True Null Hypothesis (true + null_hypothesis)

Distribution by Scientific Domains


Selected Abstracts


On the use of non-local prior densities in Bayesian hypothesis tests

JOURNAL OF THE ROYAL STATISTICAL SOCIETY: SERIES B (STATISTICAL METHODOLOGY), Issue 2 2010
Valen E. Johnson
Summary., We examine philosophical problems and sampling deficiencies that are associated with current Bayesian hypothesis testing methodology, paying particular attention to objective Bayes methodology. Because the prior densities that are used to define alternative hypotheses in many Bayesian tests assign non-negligible probability to regions of the parameter space that are consistent with null hypotheses, resulting tests provide exponential accumulation of evidence in favour of true alternative hypotheses, but only sublinear accumulation of evidence in favour of true null hypotheses. Thus, it is often impossible for such tests to provide strong evidence in favour of a true null hypothesis, even when moderately large sample sizes have been obtained. We review asymptotic convergence rates of Bayes factors in testing precise null hypotheses and propose two new classes of prior densities that ameliorate the imbalance in convergence rates that is inherited by most Bayesian tests. Using members of these classes, we obtain analytic expressions for Bayes factors in linear models and derive approximations to Bayes factors in large sample settings. [source]


Resampling-Based Empirical Bayes Multiple Testing Procedures for Controlling Generalized Tail Probability and Expected Value Error Rates: Focus on the False Discovery Rate and Simulation Study

BIOMETRICAL JOURNAL, Issue 5 2008
Sandrine Dudoit
Abstract This article proposes resampling-based empirical Bayes multiple testing procedures for controlling a broad class of Type I error rates, defined as generalized tail probability (gTP) error rates, gTP (q,g) = Pr(g (Vn,Sn) > q), and generalized expected value (gEV) error rates, gEV (g) = E [g (Vn,Sn)], for arbitrary functions g (Vn,Sn) of the numbers of false positives Vn and true positives Sn. Of particular interest are error rates based on the proportion g (Vn,Sn) = Vn /(Vn + Sn) of Type I errors among the rejected hypotheses, such as the false discovery rate (FDR), FDR = E [Vn /(Vn + Sn)]. The proposed procedures offer several advantages over existing methods. They provide Type I error control for general data generating distributions, with arbitrary dependence structures among variables. Gains in power are achieved by deriving rejection regions based on guessed sets of true null hypotheses and null test statistics randomly sampled from joint distributions that account for the dependence structure of the data. The Type I error and power properties of an FDR-controlling version of the resampling-based empirical Bayes approach are investigated and compared to those of widely-used FDR-controlling linear step-up procedures in a simulation study. The Type I error and power trade-off achieved by the empirical Bayes procedures under a variety of testing scenarios allows this approach to be competitive with or outperform the Storey and Tibshirani (2003) linear step-up procedure, as an alternative to the classical Benjamini and Hochberg (1995) procedure. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) [source]


Increasing accuracy of causal inference in experimental analyses of biodiversity

FUNCTIONAL ECOLOGY, Issue 6 2004
L. BENEDETTI-CECCHI
Summary 1Manipulative experiments are often used to identify causal linkages between biodiversity and productivity in terrestrial and aquatic habitats. 2Most studies have identified an effect of biodiversity, but their interpretation has stimulated considerable debate. The main difficulties lie in separating the effect of species richness from those due to changes in identity and relative density of species. 3Various experimental designs have been adopted to circumvent problems in the analysis of biodiversity. Here I show that these designs may not be able to maintain the probability of type I errors at the nominal level (, = 0·05) under a true null hypothesis of no effect of species richness, in the presence of effects of density and identity of species. 4Alternative designs have been proposed to discriminate unambiguously the effects of identity and density of species from those due to number of species. Simulations show that the proposed experiments may have increased capacity to control for type I errors when effects of density and identity of species are also present. These designs have enough flexibility to be useful in the experimental analysis of biodiversity in various assemblages and under a wide range of environmental conditions. [source]


On the use of non-local prior densities in Bayesian hypothesis tests

JOURNAL OF THE ROYAL STATISTICAL SOCIETY: SERIES B (STATISTICAL METHODOLOGY), Issue 2 2010
Valen E. Johnson
Summary., We examine philosophical problems and sampling deficiencies that are associated with current Bayesian hypothesis testing methodology, paying particular attention to objective Bayes methodology. Because the prior densities that are used to define alternative hypotheses in many Bayesian tests assign non-negligible probability to regions of the parameter space that are consistent with null hypotheses, resulting tests provide exponential accumulation of evidence in favour of true alternative hypotheses, but only sublinear accumulation of evidence in favour of true null hypotheses. Thus, it is often impossible for such tests to provide strong evidence in favour of a true null hypothesis, even when moderately large sample sizes have been obtained. We review asymptotic convergence rates of Bayes factors in testing precise null hypotheses and propose two new classes of prior densities that ameliorate the imbalance in convergence rates that is inherited by most Bayesian tests. Using members of these classes, we obtain analytic expressions for Bayes factors in linear models and derive approximations to Bayes factors in large sample settings. [source]


Event-Induced Volatility and Tests for Abnormal Performance

THE JOURNAL OF FINANCIAL RESEARCH, Issue 2 2003
Robert Savickas
Abstract I analyze a simple test statistic for mean abnormal returns in the presence of stochastic volatility during both event and nonevent windows and in the presence of event-induced variance increases. Unlike previous tests, the parametric test evaluated here does not require that the volatility effect of the event be the same across all securities. Simulations show that the test exhibits nontrivial gains in power over previously developed parametric and nonparametric tests, and the true null hypothesis is rejected at appropriate levels. [source]