作者：
Alain DesgagnéPierre Lafaye de MicheauxFrédéric Ouimeta Département de Mathématiques
Université du Québec à Montréal Montréal Canada b AMIS
Université Paul-Valéry Montpellier 3 Montpellier Francec PreMeDICaL - Precision Medicine by Data Integration and Causal Learning Inria Sophia Antipolis Franced Desbrest Institute of Epidemiology and Public Health Université de Montpellier Montpellier Francee School of Mathematics and Statistics UNSW Sydney NSW Australia f Division of Physics
Mathematics and Astronomy California Institute of Technology Pasadena CA USAg Department of Mathematics and Statistics McGill University Montreal Canadah Centre de recherches Mathématiques Université de Montréal Montréal Canada
Temperature data, like many other measurements in quantitative fields, are usually modelled using a normal distribution. However, some distributions can offer a better fit while avoiding underestimation of tail event ...
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Temperature data, like many other measurements in quantitative fields, are usually modelled using a normal distribution. However, some distributions can offer a better fit while avoiding underestimation of tail event probabilities. To this point, we extend Pearson's notions of skewness and kurtosis to build a powerful family of goodness-of-fit tests based on Rao's score for the exponential power distributionEPDλ(μ,σ), including tests for normality and Laplacity whenλis set to 1 or 2. We find the asymptotic distribution of our test statistic, which is the sum of the squares of twoZ-scores, under the null and under local alternatives. We also develop an innovative regression strategy to obtainZ-scores that are nearly independent and distributed as standard Gaussians, resulting in aχ22distribution valid for any sample size (up to very high precision forn≥20). The caseλ=1leads to a powerful test of fit for the Laplace(μ,σ) distribution, whose empirical power is superior to all 39 competitors in the literature, over a wide range of 400 alternatives. Theoretical proofs in this case are particularly challenging and substantial. We applied our tests to three temperature datasets. The new tests are implemented in theRpackagePoweR.
Functional magnetic resonance imaging (fMRI) functional connectivity between brain regions is often computed using parcellations defined by functional or structural atlases. Typically, some kind of voxel averaging is ...
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Functional magnetic resonance imaging (fMRI) functional connectivity between brain regions is often computed using parcellations defined by functional or structural atlases. Typically, some kind of voxel averaging is performed to obtain a single temporal correlation estimate per region pair. However, several estimators can be defined for this task, with various assumptions and degrees of robustness to local noise, global noise, and region size. In this paper, we systematically present and study the properties of 9 different functional connectivity estimators taking into account the spatial structure of fMRI data, based on a simple fMRI data spatial model. These include 3 existing estimators and 6 novel estimators. We demonstrate the empirical properties of the estimators using synthetic, animal, and human data, in terms of graph structure, repeatability and reproducibility, discriminability, dependence on region size, as well as local and global noise robustness. We prove analytically the link between regional intra-correlation and inter-region correlation, and show that the choice of estimator has a strong influence on inter-correlation values. Some estimators, including the commonly used correlation of averages (ca), are positively biased, and have more dependence to region size and intra-correlation than robust alternatives, resulting in spatially-dependent bias. We define the new local correlation of averages estimator with better theoretical guarantees, lower bias, significantly lower dependence on region size (p = 1.8e−15), and significantly higher reproducibility of graph metrics (p = 6.1e−5) at negligible cost to discriminative power, compared to the ca estimator. The difference in connectivity pattern between the estimators is not distributed randomly throughout the brain, but rather shows a clear ventral-dorsal gradient, suggesting that region size and intra-correlation plays an important role in shaping functional networks defined using the ca estimator,
Missing values are unavoidable when working with data. To help address this challenge, we have launched the ‘R-miss-tastic’ platform, which aims to provide an overview of standard missing values problems, methods, a...
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Temperature data, like many other measurements in quantitative fields, are usually modeled using a normal distribution. However, some distributions can offer a better fit while avoiding underestimation of tail event p...
详细信息
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