Unified frequentist and Bayesian testing of a precise hypothesis

Berger, James O.; Boukai, Benzion; Wang, Y.

doi:10.1214/ss/1030037904

Cited by 163 publications

(62 citation statements)

References 25 publications

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“…The cred i bil ity inter val rep re sents the range inwhichtheORfallswithaprob a bil ityof90%.Wecallp the pos te rior prob a bil ity for the effect to be larger/smaller than 1 (when the pos te rior mean was larger/smaller than 1). In other words, p shows how much of the pos te rior dis tri bu tion of the over all effectliesaboveorbelow1:avalueofp close to 1 refers to a reli able esti mate (for more infor ma tion on the Bayes ian p, see Berger et al 1997;Casella and Berger 1987).…”

Section: Pairwise Meta-analysesmentioning

confidence: 99%

Employment Instability and Fertility in Europe: A Meta-Analysis

et al. 2021

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The relationship between employment instability and fertility is a major topic in demographic research, with a proliferation of published papers on this matter, especially since the Great Recession. Employment instability, which most often manifests in unemployment or time-limited employment, is usually deemed to have a negative effect on fertility, although different fertility reactions are hypothesized by sociological theories, and micro-level evidence is fragmented and contradictory. We used meta-analytic techniques to synthesize European research findings, offer general conclusions about the effects of employment instability on fertility (in terms of direction and size), and rank different sources of employment instability. Our results suggest that employment instability has a nonnegligible negative effect on fertility. Men's unemployment is more detrimental for fertility than men's time-limited employment; conversely, a woman having a fixed-term contract is least likely to have a child. Next, the negative effect of employment instability on fertility has become stronger over time, and is more severe in Southern European countries, where social protection for families and the unemployed is least generous. Finally, meta-regression estimates demonstrate that failing to account for income and partner characteristics leads to an overestimation of the negative effect of employment instability on fertility. We advance the role of these two factors as potential mechanisms by which employment instability affects fertility. Overall, this meta-analysis provides the empirical foundation for new studies on the topic.

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Section: Pairwise Meta-analysesmentioning

confidence: 99%

Employment Instability and Fertility in Europe: A Meta-Analysis

et al. 2021

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“…Figure 5 displays a scatter plot matrix of − log 10 (p), where p either corresponds to the Model I through IV unadjusted p-value for tests of DE or to the Model V posterior probability for non-DE for mutants ceg1-250 (panel (a)) and spt4∆ (panel (b)). Note that by relating Model I through IV results to Model V results we may seemingly be perpetuating the "severe pedagogical problem of misinterpreting p-values as posterior probabilities"(Berger et al (1997)). However, this is not the case.…”

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confidence: 99%

Identifying differentially expressed genes from microarray experiments via statistic synthesis

Yang¹,

Xiao²,

Segal³

2004

Bioinformatics

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Our new approach, which addresses both ranking and selection of differentially expressed genes, integrates differing statistics via a distance synthesis scheme. Using a set of (Affymetrix) spike-in datasets, in which differentially expressed genes are known, we demonstrate that our method compares favorably with the best individual statistics, while achieving robustness properties lacked by the individual statistics. We further evaluate performance on one other microarray study.

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“…Distributional assumptions for observations or unknown quantities can be included at will. Furthermore, it is well known that Bayesian model estimates and decisions can maintain frequentist properties, such as unbiasedness, interval coverage, and error rates (Box, 1980;Woodroofe, 1976;Diaconis & Freedman, 1986;Little, 2006;Severini, 1993;Thatcher, 1964;Nicolaou, 1993;Berger et al, 1997;Peers, 1968). Importantly, regardless of assumptions, the inferential procedure remains the same in that inferences are drawn from the posterior distribution instead of a hypothetical sampling distribution.…”

Section: Constantmentioning

confidence: 99%

Outgrowing the Procrustean Bed of Normality: The Utility of Bayesian Modeling for Asymmetrical Data Analysis

Martin¹,

Williams²

2017

Preprint

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Psychological data often violate the normality assumptions made by commonly used statistical methods. These violations are addressed in a variety of ways such as transformations or assuming the employed method is robust to violations. Here we argue that data transformations are unnecessary at best and severely misleading at worst. An alternative approach is to use a Bayesian model that permits skewness and other perturbations to classical assumptions (e.g., heteroskedasticity). Through simulation, we demonstrate that a Bayesian skew-normal model has optimal frequentist properties (i.e., "type 1" error, "power", unbiasedness) compared to normal-assumptive models with or without transformation. Furthermore, the Bayesian skew-normal model has greater predictive utility, as indicated by posterior predictive checking and approximate leave-one-out cross-validation. After an applied example, we discuss practical implications of our findings for psychological science in general, and specifically how Bayesian modeling can improve reproducibility in psychology.

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Unified frequentist and Bayesian testing of a precise hypothesis

Cited by 163 publications

References 25 publications

Employment Instability and Fertility in Europe: A Meta-Analysis

Employment Instability and Fertility in Europe: A Meta-Analysis

Identifying differentially expressed genes from microarray experiments via statistic synthesis

Outgrowing the Procrustean Bed of Normality: The Utility of Bayesian Modeling for Asymmetrical Data Analysis

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