An official website of the United States government
Abstract We develop alternative families of Bayes factors for use in hypothesis tests as alternatives to the popular default Bayes factors. The alternative Bayes factors are derived for the statistical analyses most commonly used in psychological research – one-sample and two-samplet tests, regression, and ANOVA analyses. They possess the same desirable theoretical and practical properties as the default Bayes factors and satisfy additional theoretical desiderata while mitigating against two features of the default priors that we consider implausible. They can be conveniently computed via an R package that we provide. Furthermore, hypothesis tests based on Bayes factors and those based on significance tests are juxtaposed. This discussion leads to the insight that default Bayes factors as well as the alternative Bayes factors are equivalent to test-statistic-based Bayes factors as proposed by Johnson.Journal of the Royal Statistical Society Series B: Statistical Methodology,67, 689–701. (2005). We highlight test-statistic-based Bayes factors as a general approach to Bayes-factor computation that is applicable to many hypothesis-testing problems for which an effect-size measure has been proposed and for which test power can be computed.
more »
« less
Double Reduction Estimation and Equilibrium Tests in Natural Autopolyploid Populations
Abstract Many bioinformatics pipelines include tests for equilibrium. Tests for diploids are well studied and widely available, but extending these approaches to autopolyploids is hampered by the presence of double reduction, the comigration of sister chromatid segments into the same gamete during meiosis. Though a hindrance for equilibrium tests, double reduction rates are quantities of interest in their own right, as they provide insights about the meiotic behavior of autopolyploid organisms. Here, we develop procedures to (i) test for equilibrium while accounting for double reduction, and (ii) estimate the double reduction rate given equilibrium. To do so, we take two approaches: a likelihood approach, and a novel U-statistic minimization approach that we show generalizes the classical equilibrium χ2 test in diploids. For small sample sizes and uncertain genotypes, we further develop a bootstrap procedure based on our U-statistic to test for equilibrium. We validate our methods on both simulated and real data.
more »
« less
- Award ID(s):
- 2132247
- PAR ID:
- 10369484
- Publisher / Repository:
- Oxford University Press
- Date Published:
- Journal Name:
- Biometrics
- Volume:
- 79
- Issue:
- 3
- ISSN:
- 0006-341X
- Format(s):
- Medium: X Size: p. 2143-2156
- Size(s):
- p. 2143-2156
- Sponsoring Org:
- National Science Foundation
More Like this
-
-
Physically unclonable hardware fingerprints can be used for device authentication. The photo-response non-uniformity (PRNU) is the most reliable hardware fingerprint of digital cameras and can be conveniently extracted from images. However, we find image post-processing software may introduce extra noise into images. Part of this noise remains in the extracted PRNU fingerprints and is hard to be eliminated by traditional approaches, such as denoising filters. We define this noise as software noise, which pollutes PRNU fingerprints and interferes with authenticating a camera armed device. In this paper, we propose novel approaches for fingerprint matching, a critical step in device authentication, in the presence of software noise. We calculate the cross correlation between PRNU fingerprints of different cameras using a test statistic such as the Peak to Correlation Energy (PCE) so as to estimate software noise correlation. During fingerprint matching, we derive the ratio of the test statistic on two PRNU fingerprints of interest over the estimated software noise correlation. We denote this ratio as the fingerprint to software noise ratio (FITS), which allows us to detect the PRNU hardware noise correlation component in the test statistic for fingerprint matching. Extensive experiments over 10,000 images taken by more than 90 smartphones are conducted to validate our approaches, which outperform the state-of-the-art approaches significantly for polluted fingerprints. We are the first to study fingerprint matching with the existence of software noise.more » « less
-
Abstract Key message:In tetraploid F1 populations, traditional segregation distortion tests often inaccurately flag SNPs due to ignoring polyploid meiosis processes and genotype uncertainty. We develop tests that account for these factors. Abstract:Genotype data from tetraploid F1 populations are often collected in breeding programs for mapping and genomic selection purposes. A common quality control procedure in these groups is to compare empirical genotype frequencies against those predicted by Mendelian segregation, where SNPs detected to havesegregation distortionare discarded. However, current tests for segregation distortion are insufficient in that they do not account for double reduction and preferential pairing, two meiotic processes in polyploids that naturally change gamete frequencies, leading these tests to detect segregation distortion too often. Current tests also do not account for genotype uncertainty, again leading these tests to detect segregation distortion too often. Here, we incorporate double reduction, preferential pairing, and genotype uncertainty in likelihood ratio and Bayesian tests for segregation distortion. Our methods are implemented in a user-friendly R package, . We demonstrate the superiority of our methods to those currently used in the literature on both simulations and real data.more » « less
-
Summary In this paper, we develop a systematic theory for high-dimensional analysis of variance in multivariate linear regression, where the dimension and the number of coefficients can both grow with the sample size. We propose a new U-type statistic to test linear hypotheses and establish a high-dimensional Gaussian approximation result under fairly mild moment assumptions. Our general framework and theory can be used to deal with the classical one-way multivariate analysis of variance, and the nonparametric one-way multivariate analysis of variance in high dimensions. To implement the test procedure, we introduce a sample-splitting-based estimator of the second moment of the error covariance and discuss its properties. A simulation study shows that our proposed test outperforms some existing tests in various settings.more » « less
-
Summary Kernel two-sample tests have been widely used for multivariate data to test equality of distributions. However, existing tests based on mapping distributions into a reproducing kernel Hilbert space mainly target specific alternatives and do not work well for some scenarios when the dimension of the data is moderate to high due to the curse of dimensionality. We propose a new test statistic that makes use of a common pattern under moderate and high dimensions and achieves substantial power improvements over existing kernel two-sample tests for a wide range of alternatives. We also propose alternative testing procedures that maintain high power with low computational cost, offering easy off-the-shelf tools for large datasets. The new approaches are compared to other state-of-the-art tests under various settings and show good performance. We showcase the new approaches through two applications: the comparison of musks and nonmusks using the shape of molecules, and the comparison of taxi trips starting from John F. Kennedy airport in consecutive months. All proposed methods are implemented in an R package kerTests.more » « less
