Bayesian Significance Test Research Articles

COMPARING X-RAY AND DYNAMICAL MASS PROFILES IN THE EARLY-TYPE GALAXY NGC 4636

We present the results of an X-ray mass analysis of the early-type galaxy NGC 4636, using Chandra data. We have compared the X-ray mass density profile with that derived from a dynamical analysis of the system's globular clusters (GCs). Given the observed interaction between the central active galactic nucleus and the X-ray emitting gas in NGC 4636, we would expect to see a discrepancy in the masses recovered by the two methods. Such a discrepancy exists within the central ~10kpc, which we interpret as the result of non-thermal pressure support or a local inflow. However, over the radial range ~10-30kpc, the mass profiles agree within the 1-sigma errors, indicating that even in this highly disturbed system, agreement can be sought at an acceptable level of significance over intermediate radii, with both methods also indicating the need for a dark matter halo. However, at radii larger than 30kpc, the X-ray mass exceeds the dynamical mass, by a factor of 4-5 at the largest disagreement. A Fully Bayesian Significance Test finds no statistical reason to reject our assumption of velocity isotropy, and an analysis of X-ray mass profiles in different directions from the galaxy centre suggests that local disturbances at large radius are not the cause of the discrepancy. We instead attribute the discrepancy to the paucity of GC kinematics at large radius, coupled with not knowing the overall state of the gas at the radius where we are reaching the group regime (>30kpc), or a combination of the two.

Full Bayesian Analysis for a Class of Jump-Diffusion Models

The Full Bayesian Significance Test (FBST) is adjusted for jump detection in a diffusion process. Under a natural parameterization, pure diffusion can be seen as a precise hypothesis. The evidence measure defined by FBST deals with absolutely continuous posterior distributions, when posterior rates for precise hypotheses are not appropriate. Applications to simulated and real data are shown.

A straightforward multiallelic significance test for the Hardy-Weinberg equilibrium law

Much forensic inference based upon DNA evidence is made assuming Hardy-Weinberg Equilibrium (HWE) for the genetic loci being used. Several statistical tests to detect and measure deviation from HWE have been devised, and their limitations become more obvious when testing for deviation within multiallelic DNA loci. The most popular methods-Chi-square and Likelihood-ratio tests-are based on asymptotic results and cannot guarantee a good performance in the presence of low frequency genotypes. Since the parameter space dimension increases at a quadratic rate on the number of alleles, some authors suggest applying sequential methods, where the multiallelic case is reformulated as a sequence of “biallelic” tests. However, in this approach it is not obvious how to assess the general evidence of the original hypothesis; nor is it clear how to establish the significance level for its acceptance/rejection. In this work, we introduce a straightforward method for the multiallelic HWE test, which overcomes the aforementioned issues of sequential methods. The core theory for the proposed method is given by the Full Bayesian Significance Test (FBST), an intuitive Bayesian approach which does not assign positive probabilities to zero measure sets when testing sharp hypotheses. We compare FBST performance to Chi-square, Likelihood-ratio and Markov chain tests, in three numerical experiments. The results suggest that FBST is a robust and high performance method for the HWE test, even in the presence of several alleles and small sample sizes.

Comparative Enumeration Gene Expression

AbstractThis paper is about differential gene expression measured by transcript counting methods such as SAGE or MPSS. It introduces two significance tests for detection of differential expressed tags: frequentist and Bayesian. Under the frequentist view, it is proposed a test that computes the critical level as a function of each tag total frequency. Under the Bayesian view the Full Bayesian Significance Test is used considering the logistic normal distribution. The two proposed significance levels, the frequentist and the Bayesian, are compared for a data set with four libraries. The linking function between them is a Beta distribution function with mean 0.39 and standard deviation 0.30.

Bayesian significance testing and multiple comparisons from MCMC outputs

This article proposes a Bayesian method to directly evaluate and test hypotheses in multiple comparisons. Transformation and integration over the coordinates relevant to the hypothesis are shown to...

Can a significance test be genuinely Bayesian?

The Full Bayesian Significance Test, FBST, is extensively reviewed. Its test statistic, a genuine Bayesian measure of evidence, is discussed in detail. Its behavior in some problems of statistical inference like testing for independence in contingency tables is discussed.

The full Bayesian significance test for mixture models: results in gene expression clustering

Gene clustering is a useful exploratory technique to group together genes with similar expression levels under distinct cell cycle phases or distinct conditions. It helps the biologist to identify potentially meaningful relationships between genes. In this study, we propose a clustering method based on multivariate normal mixture models, where the number of clusters is predicted via sequential hypothesis tests: at each step, the method considers a mixture model of m components (m = 2 in the first step) and tests if in fact it should be m - 1. If the hypothesis is rejected, m is increased and a new test is carried out. The method continues (increasing m) until the hypothesis is accepted. The theoretical core of the method is the full Bayesian significance test, an intuitive Bayesian approach, which needs no model complexity penalization nor positive probabilities for sharp hypotheses. Numerical experiments were based on a cDNA microarray dataset consisting of expression levels of 205 genes belonging to four functional categories, for 10 distinct strains of Saccharomyces cerevisiae. To analyze the method's sensitivity to data dimension, we performed principal components analysis on the original dataset and predicted the number of classes using 2 to 10 principal components. Compared to Mclust (model-based clustering), our method shows more consistent results.

Bayesian significance testing and multiple comparisons from MCMC outputs

This article proposes a Bayesian method to directly evaluate and test hypotheses in multiple comparisons. Transformation and integration over the coordinates relevant to the hypothesis are shown to enable us to directly test the hypotheses expressed as a linear equation of a parameter vector, given a linear constraint. When the conditional posterior distribution of the parameter vector we are interested in is the multivariate normal distribution, the proposed method can be applied to calculate the p -value of hypotheses pertaining to the parameters in any complex model such as generalized linear mixed effect models with latent variables, by using outputs from Markov chain Monte Carlo (MCMC) methods. Further, the proposed testing can be implemented without prior information. Some applications are presented, and the simulation results are provided to compare the powers of this method with those of other methods of conventional multiple comparisons. Simulation studies have shown that the proposed method is valid for multiple comparisons under nonequivalent variances and mean comparisons in latent variable modeling with categorical variables.

The Rules of Logic Composition for the Bayesian Epistemic e-Values

In this paper, the relationship between the e-value of a complex hypothesis, H, and those of its constituent elementary hypotheses, H j , j = 1… k, is analyzed, in the independent setup. The e-value of a hypothesis H, ev(H), is a Bayesian epistemic, credibility or truth value defined under the Full Bayesian Significance Testing (FBST) mathematical apparatus. The questions addressed concern the important issue of how the truth value of H, and the truth function of the corresponding FBST structure M, relate to the truth values of its elementary constituents, H j , and to the truth functions of their corresponding FBST structures M j , respectively.

Testing and Estimating the Non‐Disjunction Fraction in Meiosis I using Reference Priors

In this paper we analyze the fraction of non-disjunction in Meiosis I assuming reference (non-informative) priors. We consider Jeffreys's approach to built a non-informative prior (Jeffreys's prior) for the fraction of non-disjunction in Meiosis I. We prove that Jeffreys's prior is a proper distribution. We perform Monte Carlo studies in order to compare Bayes estimates obtained assuming Jeffreys's and uniform priors. We consider full Bayesian significance test (FBST) and Bayes factor (BF) for testing precise hypothesis on the fraction of non-disjunction in Meiosis I. The ultimate goal of this paper is to compare these two test procedures through simulation studies using both prior specifications. An application to Down Syndrome data is also presented.

Full Bayesian Significance Test for Zero-Inflated Distributions

ABSTRACT In this article, we discuss an application of the Full Bayesian Significance Test (FBST) introduced by Pereira and Stern (1999) to compute the evidence of the Poisson distribution against the Zero-Inflated Poisson distribution (ZIP). The FBST is intuitive and easy to implement via Winbugs as an alternative to the classical tests formulated by Xie et al. (2001) in statistical process context. This evidence measure is based on the augmented data and used to test the fitting of the ZIP model for count data with excess of zeros in two illustrative examples in the statistical process control and the horticultural research.

Polymorphisms (Snps) in Multiple Genes of the Tgf-ß/Bmp Pathway Are Associated with a Global Measure of Sickle Cell Disease Severity.

A global estimation of sickle cell disease severity has been difficult to establish making the integration of clinical and laboratory abnormalities of into a predictive model of disease complications and death, an unrealized goal. A useful model might help us to understand the interactions among common clinical and laboratory abnormalities and allow patients at risk of certain complications and early death to be identified early so that targeted treatment, if available, could be provided. To approach this problem we first integrated clinical and laboratory data from nearly 3500 individuals from the Cooperative Study of Sickle Cell Disease and applied to this data advanced statistical machine learning techniques to identify the significant associations between selected complications of disease and laboratory variables. We looked for predictors of the risk for early death in three separate age groups. The resulting model revealed that complex networks of interactions between clinical and laboratory variables underlie common disease complications and ultimately death. Predictors of risk in this model were the HBA1, HBA2 genotype, stroke, sepsis and acute chest syndrome. While this model can predict the risk for early death, given the presence of other disease complications and variations among common laboratory variables, it did not provide an understanding of the genetic basis for our observations. Accordingly, in over 1000 patients with sickle cell disease we genotyped SNPs in genes chosen because of their possible link to the pathophysiology of disease. We then used our estimate of global disease severity to find associations of genotypes with severity. In the initial screening studies we identified several genes in the TGF-ß/BMP pathway that were associated with selected disease subphenotypes (Sebastiani et al Nature Genet 37: 435, 2005; Baldwin et al. Blood 106: 372, 2005). The TGF-b/BMP pathway regulates a wide range of biological functions including cell proliferation, cellular differentiation, extracellular matrix production, cell death, tissue repair and immune regulation. To expand our initial findings, we typed haplotype tagging SNPS in a more comprehensive fashion in 21 genes that are key members of this pathway. The genes included BMP6, BMP receptors, TGF-b receptors, SMADs, MAP kinases and their associated co-factors such as SARA, CDH1 and SMURF1. We used a Bayesian significance test to model the associations between the score of disease severity and individual SNPs, as well as a traditional association test with p-values computed using permutation tests. To reduce the problem of multiple comparisons, we selected as significantly associated with disease severity, only those SNPs that passed both tests with strong evidence of association. The most striking associations were found for BMP6, its receptors BMPR1 and BMPR2, several SMAD proteins and SARA1. Our results confirm the importance of the TGF-ß signaling pathway in sickle cell disease pathophysiology and suggest that subtle variation in this cell signaling network can be associated with the severity of disease.

An Empirical Bayesian Significance Test of cDNA Library Data

Automated high-throughput sequencing of cDNA clones from numerous libraries has generated a wealth of information about both genome sequence and relative transcript abundances. A common statistical challenge in the analysis of library sequences is to infer whether there is differential expression for the same transcript under two different conditions, such as normal and diseased tissue. In contrast to the continuously variable intensity measurements from microarray experiments, data from cDNA library sequencing presents itself as a discrete count of the incidence of some clone or transcript in a finite sample. In this paper, we first propose a statistical model for data generated from cDNA library sequencing efforts. The model is based on the Poisson mixed with generalized inverse Gaussian (PGIG), introduced by Sichel (1971, 1975). PGIG has been used in modeling population abundance, ecological studies, word frequencies in publications, etc. Using data from the literature, we show that the proposed model provides a good fit to the observed data. Using this new model for cDNA library data, we developed an empirical Bayesian significance test (EBST) for inferring the statistical significance of differential gene expression from discrete data.

A Critique on Contemporary Reporting of Likelihood Ratios in Test Power Analysis

A Critique on Contemporary Reporting of Likelihood Ratios in Test Power Analysis

Bayesian evidence test for precise hypotheses

The full Bayesian significance test (FBST) for precise hypotheses is presented, with some illustrative applications. In the FBST we compute the evidence against the precise hypothesis. We discuss some of the theoretical properties of the FBST, and provide an invariant formulation for coordinate transformations, provided a reference density has been established. This evidence is the probability of the highest relative surprise set, “tangential” to the sub-manifold (of the parameter space) that defines the null hypothesis.

Model selection: Full Bayesian approach

AbstractWe show how the Full Bayesian Significance Test (FBST) can be used as a model selection criterion. The FBST was presented in Pereira and Stern as a coherent Bayesian significance test. Copyright © 2001 John Wiley & Sons, Ltd.

ベイズ的アプローチによる因子平均の群間差・線形対比の有意性検定

ベイズ的アプローチによる因子平均の群間差・線形対比の有意性検定

Evidence and Credibility: Full Bayesian Significance Test for Precise Hypotheses

A Bayesian measure of evidence for precise hypotheses is presented. The intention is to give a Bayesian alternative to significance tests or, equivalently, to p-values. In fact, a set is defined in the parameter space and the posterior probability, its credibility, is evaluated. This set is the "Highest Posterior Density Region" that is "tangent" to the set that defines the null hypothesis. Our measure of evidence is the complement of the credibility of the "tangent" region.

A Bayesian Significance Test of the Stationarity of Regression Parameters

This paper presents a Bayesian significance test for stationarity of a regression equation using the highest posterior density credible set. In addition, a solution to the Behrens- Fisher problem is provided. From a Monte Carlo simulation study, it has been shown that the Bayesian significance test has stronger power than the Cusum and the Cusum of squares tests. The Bayesian significance test may be useful in detecting individual parameter nonstationarity.

A Bayesian significance test of the stationarity of regression parameters

This paper presents a Bayesian significance test for stationarity of a regression equation using the highest posterior density credible set. In addition, a solution to the BehrensFisher problem is provided. From a Monte Carlo simulation study, it has been shown that the Bayesian significance test has stronger power than the Cusum and the Cusum of squares tests. The Bayesian significance test may be useful in detecting individual parameter nonstationarity.