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1. Identifying and correcting for misspecifications in GWAS summary statistics and polygenic scores

Author

Florian Privé, Julyan Arbel, Hugues Aschard, and Bjarni J. Vilhjálmsson

Subjects
GWAS summary statistics, misspecifications, polygenic scores, Genetics, QH426-470
Abstract

Summary: Publicly available genome-wide association studies (GWAS) summary statistics exhibit uneven quality, which can impact the validity of follow-up analyses. First, we present an overview of possible misspecifications that come with GWAS summary statistics. Then, in both simulations and real-data analyses, we show that additional information such as imputation INFO scores, allele frequencies, and per-variant sample sizes in GWAS summary statistics can be used to detect possible issues and correct for misspecifications in the GWAS summary statistics. One important motivation for us is to improve the predictive performance of polygenic scores built from these summary statistics. Unfortunately, owing to the lack of reporting standards for GWAS summary statistics, this additional information is not systematically reported. We also show that using well-matched linkage disequilibrium (LD) references can improve model fit and translate into more accurate prediction. Finally, we discuss how to make polygenic score methods such as lassosum and LDpred2 more robust to these misspecifications to improve their predictive power.

Published
2022
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2. On the Hurwitz zeta function with an application to the beta-exponential distribution

Author

Julyan Arbel, Olivier Marchal, and Bernardo Nipoti

Subjects
Hurwitz zeta function, Polygamma function, Beta-exponential distribution, Monotonicity, Cumulants, Mathematics, QA1-939
Abstract

Abstract We prove a monotonicity property of the Hurwitz zeta function which, in turn, translates into a chain of inequalities for polygamma functions of different orders. We provide a probabilistic interpretation of our result by exploiting a connection between Hurwitz zeta function and the cumulants of the beta-exponential distribution.

Published
2020
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3. Approximate Bayesian Computation Via the Energy Statistic

Author

Hien Duy Nguyen, Julyan Arbel, Hongliang Lu, and Florence Forbes

Subjects
Approximate Bayesian computation, energy statistic, Kullback–Leibler divergence, importance sampling, maximum mean discrepancy, Wasserstein distance, Electrical engineering. Electronics. Nuclear engineering, TK1-9971
Abstract

Approximate Bayesian computation (ABC) has become an essential part of the Bayesian toolbox for addressing problems in which the likelihood is prohibitively expensive or entirely unknown, making it intractable. ABC defines a pseudo-posterior by comparing observed data with simulated data, traditionally based on some summary statistics, the elicitation of which is regarded as a key difficulty. Recently, using data discrepancy measures has been proposed in order to bypass the construction of summary statistics. Here we propose to use the importance-sampling ABC (IS-ABC) algorithm relying on the so-called two-sample energy statistic. We establish a new asymptotic result for the case where both the observed sample size and the simulated data sample size increase to infinity, which highlights to what extent the data discrepancy measure impacts the asymptotic pseudo-posterior. The result holds in the broad setting of IS-ABC methodologies, thus generalizing previous results that have been established only for rejection ABC algorithms. Furthermore, we propose a consistent V-statistic estimator of the energy statistic, under which we show that the large sample result holds, and prove that the rejection ABC algorithm, based on the energy statistic, generates pseudo-posterior distributions that achieves convergence to the correct limits, when implemented with rejection thresholds that converge to zero, in the finite sample setting. Our proposed energy statistic based ABC algorithm is demonstrated on a variety of models, including a Gaussian mixture, a moving-average model of order two, a bivariate beta and a multivariate g-and-k distribution. We find that our proposed method compares well with alternative discrepancy measures.

Published
2020
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4. Clustering Species With Residual Covariance Matrix in Joint Species Distribution Models

Author

Daria Bystrova, Giovanni Poggiato, Billur Bektaş, Julyan Arbel, James S. Clark, Alessandra Guglielmi, and Wilfried Thuiller

Subjects
Biodiversity modeling, dimension reduction, joint species distribution model, latent factors, Bayesian nonparametrics, plant communities, Evolution, QH359-425, Ecology, QH540-549.5
Abstract

Modeling species distributions over space and time is one of the major research topics in both ecology and conservation biology. Joint Species Distribution models (JSDMs) have recently been introduced as a tool to better model community data, by inferring a residual covariance matrix between species, after accounting for species' response to the environment. However, these models are computationally demanding, even when latent factors, a common tool for dimension reduction, are used. To address this issue, Taylor-Rodriguez et al. (2017) proposed to use a Dirichlet process, a Bayesian nonparametric prior, to further reduce model dimension by clustering species in the residual covariance matrix. Here, we built on this approach to include a prior knowledge on the potential number of clusters, and instead used a Pitman–Yor process to address some critical limitations of the Dirichlet process. We therefore propose a framework that includes prior knowledge in the residual covariance matrix, providing a tool to analyze clusters of species that share the same residual associations with respect to other species. We applied our methodology to a case study of plant communities in a protected area of the French Alps (the Bauges Regional Park), and demonstrated that our extensions improve dimension reduction and reveal additional information from the residual covariance matrix, notably showing how the estimated clusters are compatible with plant traits, endorsing their importance in shaping communities.

Published
2021
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5. Position: Bayesian Deep Learning is Needed in the Age of Large-Scale AI.

Author

Theodore Papamarkou, Maria Skoularidou, Konstantina Palla, Laurence Aitchison, Julyan Arbel, David B. Dunson, Maurizio Filippone, Vincent Fortuin, Philipp Hennig, José Miguel Hernández-Lobato, Aliaksandr Hubin, Alexander Immer, Theofanis Karaletsos, Mohammad Emtiyaz Khan, Agustinus Kristiadi, Yingzhen Li, Stephan Mandt, Christopher Nemeth, Michael A. Osborne, Tim G. J. Rudner, David Rügamer, Yee Whye Teh, Max Welling, Andrew Gordon Wilson, and Ruqi Zhang

Published
2024

8. Position Paper: Bayesian Deep Learning in the Age of Large-Scale AI.

Author

Theodore Papamarkou, Maria Skoularidou, Konstantina Palla, Laurence Aitchison, Julyan Arbel, David B. Dunson, Maurizio Filippone, Vincent Fortuin, Philipp Hennig, José Miguel Hernández-Lobato, Aliaksandr Hubin, Alexander Immer, Theofanis Karaletsos, Mohammad Emtiyaz Khan, Agustinus Kristiadi, Yingzhen Li, Stephan Mandt, Christopher Nemeth, Michael A. Osborne, Tim G. J. Rudner, David Rügamer, Yee Whye Teh, Max Welling, Andrew Gordon Wilson, and Ruqi Zhang

Published
2024
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32. Multivariate expectile-based distribution: properties, Bayesian inference, and applications

Author

Julyan Arbel, Stéphane Girard, Hien Duy Nguyen, Antoine Usseglio-Carleve, Modèles statistiques bayésiens et des valeurs extrêmes pour données structurées et de grande dimension (STATIFY), Inria Grenoble - Rhône-Alpes, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Laboratoire Jean Kuntzmann (LJK), Institut National de Recherche en Informatique et en Automatique (Inria)-Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes (UGA)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP ), Université Grenoble Alpes (UGA)-Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes (UGA)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP ), Université Grenoble Alpes (UGA), University of Queensland [Brisbane], EA2151 Laboratoire de Mathématiques d'Avignon (LMA), Avignon Université (AU), and Chaire Stress Test - BNP Paribas/Ecole polytechnique/Fondation de l'X.

Subjects
Statistics and Probability, Multivariate expectiles, [STAT.AP]Statistics [stat]/Applications [stat.AP], Multivariate distribution, Risk measure, Applied Mathematics, Bayesian inference, [STAT.TH]Statistics [stat]/Statistics Theory [stat.TH], Statistics, Probability and Uncertainty, Maximum likelihood estimation, [STAT.CO]Statistics [stat]/Computation [stat.CO], [STAT.ME]Statistics [stat]/Methodology [stat.ME]
Abstract

International audience; Expectiles form a family of risk measures that have recently gained interest over the more common value-at-risk or return levels, primarily due to their capability to be determined by the probabilities of tail values and magnitudes of realisations at once. However, a prevalent and ongoing challenge of expectile inference is the problem of uncertainty quantification, which is especially critical in sensitive applications, such as in medical, environmental or engineering tasks. We address this issue by developing a novel distribution, termed the multivariate expectilebased distribution (MED), that possesses an expectile as a closed-form parameter. Desirable properties of the distribution, such as log-concavity, make it an excellent fitting distribution in multivariate applications. Maximum likelihood estimation and Bayesian inference algorithms are described. Simulated examples and applications to expectile and mode estimation illustrate the usefulness of the MED for uncertainty quantification.

Published
2023
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36. BNPdensity: Bayesian nonparametric mixture modelling in R

Author

Guillaume Kon Kam King, Antonio Lijoi, Luis E. Nieto-Barajas, Igor Prünster, Julyan Arbel, Modèles statistiques bayésiens et des valeurs extrêmes pour données structurées et de grande dimension (STATIFY), Inria Grenoble - Rhône-Alpes, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Laboratoire Jean Kuntzmann (LJK), Institut National de Recherche en Informatique et en Automatique (Inria)-Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes (UGA)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP ), Université Grenoble Alpes (UGA)-Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes (UGA)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP ), Université Grenoble Alpes (UGA), Mathématiques et Informatique Appliquées du Génome à l'Environnement [Jouy-En-Josas] (MaIAGE), Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement (INRAE), Bocconi Institute for Data Science and Analytics (BIDSA), Bocconi University [Milan, Italy], Instituto Tecnológico Autónomo de México (ITAM), Ministry of Education, Universities and Research (MIUR) Research Projects of National Relevance (PRIN)2015SNS29B, ANR-15-IDEX-0002,UGA,IDEX UGA(2015), and ANR-19-P3IA-0003,MIAI,MIAI @ Grenoble Alpes(2019)

Subjects
Statistics and Probability, Generalization, Nonparametric statistics, Inference, BAYESIAN NONPARAMETRIC INFERENCE, DENSITY ESTIMATION, FERGUSON AND KLASS ALGORITHM, INFINITE MIXTURE MODELS, R, RANDOM PROBABILITY MEASURES, Mixture model, Dirichlet distribution, symbols.namesake, [MATH.MATH-ST]Mathematics [math]/Statistics [math.ST], Prior probability, symbols, Probability distribution, Statistics, Probability and Uncertainty, Algorithm, Parametric statistics, Mathematics
Abstract

International audience; Robust statistical data modelling under potential model mis-specification often requires leaving the parametric world for the nonparametric. In the latter, parameters are infinite dimensional objects such as functions, probability distributions or infinite vectors. In the Bayesian nonparametric approach, prior distributions are designed for these parameters, which provide a handle to manage the complexity of nonparametric models in practice. However, most modern Bayesian nonparametric models seem often out of reach to practitioners, as inference algorithms need careful design to deal with the infinite number of parameters. The aim of this work is to facilitate the journey by providing computational tools for Bayesian nonparametric inference. The article describes a set of functions available in the R package BNPdensity in order to carry out density estimation with an infinite mixture model, including all types of censored data. The package provides access to a large class of such models based on normalized random measures, which represent a generalization of the popular Dirichlet process mixture. One striking advantage of this generalization is that it offers much more robust priors on the number of clusters than the Dirichlet. Another crucial advantage is the complete flexibility in specifying the prior for the scale and location parameters of the clusters, because conjugacy is not required. Inference is performed using a theoretically grounded approximate sampling methodology known as the Ferguson & Klass algorithm. The package also offers several goodness of fit diagnostics such as QQ-plots, including a cross-validation criterion, the conditional predictive ordinate. The proposed methodology is illustrated on a classical ecological risk assessment method called the Species Sensitivity Distribution (SSD) problem, showcasing the benefits of the Bayesian nonparametric framework.

Published
2021
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37. Réduction de la dimension dans les modèles de distributions jointes d’espèces

Author

Daria BYSTROVA, Giovanni POGGIATO, Julyan ARBEL, and Wilfried THUILLER

Abstract

Nous présentons les modèles à facteurs latents dans le contexte des modèles de distribution joints d'espèces (JSDM), en soulignant leur utilité en écologie des communautés. Ces modèles permettent de faire face à la grande dimension des données d'observation dans l'espace et le temps, et qui limitent l'application des JSDMs. L'inférence se fait selon une approche bayésienne et est illustrée sur des données d'espèces végétales.

Published
2022
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38. Improving MCMC convergence diagnostic with a local version of R-hat

Author

Julyan Arbel, Stéphane Girard, Théo Moins, Anne Dutfoy, Khalil Leachouri, Modèles statistiques bayésiens et des valeurs extrêmes pour données structurées et de grande dimension (STATIFY), Inria Grenoble - Rhône-Alpes, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Laboratoire Jean Kuntzmann (LJK), Institut National de Recherche en Informatique et en Automatique (Inria)-Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes (UGA)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP ), Université Grenoble Alpes (UGA)-Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes (UGA)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP ), Université Grenoble Alpes (UGA), EDF (EDF), and Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )

Subjects
[STAT.AP]Statistics [stat]/Applications [stat.AP], [STAT.TH]Statistics [stat]/Statistics Theory [stat.TH], [STAT.CO]Statistics [stat]/Computation [stat.CO], [STAT.ME]Statistics [stat]/Methodology [stat.ME], ComputingMilieux_MISCELLANEOUS
Abstract

International audience

Published
2021

39. A simple proof of Pitman–Yor’s Chinese restaurant process from its stick-breaking representation

Author

Caroline Lawless, Julyan Arbel, Modelling and Inference of Complex and Structured Stochastic Systems (MISTIS ), Inria Grenoble - Rhône-Alpes, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Laboratoire Jean Kuntzmann (LJK ), and Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Institut National de Recherche en Informatique et en Automatique (Inria)-Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes [2016-2019] (UGA [2016-2019])-Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes [2016-2019] (UGA [2016-2019])

Subjects
Statistics and Probability, Statistics::Theory, Science (General), Computer science, Mathematics - Statistics Theory, Statistics Theory (math.ST), 01 natural sciences, Constructive, Bayesian nonparametrics, Q1-390, Statistics::Machine Learning, 010104 statistics & probability, 97k50, Mathematics::Probability, 0502 economics and business, Elementary proof, QA1-939, FOS: Mathematics, Calculus, Partition (number theory), 62f15, 0101 mathematics, [STAT.CO]Statistics [stat]/Computation [stat.CO], Cluster analysis, 050205 econometrics, [STAT.AP]Statistics [stat]/Applications [stat.AP], stick-breaking process, Applied Mathematics, 05 social sciences, [STAT.TH]Statistics [stat]/Statistics Theory [stat.TH], pitman-yor process, Dirichlet process, Random measure, Modeling and Simulation, partitions, Chinese restaurant process, [STAT.ME]Statistics [stat]/Methodology [stat.ME], bayesian nonparametrics, Mathematics, clustering
Abstract

For a long time, the Dirichlet process has been the gold standard discrete random measure in Bayesian nonparametrics. The Pitman--Yor process provides a simple and mathematically tractable generalization, allowing for a very flexible control of the clustering behaviour. Two commonly used representations of the Pitman--Yor process are the stick-breaking process and the Chinese restaurant process. The former is a constructive representation of the process which turns out very handy for practical implementation, while the latter describes the partition distribution induced. However, the usual proof of the connection between them is indirect and involves measure theory. We provide here an elementary proof of Pitman--Yor's Chinese Restaurant process from its stick-breaking representation., Comment: 11 pages

Published
2019
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40. Approximate Bayesian computation with surrogate posteriors

Author

Florence Forbes, Hien Duy Nguyen, TrungTin Nguyen, Julyan Arbel, Modèles statistiques bayésiens et des valeurs extrêmes pour données structurées et de grande dimension (STATIFY), Inria Grenoble - Rhône-Alpes, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Laboratoire Jean Kuntzmann (LJK), Institut National de Recherche en Informatique et en Automatique (Inria)-Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes (UGA)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP ), Université Grenoble Alpes (UGA)-Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes (UGA)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP ), Université Grenoble Alpes (UGA), University of Queensland [Brisbane], Laboratoire de Mathématiques Nicolas Oresme (LMNO), Centre National de la Recherche Scientifique (CNRS)-Université de Caen Normandie (UNICAEN), Normandie Université (NU)-Normandie Université (NU), School of Engineering and Mathematical Sciences, La Trobe University, Université de Caen Normandie (UNICAEN), Normandie Université (NU), and Normandie Université (NU)-Normandie Université (NU)-Centre National de la Recherche Scientifique (CNRS)

Subjects
[STAT.AP]Statistics [stat]/Applications [stat.AP], discrepancy measures, [STAT.TH]Statistics [stat]/Statistics Theory [stat.TH], divergence measures, Statistics::Computation, surrogate models, L2 distance, [MATH.MATH-ST]Mathematics [math]/Statistics [math.ST], multimodal posterior distributions, Approximate Bayesian computation, Wasserstein distance, Gaussian mixtures, summary statistics, [STAT.CO]Statistics [stat]/Computation [stat.CO], [STAT.ME]Statistics [stat]/Methodology [stat.ME], ComputingMilieux_MISCELLANEOUS
Abstract

A key ingredient in approximate Bayesian computation (ABC) procedures is the choice of a discrepancy that describes how different the simulated and observed data are, often based on a set of summary statistics when the data cannot be compared directly. Unless discrepancies and summaries are available from experts or prior knowledge, which seldom occurs, they have to be chosen and this can affect the approximations. Their choice is an active research topic, which has mainly considered data discrepancies requiring samples of observations or distances between summary statistics, to date. In this work, we introduce a preliminary learning step in which surrogate posteriors are built from finite Gaussian mixtures using an inverse regression approach. These surrogate posteriors are then used in place of summary statistics and compared using metrics between distributions in place of data discrepancies. Two such metrics are investigated, a standard L2 distance and an optimal transport-based distance. The whole procedure can be seen as an extension of the semi-automatic ABC framework to functional summary statistics. The resulting ABC quasi-posterior distribution is shown to converge to the true one, under standard conditions. Performance is illustrated on both synthetic and real data sets, where it is shown that our approach is particularly useful when the posterior is multimodal.

Published
2021

41. A Bayesian Framework for Poisson Process Characterization of Extremes with Objective Prior

Author

Théo Moins, Julyan Arbel, Anne Dutfoy, Stéphane Girard, Modèles statistiques bayésiens et des valeurs extrêmes pour données structurées et de grande dimension (STATIFY), Inria Grenoble - Rhône-Alpes, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Laboratoire Jean Kuntzmann (LJK), Institut National de Recherche en Informatique et en Automatique (Inria)-Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes (UGA)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP ), Université Grenoble Alpes (UGA)-Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes (UGA)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP ), Université Grenoble Alpes (UGA), PERformance et prévention des Risques Industriels du parC par la simuLation et les EtudeS (EDF R&D PERICLES), EDF R&D (EDF R&D), and EDF (EDF)-EDF (EDF)

Subjects
[STAT]Statistics [stat], ComputingMilieux_MISCELLANEOUS
Abstract

International audience

Published
2021

42. On Reparameterisations of the Poisson Process Model for Extremes in a Bayesian Framework

Author

Théo Moins, Julyan Arbel, Anne Dutfoy, Stéphane Girard, Modèles statistiques bayésiens et des valeurs extrêmes pour données structurées et de grande dimension (STATIFY), Inria Grenoble - Rhône-Alpes, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Laboratoire Jean Kuntzmann (LJK), Institut National de Recherche en Informatique et en Automatique (Inria)-Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes (UGA)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP ), Université Grenoble Alpes (UGA)-Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes (UGA)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP ), Université Grenoble Alpes (UGA), PERformance et prévention des Risques Industriels du parC par la simuLation et les EtudeS (EDF R&D PERICLES), EDF R&D (EDF R&D), and EDF (EDF)-EDF (EDF)

Subjects
Processus de Poisson, Extreme-Value theory, [MATH.MATH-ST]Mathematics [math]/Statistics [math.ST], Poisson processes, Bayesian inference, Théorie des valeurs extrêmes, Inférence bayésienne
Abstract

National audience; Combining extreme value analysis with Bayesian methods has several advantages, such as the consideration of prior information or the ability to study irregular cases for frequentist statistics. We focus here on a model of extremes by Poisson process, and propose an alternative of a recent study on a parameterisation of the model which orthogonalizes the parameters to improve posterior sampling by Markov chain Monte-Carlo method (MCMC).; Combiner l'analyse des valeurs extrêmes avec des méthodes bayésiennes a plusieurs avantages, comme la prise en compte d'information a priori ou encore la possibilité d'étudier des cas irréguliers en statistique fréquentiste. Nous nous attardons ici sur un modèle d'extrêmes par processus de Poisson, et proposons une approche alternative à une étude récente sur une reparamétrisation du modèle qui orthogonalise les paramètres pour améliorer l'échantillonnage a posteriori par méthode de Monte-Carlo par chaînes de Markov (MCMC).

Published
2021

43. Generalized Weibull-tail distributions

Author

Mariia Vladimirova, Julyan Arbel, Stéphane Girard, Modèles statistiques bayésiens et des valeurs extrêmes pour données structurées et de grande dimension (STATIFY), Inria Grenoble - Rhône-Alpes, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Laboratoire Jean Kuntzmann (LJK), Institut National de Recherche en Informatique et en Automatique (Inria)-Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes (UGA)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP ), Université Grenoble Alpes (UGA)-Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes (UGA)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP ), and Université Grenoble Alpes (UGA)

Subjects
Lois généralisé à queue de type Weibul, Sous-Weibull, [MATH.MATH-ST]Mathematics [math]/Statistics [math.ST], Generalized Weibull-tail, Lois à queue de type Weibull, Sub-Weibull, Weibull-tail, Stability, Stabilité
Abstract

International audience; Weibull-tail random variables are defined as non-negative random variables whose right tail behaves similarly to that of a Weibull random variable. We introduce generalized Weibull-tail random variables, extensions which have a property of stability. We study the preservation of tail parameters under operations like multiplication, power, and linear combination.; Des variables aléatoires à queue de type Weibull sont définies comme des variables aléatoires positives dont la queue droite se comporte de manière similaire à celle d'une variable aléatoire de Weibull. Nous introduisons des variables aléatoires de queue Weibull généralisées, des extensions qui ont une propriété de stabilité. Nous étudions la préservation des paramètres de queue de ces variables aléatoires sous des opérations telles que la multiplication, la puissance et la combinaison linéaire.

Published
2021

44. On the interpretations of joint modelling in community ecology

Author

Wilfried Thuiller, Daria Bystrova, James S. Clark, Giovanni Poggiato, Julyan Arbel, Tamara Münkemüller, Laboratoire d'Ecologie Alpine (LECA ), Université Savoie Mont Blanc (USMB [Université de Savoie] [Université de Chambéry])-Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes (UGA), Modèles statistiques bayésiens et des valeurs extrêmes pour données structurées et de grande dimension (STATIFY), Inria Grenoble - Rhône-Alpes, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Laboratoire Jean Kuntzmann (LJK), Institut National de Recherche en Informatique et en Automatique (Inria)-Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes (UGA)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP ), Université Grenoble Alpes (UGA)-Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes (UGA)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP ), Université Grenoble Alpes (UGA), Laboratoire des EcoSystèmes et des Sociétés en Montagne (UR LESSEM), Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement (INRAE), Nicholas School of the Environment, Duke University [Durham], Duke University, Department of Statistical Science, ERA-Net BiodivERsA -Belmont Forum, ANR-18-CE02-0025,GAMBAS,Nouvelles avancées dans la modélisation de la biodiversité et des services écosystémiques : améliorations statistiques et pertinences écologiques des modèles de distribution multi-espèces(2018), ANR-18-MPGA-0004,FORBIC,Prévision du changement de la biodiversité(2018), and ANR-18-EBI4-0009,FutureWeb,Climate and land use change threat to the vertebrate European food web structure and functioning(2018)

Subjects
0106 biological sciences, Community, Ecology, 010604 marine biology & hydrobiology, Ecology (disciplines), Climate, Rare species, Species distribution, Biodiversity, Biotic interactions, 15. Life on land, Joint Species Distribution Models, 010603 evolutionary biology, 01 natural sciences, Models, Biological, Field (geography), Community data, Geography, [SDE]Environmental Sciences, Joint (building), Biodiversity modelling, Ecology, Evolution, Behavior and Systematics, Environmental niche
Abstract

International audience; Explaining and modelling species communities is more than ever a central goal of ecology. Recently, joint species distribution models (JSDMs), which extend species distribution models (SDMs) by considering correlations among species, have been proposed to improve species community analyses and rare species predictions while potentially inferring species interactions. Here, we illustrate the mathematical links between SDMs and JSDMs and their ecological implications and demonstrate that JSDMs, just like SDMs, cannot separate environmental effects from biotic interactions. We provide a guide to the conditions under which JSDMs are (or are not) preferable to SDMs for species community modelling. More generally, we call for a better uptake and clarification of novel statistical developments in the field of biodiversity modelling.

Published
2021
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45. Identifying and correcting for misspecifications in GWAS summary statistics and polygenic scores

Author

Bjarni J. Vilhjálmsson, Julyan Arbel, Florian Privé, and Hugues Aschard

Subjects
Computer science, media_common.quotation_subject, Statistics, Genome-wide association study, Quality (business), Summary statistics, media_common
Abstract

Publicly available genome-wide association studies (GWAS) summary statistics exhibit uneven quality, which can impact the validity of follow-up analyses. First, we present an overview of possible misspecifications that come with GWAS summary statistics. Then, in both simulations and real data analyses, we show that additional information such as imputation INFO scores, allele frequencies, and per-variant sample sizes in GWAS summary statistics can be used to detect possible issues and correct for misspecifications in the GWAS summary statistics. One important motivation for us is to improve the predictive performance of polygenic scores built from these summary statistics. Unfortunately, due to the lack of reporting standards for GWAS summary statistics, this additional information is not systematically reported. We also show that using well-matched LD references can improve model fit and translate into more accurate prediction. Finally, we discuss how to make polygenic score methods such as lassosum and LDpred2 more robust to these misspecifications to improve their predictive power.

Published
2021
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46. Dirichlet process mixtures under affine transformations of the data

Author

Riccardo Corradin, Julyan Arbel, Bernardo Nipoti, Modèles statistiques bayésiens et des valeurs extrêmes pour données structurées et de grande dimension (STATIFY), Inria Grenoble - Rhône-Alpes, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Laboratoire Jean Kuntzmann (LJK), Institut National de Recherche en Informatique et en Automatique (Inria)-Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes (UGA)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP ), Université Grenoble Alpes (UGA)-Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes (UGA)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP ), Université Grenoble Alpes (UGA), Università degli Studi di Milano-Bicocca [Milano] (UNIMIB), Trinity College Dublin, Università degli Studi di Milano-Bicocca = University of Milano-Bicocca (UNIMIB), Arbel, J, Corradin, R, and Nipoti, B

Subjects
FOS: Computer and information sciences, Statistics and Probability, Computer science, Data transformation (statistics), 02 engineering and technology, Asymptotic robustne, 01 natural sciences, Clustering, Methodology (stat.ME), Bayesian nonparametrics, 010104 statistics & probability, Robustness (computer science), 0202 electrical engineering, electronic engineering, information engineering, 0101 mathematics, Invariant (mathematics), Cluster analysis, [STAT.CO]Statistics [stat]/Computation [stat.CO], Statistics - Methodology, [STAT.AP]Statistics [stat]/Applications [stat.AP], Dirichlet process mixture models, 020207 software engineering, Density estimation, [STAT.TH]Statistics [stat]/Statistics Theory [stat.TH], Multivariate density estimation, Dirichlet process, Computational Mathematics, Range (mathematics), Affine data transformation, Dirichlet process mixture model, Astronomical data, Affine transformation, Statistics, Probability and Uncertainty, Affine data transformations, Algorithm, Asymptotics, [STAT.ME]Statistics [stat]/Methodology [stat.ME], 62G07, 62F15, 62G35, Asymptotic robustness
Abstract

Location-scale Dirichlet process mixtures of Gaussians (DPM-G) have proved extremely useful in dealing with density estimation and clustering problems in a wide range of domains. Motivated by an astronomical application, in this work we address the robustness of DPM-G models to affine transformations of the data, a natural requirement for any sensible statistical method for density estimation and clustering. First, we devise a coherent prior specification of the model which makes posterior inference invariant with respect to affine transformations of the data. Second, we formalise the notion of asymptotic robustness under data transformation and show that mild assumptions on the true data generating process are sufficient to ensure that DPM-G models feature such a property. Our investigation is supported by an extensive simulation study and illustrated by the analysis of an astronomical dataset consisting of physical measurements of stars in the field of the globular cluster NGC 2419., Comment: 36 pages, 7 Figures

Published
2021
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47. Approximating the clusters' prior distribution in Bayesian nonparametric models

Author

Daria Bystrova, Julyan Arbel, Guillaume Kon Kam King, François Deslandes, Modèles statistiques bayésiens et des valeurs extrêmes pour données structurées et de grande dimension (STATIFY), Inria Grenoble - Rhône-Alpes, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Laboratoire Jean Kuntzmann (LJK), Institut National de Recherche en Informatique et en Automatique (Inria)-Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes (UGA)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP ), Université Grenoble Alpes (UGA)-Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes (UGA)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP ), Université Grenoble Alpes (UGA), Mathématiques et Informatique Appliquées du Génome à l'Environnement [Jouy-En-Josas] (MaIAGE), Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement (INRAE), Université Paris-Saclay, and Bystrova, Daria

Subjects
[STAT]Statistics [stat], [STAT] Statistics [stat]
Abstract

International audience; In Bayesian nonparametrics, knowledge of the prior distribution induced on the number of clusters is key for prior specification and calibration. However, evaluating this prior is infamously difficult even for moderate sample size. We evaluate several statistical approximations to the prior distribution on the number of clusters for Gibbs-type processes, a class including the Pitman-Yor process and the normalized generalized gamma process. We introduce a new approximation based on the predictive distribution of Gibbs-type process, which compares favourably with the existing methods. We thoroughly discuss the limitations of these various approximations by comparing them against an exact implementation of the prior distribution of the number of clusters.

Published
2021

48. LDpred2:better, faster, stronger

Author

Julyan Arbel, Bjarni J. Vilhjálmsson, Florian Privé, National Center for Register-Based Research [Aarhus], Aarhus University [Aarhus], Modèles statistiques bayésiens et des valeurs extrêmes pour données structurées et de grande dimension (STATIFY), Inria Grenoble - Rhône-Alpes, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Laboratoire Jean Kuntzmann (LJK), Institut National de Recherche en Informatique et en Automatique (Inria)-Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes (UGA)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP ), Université Grenoble Alpes (UGA)-Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes (UGA)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP ), and Université Grenoble Alpes (UGA)

Subjects
Statistics and Probability, AcademicSubjects/SCI01060, Computer science, Machine learning, computer.software_genre, Biochemistry, 03 medical and health sciences, 0302 clinical medicine, Chromosome (genetic algorithm), Robustness (computer science), [STAT.CO]Statistics [stat]/Computation [stat.CO], Molecular Biology, 030304 developmental biology, 0303 health sciences, business.industry, Genetics and Population Analysis, Genetic variants, Contrast (statistics), Chromosome, Original Papers, Human genetics, Computer Science Applications, Computational Mathematics, [SDV.GEN.GH]Life Sciences [q-bio]/Genetics/Human genetics, Computational Theory and Mathematics, Benchmark (computing), Artificial intelligence, business, computer, 030217 neurology & neurosurgery
Abstract

Motivation Polygenic scores have become a central tool in human genetics research. LDpred is a popular method for deriving polygenic scores based on summary statistics and a matrix of correlation between genetic variants. However, LDpred has limitations that may reduce its predictive performance. Results Here, we present LDpred2, a new version of LDpred that addresses these issues. We also provide two new options in LDpred2: a ‘sparse’ option that can learn effects that are exactly 0, and an ‘auto’ option that directly learns the two LDpred parameters from data. We benchmark predictive performance of LDpred2 against the previous version on simulated and real data, demonstrating substantial improvements in robustness and predictive accuracy compared to LDpred1. We then show that LDpred2 also outperforms other polygenic score methods recently developed, with a mean AUC over the 8 real traits analyzed here of 65.1%, compared to 63.8% for lassosum, 62.9% for PRS-CS and 61.5% for SBayesR. Note that LDpred2 provides more accurate polygenic scores when run genome-wide, instead of per chromosome. Availability and implementation LDpred2 is implemented in R package bigsnpr. Supplementary information Supplementary data are available at Bioinformatics online.

Published
2020
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50. Sub-Weibull distributions: generalizing sub-Gaussian and sub-Exponential properties to heavier-tailed distributions

Author

Stéphane Girard, Hien D. Nguyen, Julyan Arbel, Mariia Vladimirova, Modèles statistiques bayésiens et des valeurs extrêmes pour données structurées et de grande dimension (STATIFY), Inria Grenoble - Rhône-Alpes, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Laboratoire Jean Kuntzmann (LJK), Institut National de Recherche en Informatique et en Automatique (Inria)-Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes (UGA)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP ), Université Grenoble Alpes (UGA)-Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes (UGA)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP ), Université Grenoble Alpes (UGA), La Trobe University [Melbourne], ANR-15-IDEX-0002,UGA,IDEX UGA(2015), Institut National de Recherche en Informatique et en Automatique (Inria)-Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes [2020-....] (UGA [2020-....])-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP ), Université Grenoble Alpes [2020-....] (UGA [2020-....])-Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes [2020-....] (UGA [2020-....])-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP ), and Université Grenoble Alpes [2020-....] (UGA [2020-....])

Subjects
Statistics and Probability, Class (set theory), Gaussian, Bayesian probability, Parameterized complexity, Mathematics - Statistics Theory, Statistics Theory (math.ST), 010501 environmental sciences, Moment-generating function, 01 natural sciences, Exponential function, 010104 statistics & probability, symbols.namesake, [MATH.MATH-ST]Mathematics [math]/Statistics [math.ST], symbols, FOS: Mathematics, Statistical physics, 0101 mathematics, Statistics, Probability and Uncertainty, Tail index, 0105 earth and related environmental sciences, Mathematics, Weibull distribution
Abstract

We propose the notion of sub-Weibull distributions, which are characterised by tails lighter than (or equally light as) the right tail of a Weibull distribution. This novel class generalises the sub-Gaussian and sub-Exponential families to potentially heavier-tailed distributions. Sub-Weibull distributions are parameterized by a positive tail index $\theta$ and reduce to sub-Gaussian distributions for $\theta=1/2$ and to sub-Exponential distributions for $\theta=1$. A characterisation of the sub-Weibull property based on moments and on the moment generating function is provided and properties of the class are studied. An estimation procedure for the tail parameter is proposed and is applied to an example stemming from Bayesian deep learning., Comment: 10 pages, 3 figures

Published
2020
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