Approximate Bayesian Inference in Semiparametric Copula Models

Grazian, Clara; Liseo, Brunero

doi:10.1214/17-ba1080

Cited by 19 publications

(27 citation statements)

References 46 publications

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“…This is in contrast to Gaussian Bayesian variable selection, where in some examples fixed (such as = 100 or = ) can provide good results (Smith and Kohn, 1996). Moreover, in the second example we also find that integrating out uncertainty in as in Grazian and Liseo (2017) does not meaningfully effect covariate selection or prediction. The method is scalable to higher dimensions because estimation by stochastic search over is fast when exploiting the matrix identities in the Web Appendix.…”

Section: Discussionmentioning

confidence: 65%

“…It is common to use twostage estimators, where is estimated first, followed by , because they are much faster and often involve only a minor loss of efficiency (Joe, 2005). Grazian and Liseo (2017) and Klein and Smith (2019) integrate out uncertainty for using a Bayesian nonparametric estimator, but find that this does not improve the accuracy of inference meaningfully, as we also demonstrate in an empirical example in Part F of the Web Appendix. Therefore, we adopt a two-stage estimator, and use the adaptive kernel density estimator (KDE) of Shimazaki and Shinomoto (2010) to estimate .…”

Section: Estimation and Inferencementioning

confidence: 82%

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Bayesian variable selection for non‐Gaussian responses: a marginally calibrated copula approach

Klein

Smith

2020

Biometrics

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We propose a new highly flexible and tractable Bayesian approach to undertake variable selection in non‐Gaussian regression models. It uses a copula decomposition for the joint distribution of observations on the dependent variable. This allows the marginal distribution of the dependent variable to be calibrated accurately using a nonparametric or other estimator. The family of copulas employed are “implicit copulas” that are constructed from existing hierarchical Bayesian models widely used for variable selection, and we establish some of their properties. Even though the copulas are high dimensional, they can be estimated efficiently and quickly using Markov chain Monte Carlo. A simulation study shows that when the responses are non‐Gaussian, the approach selects variables more accurately than contemporary benchmarks. A real data example in the Web Appendix illustrates that accounting for even mild deviations from normality can lead to a substantial increase in accuracy. To illustrate the full potential of our approach, we extend it to spatial variable selection for fMRI. Using real data, we show our method allows for voxel‐specific marginal calibration of the magnetic resonance signal at over 6000 voxels, leading to an increase in the quality of the activation maps.

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Section: Discussionmentioning

confidence: 65%

Section: Estimation and Inferencementioning

confidence: 82%

Bayesian variable selection for non‐Gaussian responses: a marginally calibrated copula approach

Klein

Smith

2020

Biometrics

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“…In a second approach, we follow Grazian and Liseo (2017) and integrate out the posterior uncertainty for F Y when estimating the copula parameters using an MCMC scheme. To do so, at each sweep of the MCMC scheme, we re-compute the pseudo data…”

Section: Posterior Evaluationmentioning

confidence: 99%

Implicit Copulas from Bayesian Regularized Regression Smoothers

Klein¹,

Smith²

2019

Bayesian Anal.

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We show how to extract the implicit copula of a response vector from a Bayesian regularized regression smoother with Gaussian disturbances. The copula can be used to compare smoothers that employ different shrinkage priors and function bases. We illustrate with three popular choices of shrinkage priors-a pairwise prior, the horseshoe prior and a g prior augmented with a point mass as employed for Bayesian variable selection-and both univariate and multivariate function bases. The implicit copulas are high-dimensional, have flexible dependence structures that are far from that of a Gaussian copula, and are unavailable in closed form. However, we show how they can be evaluated by first constructing a Gaussian copula conditional on the regularization parameters, and then integrating over these. Combined with non-parametric margins the regularized smoothers can be used to model the distribution of non-Gaussian univariate responses conditional on the covariates. Efficient Markov chain Monte Carlo schemes for evaluating the copula are given for this case. Using both simulated and real data, we show how such copula smoothing models can improve the quality of resulting function estimates and predictive distributions.

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“…Dalla Valle et al [2018] extended the approach of Wu et al [2015] to bivariate conditional copulas, introducing dependence from covariates and implementing Bayesian nonparametric inference via an infinite mixture model. A different approach is followed by Grazian and Liseo [2017], who described an approximate Bayesian inference method for semiparametric bivariate copulas, based on the empirical likelihood. This approach is extended by Grazian et al [2021], who compared several Bayesian methods to approximate the posterior distribution of functionals of the dependence including covariates, using nonparametric models which avoid the selection of the copula function.…”

Section: Introductionmentioning

confidence: 99%

Bayesian Nonparametric Modelling of Conditional Multidimensional Dependence Structures

Barone¹,

Valle²

2021

Preprint

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In recent years, conditional copulas, that allow dependence between variables to vary according to the values of one or more covariates, have attracted increasing attention. In high dimension, vine copulas offer greater flexibility compared to multivariate copulas, since they are constructed using bivariate copulas as building blocks. In this paper we present a novel inferential approach for multivariate distributions, which combines the flexibility of vine constructions with the advantages of Bayesian nonparametrics, not requiring the specification of parametric families for each pair copula. Expressing multivariate copulas using vines allows us to easily account for covariate specifications driving the dependence between response variables. 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 chain Monte Carlo (MCMC) sampling. Our approach is successful as for clustering as well as for density estimation. We carry out intensive simulation studies and apply the proposed approach to investigate the impact of natural disasters on financial development. Our results show that the methodology is able to capture the heterogeneity in the dataset and to reveal different behaviours of different country clusters in relation to natural disasters.

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Approximate Bayesian Inference in Semiparametric Copula Models

Cited by 19 publications

References 46 publications

Bayesian variable selection for non‐Gaussian responses: a marginally calibrated copula approach

Bayesian variable selection for non‐Gaussian responses: a marginally calibrated copula approach

Implicit Copulas from Bayesian Regularized Regression Smoothers

Bayesian Nonparametric Modelling of Conditional Multidimensional Dependence Structures

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