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Copula based factorization in Bayesian multivariate infinite mixture models

Martin Burda, Artem Prokhorov
2014 Journal of Multivariate Analysis  
Bayesian nonparametric models based on infinite mixtures of density kernels have been recently gaining in popularity due to their flexibility and feasibility of implementation even in complicated modeling  ...  In this paper, we propose a factorization scheme of multivariate dependence structures based on the copula modeling framework, whereby each marginal dimension in the mixing parameter space is modeled separately  ...  Conclusions In this paper, we propose a factorization scheme for Bayesian nonparametric mixture models based on modeling separately the marginals as univariate infinite mixtures linked by a nonparametric  ... 
doi:10.1016/j.jmva.2014.02.011 fatcat:gp46gtbzpjhd3bg7r3iqkb2tru

BAYESIAN INFERENCE METHODS FOR UNIVARIATE AND MULTIVARIATE GARCH MODELS: A SURVEY

Audrone Virbickaite, M. Concepción Ausín, Pedro Galeano
2013 Journal of economic surveys (Print)  
This survey reviews the existing literature on the most relevant Bayesian inference methods for univariate and multivariate GARCH models.  ...  These novel approaches implicitly assume infinite mixture of Gaussian distributions on the standardized returns which have been shown to be more flexible and describe better the uncertainty about future  ...  The innovations are modeled as an infinite mixture of multivariate Normals with a DP prior.  ... 
doi:10.1111/joes.12046 fatcat:jan2j3zunfaermqg7dmqu5ndty

Bayesian Nonparametric Conditional Copula Estimation of Twin Data

Luciana Dalla Valle, Fabrizio Leisen, Luca Rossini
2017 Social Science Research Network  
Our methodology extends the work of Wu et al. (2015) by introducing dependence from a covariate in an infinite mixture model.  ...  We propose a flexible Bayesian nonparametric approach for the estimation of conditional copulas, which can model any conditional copula density.  ...  The authors combine the well-known Gaussian copula density with the modeling flexibility of the Bayesian nonparametric approach, proposing to use an infinite mixture of Gaussian copulas.  ... 
doi:10.2139/ssrn.2752355 fatcat:cno4tn7xnzc5fftdobkneasnau

Bayesian Nonparametric Conditional Copula Estimation of Twin Data [article]

Luciana Dalla Valle, Fabrizio Leisen, Luca Rossini
2017 arXiv   pre-print
Our methodology extends the work of Wu et al (2015) by introducing dependence from a covariate in an infinite mixture model.  ...  We propose a flexible Bayesian nonparametric approach for the estimation of conditional copulas, which can model any conditional copula density.  ...  The authors combine the well-known Gaussian copula density with the modeling flexibility of the Bayesian nonparametric approach, proposing to use an infinite mixture of Gaussian copulas.  ... 
arXiv:1603.03484v4 fatcat:f6sem7f4vzhjlpdws4mu3fg4my

Bayesian non-parametric conditional copula estimation of twin data

Luciana Dalla Valle, Fabrizio Leisen, Luca Rossini
2017 Journal of the Royal Statistical Society, Series C: Applied Statistics  
Our methodology extends the work of Wu, Wang and Walker in 2015 by introducing dependence from a covariate in an infinite mixture model.  ...  We propose a flexible Bayesian non-parametric approach for the estimation of conditional copulas, which can model any conditional copula density.  ...  They combined the well-known Gaussian copula density with the modelling flexibility of the Bayesian non-parametric approach, proposing to use an infinite mixture of Gaussian copulas.  ... 
doi:10.1111/rssc.12237 fatcat:7wotf5ayzvfrvktnllpfbs45my

An Imputation model by Dirichlet Process Mixture of Elliptical Copulas for Data of Mixed Type [article]

Jiali Wang, Anton Westveld, Bronwyn Loong, Alan Welsh
2019 arXiv   pre-print
We consider a Bayesian nonparametric approach by using an infinite mixture of elliptical copulas induced by a Dirichlet process mixture to build a flexible copula function.  ...  Copula-based methods provide a flexible approach to build missing data imputation models of multivariate data of mixed types. However, the choice of copula function is an open question.  ...  In this paper, our aim is to develop a flexible imputation model using a Bayesian nonparametric approach. Specifically, an infinite mixture of elliptical copulas induced by a DPM model.  ... 
arXiv:1910.05473v1 fatcat:nop5rlwz6bhfnlfy5oi6z4dauy

Bayesian Nonparametric Modelling of Conditional Multidimensional Dependence Structures [article]

Rosario Barone, Luciana Dalla Valle
2021 arXiv   pre-print
More precisely, we specify the vine copula density as an infinite mixture of Gaussian copulas, defining a Dirichlet process (DP) prior on the mixing measure, and we perform posterior inference via Markov  ...  In high dimension, vine copulas offer greater flexibility compared to multivariate copulas, since they are constructed using bivariate copulas as building blocks.  ...  infinite mixture model.  ... 
arXiv:2109.10969v1 fatcat:izq7qheesfdkhdenzazg6ryiiq

Copulas in Machine Learning [chapter]

Gal Elidan
2013 Copulae in Mathematical and Quantitative Finance  
Despite overlapping goals of multivariate modeling and dependence identification, until recently the fields of machine learning in general and probabilistic graphical models in particular have been ignorant  ...  The purpose of this paper is to survey recent copula-based constructions in the field of machine learning, so as to provide a stepping stone for those interested in further exploring this emerging symbiotic  ...  The construction is based on the Bayesian nonparametric Dirichlet process infinite mixture model.  ... 
doi:10.1007/978-3-642-35407-6_3 fatcat:owohw3nb65dnvbduj63crouvhq

Copula Mixture Model for Dependency-seeking Clustering [article]

Melanie Rey
2012 arXiv   pre-print
We formulate our model as a non-parametric Bayesian mixture, while providing efficient MCMC inference.  ...  The model takes advantage of the great flexibility offered by the copulas framework to extend mixtures of Canonical Correlation Analysis to multivariate data with arbitrary continuous marginal densities  ...  Figure 2 . 2 Graphical representation of the infinite copula mixture model with base measure G0 and concentration λ.  ... 
arXiv:1206.6433v1 fatcat:hlrwkcy5fna3jozgqwqc4vieqy

Copula-Based Models for Multivariate Discrete Response Data [chapter]

Aristidis K. Nikoloulopoulos
2013 Copulae in Mathematical and Quantitative Finance  
A review of copula-based models and methods for multivariate discrete data modeling will be presented.  ...  Introduction One goal in the theory of dependence modeling and multivariate copulas is to develop copula-based models and inferential procedures for multivariate discrete responses with covariates.  ...  Bayesian methods have also been used on the estimation of an elliptical-copula based model. Pit et al. [49] proposed a general Bayesian approach for estimating a MVN copula-based model.  ... 
doi:10.1007/978-3-642-35407-6_11 fatcat:disqynvfvbfitkhsrqbw5iwyze

Approximate Bayesian inference in semiparametric copula models [article]

Clara Grazian, Brunero Liseo
2017 arXiv   pre-print
The method is based on a copula representation of the multivariate distribution and it is based on the properties of an Approximate Bayesian Monte Carlo algorithm, where the proposed values of the functional  ...  of interest are weighed in terms of their empirical likelihood.  ...  A Bayesian nonparametric approach is followed by Wu et al. (2014) , who model and estimate only the copula density function by using infinite mixture models and treat the marginals as given.  ... 
arXiv:1503.02912v4 fatcat:vniil5r5tbgl7avqfc33lyptyu

On approximating copulas by finite mixtures [article]

Mohamad A. Khaled, Robert Kohn
2018 arXiv   pre-print
Copula based multivariate models can often also be more parsimonious than fitting a flexible multivariate model, such as a mixture of normals model, directly to the data.  ...  We illustrate empirically on a financial data set that our approach for estimating a copula can be much more parsimonious and results in a better fit than approximating the copula by a mixture of normal  ...  For example, consider approximating a high dimensional multivariate model 1 by a flexible factor based model such as a mixture of factor analyzers; see, for example, Chapter 8 of McLachlan and Peel (2000  ... 
arXiv:1705.10440v2 fatcat:j3rcumi5e5adhgv4okcnnw7h5i

Flexible Multivariate Density Estimation with Marginal Adaptation [article]

Paolo Giordani, Xiuyan Mun, Robert Kohn
2009 arXiv   pre-print
The first estimator we propose is a mixture of normals copula model that is a flexible alternative to parametric copula models such as the normal and t copula.  ...  We show empirically that copula based approaches can behave much better or much worse than estimators based on mixture of normals depending on the properties of the data.  ...  Conclusions Both copula models and mixture of normals models provide estimators of multivariate densities.  ... 
arXiv:0901.0225v1 fatcat:xyd52z5v4bdi7advd7r64cddkm

Multivariate dependence analysis via tree copula models: An application to one-year forward energy contracts

Federico Bassetti, Maria Elena De Giuli, Enrica Nicolino, Claudia Tarantola
2018 European Journal of Operational Research  
We propose a novel multivariate approach for dependence analysis in the energy market. The method-ology is based on tree copulas and GARCH type processes.  ...  Working in a Bayesian framework, we perform both qualitative and quantitative learning. Posterior summaries of the quantities of interest are obtained via MCMC methods.  ...  The work was financially supported by the project "Multivariate Statistical Analysis for Extreme Value Risk Management in Energy Markets" (Contratto Aperto 840 0 057081) by Enel S.p.A.  ... 
doi:10.1016/j.ejor.2018.02.037 fatcat:inwwbtsc7rdxjoqblwo2k6b5im

A review of multivariate distributions for count data derived from the Poisson distribution

David I. Inouye, Eunho Yang, Genevera I. Allen, Pradeep Ravikumar
2017 Wiley Interdisciplinary Reviews: Computational Statistics  
is a mixture of independent multivariate Poisson distributions, and 3) where the node-conditional distributions are derived from the Poisson.  ...  We discuss the development of multiple instances of these classes and compare the models in terms of interpretability and theory.  ...  The multivariate distributions can be factorized in a variety of ways using bivariate copulas to flexibly model dependencies.  ... 
doi:10.1002/wics.1398 pmid:28983398 pmcid:PMC5624559 fatcat:p2ig6gh2vrgvrbj2farxme5mgy
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