A non-Gaussian multivariate distribution with all lower-dimensional Gaussians and related families

Dutta, Subhajit; Genton, Marc G.

doi:10.1016/j.jmva.2014.07.007

Cited by 19 publications

(8 citation statements)

References 23 publications

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“…The resulting best-fit distribution is only an approximation, since the true posterior is not necessarily Gaussian (see the Appendix). Even when the marginals of the posterior appear to be Gaussian, this does not necessarily imply that the full posterior is jointly Gaussian (see Figure 6 and Dutta & Genton 2014). This is consistent with the fact that the VI posterior does not always exactly agree with the true posterior (i.e., HMC samples).…”

Section: Variational Inferencementioning

confidence: 59%

GIGA-Lens: Fast Bayesian Inference for Strong Gravitational Lens Modeling

Huang

Sheu

et al. 2022

ApJ

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We present GIGA-Lens: a gradient-informed, GPU-accelerated Bayesian framework for modeling strong gravitational lensing systems, implemented in TensorFlow and JAX. The three components, optimization using multistart gradient descent, posterior covariance estimation with variational inference, and sampling via Hamiltonian Monte Carlo, all take advantage of gradient information through automatic differentiation and massive parallelization on graphics processing units (GPUs). We test our pipeline on a large set of simulated systems and demonstrate in detail its high level of performance. The average time to model a single system on four Nvidia A100 GPUs is 105 s. The robustness, speed, and scalability offered by this framework make it possible to model the large number of strong lenses found in current surveys and present a very promising prospect for the modeling of  ( 10 5 ) lensing systems expected to be discovered in the era of the Vera C. Rubin Observatory, Euclid, and the Nancy Grace Roman Space Telescope.

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Section: Variational Inferencementioning

confidence: 59%

GIGA-Lens: Fast Bayesian Inference for Strong Gravitational Lens Modeling

Huang

Sheu

et al. 2022

ApJ

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“…From theory of distribution point of view, if the asymmetry parameter is equal to zero, the proposed models provide new examples of random vectors with marginal distribution of the Gaussian and Tukey-h type whose bivariate or multivariate distribution are not of the same type (Dutta and Genton, 2014). A limitation for the proposed class is the lack of computationally feasible density outside of the bivariate case that prevents an inference approach based on likelihood methods.…”

Section: Discussionmentioning

confidence: 99%

A class of random fields with two-piece marginal distributions for modeling point-referenced data with spatial outliers

Bevilacqua

Caamaño‐Carrillo

Arellano–Valle

et al. 2022

TEST

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In this paper, we propose a new class of non-Gaussian random fields named two-piece random fields. The proposed class allows to generate random fields that have flexible marginal distributions, possibly skewed and/or heavytailed and, as a consequence, has a wide range of applications. We study the second-order properties of this class and provide analytical expressions for the bivariate distribution and the associated correlation functions. We exemplify our general construction by studying two examples: two-piece Gaussian and two-piece Tukey-h random fields. An interesting feature of the proposed class is that it offers a specific type of dependence that can be useful when modeling data displaying spatial outliers, a property that has been somewhat ignored from modeling viewpoint in the literature for spatial point referenced data. Since the likelihood function involves analytically intractable integrals, we adopt the weighted pairwise likelihood as a method of estimation. The effectiveness of our methodology is illustrated with simulation experiments as well as with the analysis of a georeferenced dataset of mean temperatures in Middle East.

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“…For instance, non-normal distributions that have all lower-dimensional marginals being normal (see, e.g., Dutta and Genton (2014)), and classical univariate normality tests, such as the χ 2 -test, have limited applicability in higher dimensions. Reviews on the tests for MVN have been given by Thode (2002), Henze (2002) and Ebner and Henze (2020), with the last one emphasizing on several classes of the weighted L 2 -statistics.…”

Section: Introductionmentioning

confidence: 99%

Are You All Normal? It Depends!

Chen¹,

Genton²

2020

Preprint

Self Cite

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The assumption of normality has underlain much of the development of statistics, including spatial statistics, and many tests have been proposed. In this work, we focus on the multivariate setting and we first provide a synopsis of the recent advances in multivariate normality tests for i.i.d. data, with emphasis on the skewness and kurtosis approaches. We show through simulation studies that some of these tests cannot be used directly for testing normality of spatial data, since the multivariate sample skewness and kurtosis measures, such as the Mardia's measures, deviate from their theoretical values under Gaussianity due to dependence, and some related tests exhibit inflated type I error, especially when the spatial dependence gets stronger. We review briefly the few existing tests under dependence (time or space), and then propose a new multivariate normality test for spatial data by accounting for the spatial dependence of the observations in the test statistic. The new test aggregates univariate Jarque-Bera (JB) statistics, which combine skewness and kurtosis measures, for individual variables. The asymptotic variances of sample skewness and kurtosis for standardized observations are derived given the dependence structure of the spatial data. Consistent estimators of the asymptotic variances are then constructed for finite samples. The test statistic is easy to compute, without any smoothing involved, and it is asymptotically χ 2 2p under normality, where p is the number of variables. The new test has a good control of the type I error and a high empirical power, especially for large sample sizes.

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A non-Gaussian multivariate distribution with all lower-dimensional Gaussians and related families

Cited by 19 publications

References 23 publications

GIGA-Lens: Fast Bayesian Inference for Strong Gravitational Lens Modeling

GIGA-Lens: Fast Bayesian Inference for Strong Gravitational Lens Modeling

A class of random fields with two-piece marginal distributions for modeling point-referenced data with spatial outliers

Are You All Normal? It Depends!

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