a method that circumvents this requirement, enabling SMC-based inference to be performed in the natural setting of a continuous state space. We derive fast, exact procedures for frequentist and Bayesian inference using SMC. Compared to existing methods, ours requires minimal user intervention or parameter tuning, no numerical optimization or E-M, and is faster and more accurate. for this article are available online. [ABSTRACT FROM AUTHOR]

When faced with a binary or count outcome, informative hypotheses can be tested in the generalized linear model using the distance statistic as well as modified versions of the Wald, the Score and the likelihood-ratio test (LRT). In contrast to classical null hypothesis testing, informative hypotheses allow to directly examine the direction or the order of the regression coefficients. Since knowledge about the practical performance of informative test statistics is missing in the theoretically oriented literature, we aim at closing this gap using simulation studies in the context of logistic and Poisson regression. We examine the effect of the number of constraints as well as the sample size on type I error rates when the hypothesis of interest can be expressed as a linear function of the regression parameters. The LRT shows the best performance in general, followed by the Score test. Furthermore, both the sample size and especially the number of constraints impact the type I error rates considerably more in logistic compared to Poisson regression. We provide an empirical data example together with R code that can be easily adapted by applied researchers. Moreover, we discuss informative hypothesis testing about effects of interest, which are a non-linear function of the regression parameters. We demonstrate this by means of a second empirical data example. [ABSTRACT FROM AUTHOR]

The Bayesian-frequentist hybrid model and associated inference can combine the advantages of both Bayesian and frequentist methods and avoid their limitations. However, except for few special cases in existing literature, the computation under the hybrid model is generally nontrivial or even unsolvable. This article develops a computation algorithm for hybrid inference under any general loss functions. Three simulation examples demonstrate that hybrid inference can improve upon frequentist inference by incorporating valuable prior information, and also improve Bayesian inference based on non-informative priors where the latter leads to biased estimates for the small sample sizes used in inference. The proposed method is illustrated in applications including a biomechanical engineering design and a surgical treatment of acral lentiginous melanoma. [ABSTRACT FROM AUTHOR]

Linear mixed models are standard models to analyze repeated measures or longitudinal data under the assumption of normality for random components in the model. Although the mixed models are often used in both frequentist and Bayesian inference, their evaluation from robustness perspective has not received as much attention in Bayesian inference as in frequentist. The aim of this study is to evaluate Bayesian tests in mixed models for their robustness to normality. We use a general class of exponential power distributions, EPD, and particularly focus on testing fixed effects in longitudinal models. The EPD class contains both light and heavy tailed distributions, with normality as a special case. Further, we consider a new paradigm of Bayesian testing decision theory where the hypotheses are formulated as a mixture model, with subsequent testing based on the posterior distribution of the mixture weights. It is shown that the EPD class provides a flexible alternative to normality assumption, particularly in the presence of outliers. Real data applications are also demonstrated. [ABSTRACT FROM AUTHOR]

Process yield has been a standard metric for measuring the capability and performance of manufacturing processes. Process capability index Spk, a concise unit-less gauge with yield-sensitive functionality, communicates succinctly the genuine process yield for normally distributed processes. However, in frequentist statistics, the exact sampling distribution of Spk's natural estimator is intractable. Various frequentist approaches have attempted to address its wide-scale accuracy in statistical inference. Among them, the approach of generalized confidence interval (GCI) has been demonstrated superiority. In this paper, we incorporate Markov chain Monte Carlo (MCMC) algorithms to introduce a Bayesian-type approach. Extensive simulations in comparison of accuracy and precision performances between the Spk's frequentist and Bayesian inferences are conducted. Concerning coverage rates and average interval widths of the inferential criteria, Spk's Bayesian MCMC credibility intervals perform better than frequentist GCIs in most cases, particularly, the cases with only a few samples of information acquired from the manufacturing process. [ABSTRACT FROM AUTHOR]

Smartphones are a preferred platform to access audiovisual stories. Prior theory and research suggest that using smaller screens could lead to a shallower narrative experience. In three experiments we examined the influence of screen size (smartphone vs. computer screen) on the experience of being transported into the world of the story (narrative transportation). We further examined interaction effects with manipulations meant to change transportation by means of reviews (Experiment 1, N = 120), consistency of main character information (Experiment 2, N = 139), and prior information meant to facilitate comprehension (Experiment 3, N = 129). Because our series of studies involved theoretically and practically relevant null hypotheses (i.e., screen size does not influence transportation), we added Bayes factor analyses to standard frequentist statistics. A mini meta-analysis was conducted to summarize the results. Taken together, the three experiments indicate that smaller screen size does not impair narrative transportation. Implications and future research are discussed. [ABSTRACT FROM AUTHOR]

The commitments to mitigate the negative impacts associated with final energy use stipulate the increase of energy efficiency of the built environment. This is the focus of urban energy policies and of built stock energy models that aid them. The complexities behind the phenomenon, however, hinder the development of the means for controlling and unbiased modelling. Such tasks necessitate the empirical evidence of causal relationships between architectural and technical attributes and building energy performance at the population level. This study, therefore, elaborates on the methods of inferential statistics for establishing such causal effects. The focus is on the methods of frequentist inference, active use of which may advance the understanding of the phenomenon and foster more accurate modelling practices. The case study examines the energy performance exhibited by distinct configurations of construction periods, envelope materials, sources of energy for space heating and the ventilation system types. The empirical sample consists of more than 11,000 records registered in the Norwegian energy performance certification system. The results document the effects and their significance. These methods are applicable in any urban context and may provide the empirical basis for promoting/discouraging certain technological and architectural tendencies, and simulating the phenomena through probabilistic programming. [ABSTRACT FROM AUTHOR]

Spatial confounding, that is, collinearity between fixed effects and random effects in a spatial generalized linear mixed model, can adversely affect estimates of the fixed effects. Restricted spatial regression methods have been proposed as a remedy for spatial confounding. Such methods replace inference for the fixed effects of the original model with inference for those effects under a model in which the random effects are restricted to a subspace orthogonal to the column space of the fixed effects model matrix; thus, they "deconfound" the two types of effects. We prove, however, that frequentist inference for the fixed effects of a deconfounded linear model is generally inferior to that for the fixed effects of the original spatial linear model; in fact, it is even inferior to inference for the corresponding nonspatial model. We show further that deconfounding also leads to inferior predictive inferences, though its impact on prediction appears to be relatively small in practice. Based on these results, we argue that deconfounding a spatial linear model is bad statistical practice and should be avoided. [ABSTRACT FROM AUTHOR]

In this study we focus on prediction precision for linear regression with a bivariate response variable, where the response variable of primary interest contains missing data in the training data set. We derive and provide the maximum likelihood solution and a Bayesian method based on a conjugate prior distribution. In particular we evaluate strategies in how to "borrow prediction strength" from the full set of data to prediction associated with the missing data. Regularization of the maximum likelihood estimator is theoretically shown to be beneficial, and we derive methods for how to implement such regularization under frequentist and Bayesian inference, including available software as a R-package. [ABSTRACT FROM AUTHOR]

The use of real-world data became more and more popular in the pharmaceutical industry. The impact of real-world evidence is now well emphasized by the regulatory authorities. Indeed, the analysis of this type of data can play a key role for treatment efficacy and safety. The aim of this work is to assess various methods and give guidance on the comparisons of drugs, mostly with respect to time-to-event data, in non-randomized studies with potentially confounding variables. For that purpose, several statistical methodologies are compared based on simulation studies. These methodologies belong to family classes of methods that are widely used for this type of problem: regression, matching, weighting and subclassification methods. The evaluation criteria used to compare methods performances are the relative bias, the mean square error, the coverage probability and the width of the confidence interval. In this paper, we consider different scenarios of dataset features in order to study the effect of the sample size, the number of covariates and the magnitude of the treatment effect on the statistical methodologies performances. These statistical analyses are conducted within a proportional hazard model framework. Furthermore, we highlight the advantage of using techniques to identify relevant covariates for time-to-event outcomes by comparing two variable selection methods under a frequentist and a Bayesian inference. Based on simulation results, recommendations on each of the family of methods are provided to guide decision making. [ABSTRACT FROM AUTHOR]

Expectation propagation is a general prescription for approximation of integrals in statistical inference problems. Its literature is mainly concerned with Bayesian inference scenarios. However, expectation propagation can also be used to approximate integrals arising in frequentist statistical inference. We focus on likelihood-based inference for binary response mixed models and show that fast and accurate quadrature-free inference can be realized for the probit link case with multivariate random effects and higher levels of nesting. The approach is supported by asymptotic calculations in which expectation propagation is seen to provide consistent estimation of the exact likelihood surface. Numerical studies reveal the availability of fast, highly accurate and scalable methodology for binary mixed model analysis. [ABSTRACT FROM AUTHOR]

This paper is a reader-friendly introduction to Bayesian inference applied to psychological science. We begin by explaining the difference between frequentist and epistemic interpretations of probability that underpin respectively frequentist and Bayesian statistics. We use a concrete example—a student wondering whether s/he carries the virus statisticus malignum—to explain how both approaches are different one from another. We illustrate Bayesian inference with intuitive examples, before introducing the mathematical framework. Different schools of thoughts and recommendations are discussed to illustrate how to use priors in Bayes Factor testing. We discuss how psychology could benefit from a greater reliance on Bayesian methods. Finally, we illustrate how to compute Bayes Factors analyses with real data and provide the R code. [ABSTRACT FROM AUTHOR]

The biological organism is a complex structure regulated by interactions of genes and proteins. Various linear and nonlinear models can define activations of these interactions. In this study, we have aimed to improve the Gaussian graphical model (GGM), which is one of the well-known probabilistic and parametric models describing steady-state activations of biological systems, and its inference based on the graphical lasso, shortly Glasso, method. Because, GGM with Glasso can have low accuracy when the system has many genes and data are far from the normal distribution. Hereby, we construct the model like GGM, but, suggest the long-tailed symmetric distribution (LTS), rather than the normality, and use the modified maximum likelihood (MML) estimator, rather than Glasso, in inference. From the assessment of simulated and real data analyses, it is seen that LTS with MML has higher accuracy and less computational demand with explicit expressions than results of GGM with Glasso. [ABSTRACT FROM AUTHOR]

Near-death experiences (NDEs) are usually associated with positive affect, however, a small proportion are considered distressing. We aimed to look into the proportion of distressing NDEs in a sample of NDE narratives, categorise distressing narratives according to Greyson and Bush's classification (inverse, void or hellish), and compare distressing and "classical" NDEs. Participants wrote down their experience, completed the Memory Characteristics Questionnaire (assessing the phenomenology of memories) and the Greyson scale (characterising content of NDEs). The proportion of suicidal attempts, content and intensity of distressing and classical NDEs were compared using frequentist and Bayesian statistics. Distressing NDEs represent 14% of our sample (n = 123). We identified 8 inverse, 8 hellish and 1 void accounts. The proportion of suicide survivors is higher in distressing NDEs as compared to classical ones. Finally, memories of distressing NDEs appear as phenomenologically detailed as classical ones. Distressing NDEs deserve careful consideration to ensure their integration into experiencers' identity. [ABSTRACT FROM AUTHOR]

When data analysts operate within different statistical frameworks (e.g., frequentist versus Bayesian, emphasis on estimation versus emphasis on testing), how does this impact the qualitative conclusions that are drawn for real data? To study this question empirically we selected from the literature two simple scenarios—involving a comparison of two proportions and a Pearson correlation—and asked four teams of statisticians to provide a concise analysis and a qualitative interpretation of the outcome. The results showed considerable overall agreement; nevertheless, this agreement did not appear to diminish the intensity of the subsequent debate over which statistical framework is more appropriate to address the questions at hand. [ABSTRACT FROM AUTHOR]

This article resulted from our participation in the session on the "role of expert opinion and judgment in statistical inference" at the October 2017 ASA Symposium on Statistical Inference. We present a strong, unified statement on roles of expert judgment in statistics with processes for obtaining input, whether from a Bayesian or frequentist perspective. Topics include the role of subjectivity in the cycle of scientific inference and decisions, followed by a clinical trial and a greenhouse gas emissions case study that illustrate the role of judgments and the importance of basing them on objective information and a comprehensive uncertainty assessment. We close with a call for increased proactivity and involvement of statisticians in study conceptualization, design, conduct, analysis, and communication. [ABSTRACT FROM AUTHOR]

A central objective of empirical research on treatment response is to inform treatment choice. Unfortunately, researchers commonly use concepts of statistical inference whose foundations are distant from the problem of treatment choice. It has been particularly common to use hypothesis tests to compare treatments. Wald's development of statistical decision theory provides a coherent frequentist framework for use of sample data on treatment response to make treatment decisions. A body of recent research applies statistical decision theory to characterize uniformly satisfactory treatment choices, in the sense of maximum loss relative to optimal decisions (also known as maximum regret). This article describes the basic ideas and findings, which provide an appealing practical alternative to use of hypothesis tests. For simplicity, the article focuses on medical treatment with evidence from classical randomized clinical trials. The ideas apply generally, encompassing use of observational data and treatment choice in nonmedical contexts. [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]

M-estimation is a widely used technique for robust statistical inference. In this paper, we study model selection and model averaging for M-estimation to simultaneously improve the coverage probability of confidence intervals of the parameters of interest and reduce the impact of heavy-tailed errors or outliers in the response. Under general conditions, we develop robust versions of the focused information criterion and a frequentist model average estimator for M-estimation, and we examine their theoretical properties. In addition, we carry out extensive simulation studies as well as two real examples to assess the performance of our new procedure, and find that the proposed method produces satisfactory results. [ABSTRACT FROM AUTHOR]

A new general class of exponentiated sinh Cauchy regression models for location, scale, and shape parameters is introduced and studied. It may be applied to censored data and used more effectively in survival analysis when compared with the usual models. For censored data, we employ a frequentist analysis for the parameters of the proposed model. Further, for different parameter settings, sample sizes, and censoring percentages, various simulations are performed. The extended regression model is very useful for the analysis of real data and could give more adequate fits than other special regression models. [ABSTRACT FROM AUTHOR]

Research in regularization, as applied to structural equation modeling (SEM), remains in its infancy. Specifically, very little work has compared regularization approaches across both frequentist and Bayesian estimation. The purpose of this study was to address just that, demonstrating both similarity and distinction across estimation frameworks, while specifically highlighting more recent developments in Bayesian regularization. This is accomplished through the use of two empirical examples that demonstrate both ridge and lasso approaches across both frequentist and Bayesian estimation, along with detail regarding software implementation. We conclude with a discussion of future research, advocating for increased evaluation and synthesis across both Bayesian and frequentist frameworks. [ABSTRACT FROM AUTHOR]

Just as frequentist hypothesis tests have been developed to check model assumptions, prior predictive p-values and other Bayesian p-values check prior distributions as well as other model assumptions. These model checks not only suffer from the usual threshold dependence of p-values, but also from the suppression of model uncertainty in subsequent inference. One solution is to transform Bayesian and frequentist p-values for model assessment into a fiducial distribution across the models. Averaging the Bayesian or frequentist posterior distributions with respect to the fiducial distribution can reproduce results from Bayesian model averaging or classical fiducial inference. [ABSTRACT FROM AUTHOR]

In many applications of linear regression models, randomness due to model selection is commonly ignored in post-model selection inference. In order to account for the model selection uncertainty, least-squares frequentist model averaging has been proposed recently. We show that the confidence interval from model averaging is asymptotically equivalent to the confidence interval from the full model. The finite-sample confidence intervals based on approximations to the asymptotic distributions are also equivalent if the parameter of interest is a linear function of the regression coefficients. Furthermore, we demonstrate that this equivalence also holds for prediction intervals constructed in the same fashion. [ABSTRACT FROM AUTHOR]

The likelihood function of a general nonlinear, non-Gaussian state space model is a high-dimensional integral with no closed-form solution. In this article, I show how to calculate the likelihood function exactly for a large class of non-Gaussian state space models that include stochastic intensity, stochastic volatility, and stochastic duration models among others. The state variables in this class follow a nonnegative stochastic process that is popular in econometrics for modeling volatility and intensities. In addition to calculating the likelihood, I also show how to perform filtering and smoothing to estimate the latent variables in the model. The procedures in this article can be used for either Bayesian or frequentist estimation of the model’s unknown parameters as well as the latent state variables. Supplementary materials for this article are available online. [ABSTRACT FROM AUTHOR]

The estimation problem of epsilon-skew-normal (ESN) distribution parameters is considered within Bayesian approaches. This family of distributions contains the normal distribution, can be used for analyzing the asymmetric and near-normal data. Bayesian estimates under informative and non informative Jeffreys prior distributions are obtained and performances of ESN family and these estimates are shown via a simulation study. A real data set is also used to illustrate the ideas. [ABSTRACT FROM AUTHOR]

It has became more popular in the recent statistical literature to see Bayesian approaches for clinical trials, such as assurance calculations for study designs and the use of posterior probability for data analyses. When applying Bayesian analysis to clinical trial data, one common question is to use informative priors or noninformative priors. In order to explore this question, we looked for existing clinical trial data with a simple structure and a simple clinical endpoint so that the Bayesian re-analyses can be easily performed. We came across the published Phase III Macugen® data that were suitable for this exploration. In this manuscript, the Macugen Phase III development program was described, the primary data for the two Phase III pivotal studies were re-analyzed using Bayesian applications with informative priors and noninformative priors. These re-analysis results were summarized, compared, and discussed. [ABSTRACT FROM AUTHOR]

Rubin (1976) derived general conditions under which inferences that ignore missing data are valid. These conditions are sufficient but not generally necessary, and therefore may be relaxed in some special cases. We consider here the case of frequentist estimation of a conditional cdf subject to missing outcomes. We partition a set of data into outcome, conditioning, and latent variables, all of which potentially affect the probability of a missing response. We describe sufficient conditions under which a complete-case estimate of the conditional cdf of the outcome given the conditioning variable is unbiased. We use simulations on a renal transplant data set (Dienemann et al.) to illustrate the implications of these results. [ABSTRACT FROM AUTHOR]

Copyright of Spatial Economic Analysis is the property of Routledge and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

A popular strategy for understanding the probabilities that arise in physics is to interpret them via reductionist accounts of chance—indeed, it is sometimes claimed that such accounts are uniquely well-suited to make sense of the probabilities in classical statistical mechanics. Here it is argued that reductionist accounts of chance carry a steep but unappreciated cost: when applied to physical theories of the relevant type, they inevitably distort the relations of probability that they take as input. [ABSTRACT FROM PUBLISHER]

This paper considers posterior consistency in the context of high-dimensional variable selection using the Bayesian lasso algorithm. In a frequentist setting, consistency is perhaps the most basic property that we expect any reasonable estimator to achieve. However, in a Bayesian setting, consistency is often ignored or taken for granted, especially in more complex hierarchical Bayesian models. In this paper, we have derived sufficient conditions for posterior consistency in the Bayesian lasso model with the orthogonal design, where the number of parameters grows with the sample size. [ABSTRACT FROM AUTHOR]

Reference-based imputation (RBI) methods have been proposed as sensitivity analyses for longitudinal clinical trials with missing data. The RBI methods multiply impute the missing data in treatment group based on an imputation model built using data from the reference (control) group. The RBI will yield a conservative treatment effect estimate as compared to the estimate obtained from multiple imputation (MI) under missing at random (MAR). However, the RBI analysis based on the regular MI approach can be overly conservative because it not only applies discount to treatment effect estimate but also posts penalty on the variance estimate. In this article, we investigate the statistical properties of RBI methods, and propose approaches to derive accurate variance estimates using both frequentist and Bayesian methods for the RBI analysis. Results from simulation studies and applications to longitudinal clinical trial datasets are presented. [ABSTRACT FROM AUTHOR]

As Bayesian methods continue to grow in accessibility and popularity, more empirical studies are turning to Bayesian methods to model small sample data. Bayesian methods do not rely on asympotics, a property that can be a hindrance when employing frequentist methods in small sample contexts. Although Bayesian methods are better equipped to model data with small sample sizes, estimates are highly sensitive to the specification of the prior distribution. If this aspect is not heeded, Bayesian estimates can actually be worse than frequentist methods, especially if frequentist small sample corrections are utilized. We show with illustrative simulations and applied examples that relying on software defaults or diffuse priors with small samples can yield more biased estimates than frequentist methods. We discuss conditions that need to be met if researchers want to responsibly harness the advantages that Bayesian methods offer for small sample problems as well as leading small sample frequentist methods. [ABSTRACT FROM PUBLISHER]

We propose a generalization of the one-dimensional Jeffreys' rule in order to obtain non informative prior distributions for non regular models, taking into account the comments made by Jeffreys in his article of 1946. These non informatives are parameterization invariant and the Bayesian intervals have good behavior in frequentist inference. In some important cases, we can generate non informative distributions for multi-parameter models with non regular parameters. In non regular models, the Bayesian method offers a satisfactory solution to the inference problem and also avoids the problem that the maximum likelihood estimator has with these models. Finally, we obtain non informative distributions in job-search and deterministic frontier production homogenous models. [ABSTRACT FROM AUTHOR]

In this article, I provide a conceptually oriented overview of Bayesian approaches to statistical inference and contrast them with frequentist approaches that currently dominate conventional practice in educational research. The features and advantages of Bayesian approaches are illustrated with examples spanning several statistical modeling traditions and contexts in educational research. [ABSTRACT FROM AUTHOR]

A Bayesian reference analysis for determining the posterior distribution of the strength of a radiation source is performed. The only pieces of information available are the numbers of counts gathered in a gross and a background measurement along with the respective counting times and a state-of-knowledge distribution for the efficiency. This situation is addressed by combining the calculations of a “one-at-a-time” reference prior and a reference prior with partial information. The posterior distribution of the source strength obtained with the reference prior leads to credible intervals that have better frequentist coverage than corresponding intervals founded on uniform or Jeffreys’ priors. [ABSTRACT FROM AUTHOR]

In the frequentist program, inferential methods with exact control on error rates are a primary focus. The standard approach, however, is to rely on asymptotic approximations, which may not be suitable. This article presents a general framework for the construction of exact frequentist procedures based on plausibility functions. It is shown that the plausibility function-based tests and confidence regions have the desired frequentist properties in finite samples—no large-sample justification needed. An extension of the proposed method is also given for problems involving nuisance parameters. Examples demonstrate that the plausibility function-based method is both exact and efficient in a wide variety of problems. [ABSTRACT FROM AUTHOR]

With a view to predicting a scalar-valued future observation on the basis of past observations, we explore predictive sets having frequentist as well as Bayesian validity for arbitrary priors in a higher-order asymptotic sense. It is found that a connection with locally unbiased tests is useful for this purpose. Illustrative examples are given. Computation and simulation studies lend support to our asymptotic results in finite samples. The issue of expected lengths of our predictive sets is also discussed. [ABSTRACT FROM AUTHOR]

Problem: Reliability is an essential element in assessing the operational suitability of Department of Defense weapon systems. Reliability takes a prominent role in both the design and analysis of operational tests. In the current era of reduced budgets and increased reliability requirements, it is challenging to verify reliability requirements in a single test. Furthermore, all available data should be considered in order to ensure evaluations provide the most appropriate analysis of the system's reliability. Approach: This paper describes the benefits of using parametric statistical models to combine information across multiple testing events. Both frequentist and Bayesian inference techniques are employed and they are compared and contrasted to illustrate different statistical methods for combining information. We apply these methods to data collected during the developmental and operational test phases for the Stryker family of vehicles. Results: We show that, when we combine the available information across two test phases for the Stryker family of vehicles, reliability estimates are more accurate and precise than those reported previously using traditional methods that use only operational test data in their reliability assessments. [ABSTRACT FROM AUTHOR]

This article considers the uncertainty of a proportion based on a stratified random sample of a small population. Using the hypergeometric distribution, a Clopper–Pearson type upper confidence bound is presented. Another frequentist approach that uses the estimated variance of the proportion estimator is also considered as well as a Bayesian alternative. These methods are demonstrated with an illustrative example. Some aspects of planning, that is, the impact of specified strata sample sizes, on uncertainty are studied through a simulation study. [ABSTRACT FROM AUTHOR]

Bayesian alternatives to frequentist propensity score approaches have recently been proposed. However, few studies have investigated their covariate balancing properties. This article compares a recently developed two-step Bayesian propensity score approach to the frequentist approach with respect to covariate balance. The effects of different priors on covariate balance are evaluated and the differences between frequentist and Bayesian covariate balance are discussed. Results of the case study reveal that both the Bayesian and frequentist propensity score approaches achieve good covariate balance. The frequentist propensity score approach performs slightly better on covariate balance for stratification and weighting methods, whereas the two-step Bayesian approach offers slightly better covariate balance in the optimal full matching method. Results of a comprehensive simulation study reveal that accuracy and precision of prior information on propensity score model parameters do not greatly influence balance performance. Results of the simulation study also show that overall, the optimal full matching method provides the best covariate balance and treatment effect estimates compared to the stratification and weighting methods. A unique feature of covariate balance within Bayesian propensity score analysis is that we can obtain a distribution of balance indices in addition to the point estimates so that the variation in balance indices can be naturally captured to assist in covariate balance checking. [ABSTRACT FROM AUTHOR]

In this article, the label switching problem and the importance of solving it are discussed for frequentist mixture models if a simulation study is used to evaluate the performance of mixture model estimators. Two effective labelling methods are proposed by using true label for each observation. The empirical studies demonstrate that the new proposed methods work well and provide better results than the rule of thumb method of order constraint labelling. In addition, a Monte Carlo study also demonstrates that simple order constraint labelling can sometimes produce severely biased, and possibly meaningless, estimated bias and standard errors. [ABSTRACT FROM AUTHOR]

Pharmacovigilance signal detection algorithms commonly involve the calculation of observed/expected (O/E) reporting frequencies, ratios, or odds calculated from 2×2 contingency tables. Frequentist and Bayesian implementations each have strengths and limitations. No single approach has emerged as universally superior. P-plots are a graphically oriented, frequentist statistical methodology based on the distributional properties of p-values as random variables under the null versus alternative hypotheses. This leads to our current assessment of the feasibility and performance of P-plots as a novel alternative or augmentation in quantitative pharmacovigilance signal detection methodology. [ABSTRACT FROM AUTHOR]

The goal of this paper is to correct a widespread misconception about the work of Robert Leslie Ellis and John Venn, namely that it can be considered as the ‘British empiricist’ reaction against the traditional theory of probability. It is argued, instead, that there was no unified ‘British school’ of frequentism during the nineteenth century. Where Ellis arrived at frequentism from a metaphysical idealist transformation of probability theory’s mathematical calculations, Venn did so on the basis of an empiricist critique of its ‘inverse application’. [ABSTRACT FROM PUBLISHER]

This paper focuses on the opposition between two contemporary research programs in economics: behavioral economics (BE) and experimental market economics (EME). Our claim is that the arguments of this opposition can be clarified through the lens of another opposition in the philosophy of probability and in probability theory, between Bayesianism and frequentism. We show how this probabilistic opposition has indirectly shaped a controversy in psychology that opposes two research programs –Heuristics and BiasesandEcological Rationality– which play respective roles in the foundations of individual rationality in BE and EME. To understand these theoretical interrelationships, we investigate the 1996 controversy between Kahneman, Tversky, and Gigerenzer. Those psychologists held different views on how probabilistic representations influence the context-dependency of rationality. This provides a rationale to suggest that a probabilistic ghost may be haunting the experimental machine in economics, and explains how and why the oppositions between BE and EME are structured around the interplay between the norms of rationality and the context in which rationality is exercised. [ABSTRACT FROM AUTHOR]

The goal of this paper is to provide a detailed reading of John Venn'sLogic of Chance(1866) as a work of logic or, more specifically, as a specific portion of the general system of so-called ‘material’ logic developed in hisPrinciples of Empirical or Inductive Logic(1889) and to discuss it against the background of his Boolean-inspired views on the connection between logic and mathematics. It is by means of this situating ofVenn1866[The Logic of Chance. An Essay on the Foundations and Province of the Theory of Probability. With Especial Reference to Its Application to Moral and Social Science, London: Macmillan] within the entirety of his oeuvre that it becomes both possible to revisit and necessary to re-articulate its place in the history of the frequency interpretation of probability. For it is clear that if Venn's approach to logic not only allowed him to establish its foundations on the basis of a process of idealization and define it as consisting of so-called hypothetical infinite series, but also brought him to do so in strictly non-mathematical terms, he was able to anticipate much of the content (and problems) of his twentieth-century fellow frequentists. [ABSTRACT FROM PUBLISHER]

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

We examine the large sample properties of Bayes procedures in a general framework, where data may be dependent and models may be misspecified and nonsmooth. The posterior distribution of parameters is shown to be asymptotically normal, centered at the quasi maximum likelihood estimator, under mild conditions. In this framework, the Bayes factor for the test problem of Davies (1997, 1987), where a parameter is unidentified under the null hypothesis, is analyzed. The probability that the Bayes factor leads to a correct conclusion about the hypotheses in Davies’ problem is shown to approach to one. [ABSTRACT FROM PUBLISHER]

There are several approaches to setting priors in Bayesian data analysis. Some attempt to minimize the impact of the prior on the posterior, allowing the data to “speak for themselves,” or to provide Bayesian inferences that have good frequentist properties. In contrast, this note focuses on priors where scientific knowledge is used, possibly partially informative. There are many articles on the use of such subjective information. We focus on using standard software for eliciting priors from subject-matter specialists, in the form of models such as the binomial, Poisson, and normal.  Our approach uses a common spreadsheet package with the facility to display dynamic pictures of prior distributions as the user toggles scroll bars or “sliders” that manipulate parameters of particular distributions. This allows interactive exploration of the shape of a probability distribution. We have found this a useful tool when eliciting priors for Bayesian data analysis. We present examples to illustrate the scope and flexibility of the method. Supplementary materials for this article are available online. [ABSTRACT FROM AUTHOR]

An important contribution to the literature on frequentist model averaging (FMA) is the work of Hjort and Claeskens (2003), who developed an asymptotic theory for frequentist model averaging in parametric models based on a local mis-specification framework. They also proposed a simple method for constructing confidence intervals of the unknown parameters. This article shows that the confidence intervals based on the FMA estimator suggested by Hjort and Claeskens (2003) are asymptotically equivalent to that obtained from the full model under both parametric and the varying-coefficient partially linear models. Thus, as long as interval estimation rather than point estimation is concerned, the confidence interval based on the full model already fulfills the objective and model averaging provides no additional useful information. [ABSTRACT FROM AUTHOR]