Skip to main page content
U.S. flag

An official website of the United States government

Dot gov

The .gov means it’s official.
Federal government websites often end in .gov or .mil. Before sharing sensitive information, make sure you’re on a federal government site.

Https

The site is secure.
The https:// ensures that you are connecting to the official website and that any information you provide is encrypted and transmitted securely.

Access keys NCBI Homepage MyNCBI Homepage Main Content Main Navigation
. 2015 May;57(3):468-84.
doi: 10.1002/bimj.201300130. Epub 2015 Feb 9.

Bayesian semiparametric copula estimation with application to psychiatric genetics

Ori Rosen  1 , Wesley K Thompson
Affiliations

Bayesian semiparametric copula estimation with application to psychiatric genetics

Ori Rosen et al. Biom J. 2015 May.

Abstract

This paper proposes a semiparametric methodology for modeling multivariate and conditional distributions. We first build a multivariate distribution whose dependence structure is induced by a Gaussian copula and whose marginal distributions are estimated nonparametrically via mixtures of B-spline densities. The conditional distribution of a given variable is obtained in closed form from this multivariate distribution. We take a Bayesian approach, using Markov chain Monte Carlo methods for inference. We study the frequentist properties of the proposed methodology via simulation and apply the method to estimation of conditional densities of summary statistics, used for computing conditional local false discovery rates, from genetic association studies of schizophrenia and cardiovascular disease risk factors.

Keywords: B-spline densities; Cardiovascular disease risk factors; Gaussian copula; Schizophrenia.

PubMed Disclaimer

Conflict of interest statement

Conflict of Interest

The authors have declared no conflict of interest.

Figures

Figure 1
Figure 1
Boxplots of the Kullback-Leibler divergence between the true and the estimated marginal densities.
Figure 2
Figure 2
Boxplots of the Kullback-Leibler divergence between the true and the estimated marginal densities of setting (ii) with n = 103 as a function of the number, Kj, of B-spline densities.
Figure 3
Figure 3
Boxplots of the Kullback-Leibler divergence between the true and the estimated conditional densities.
Figure 4
Figure 4
Boxplots of Stein’s loss based on the true and estimated correlation matrices.
Figure 5
Figure 5
Pairwise scatteplots of the data.
Figure 6
Figure 6
Top panel from left to right: marginal density histograms and density estimates of SCZ, SBP and TG. The solid lines are density estimates based on the method of Section 3. Bottom panel: similar plots for absolute z-scores ≥ 3.3.
Figure 7
Figure 7
Conditional density estimates showing the tails only (Z1 ≥ 3.3).
Figure 8
Figure 8
Conditional local fdr estimates f^1(z1|z2,z3) for different quantiles of z2 and z3.
Figure 9
Figure 9
Density histogram of Sn(B).
See this image and copyright information in PMC

Similar articles

See all similar articles

References

    1. Andreassen O, Djurovic S, Thompson W, Schork A, Kendler K, ODonovan M, Rujescu D, Werge T, van de Bunt M, Morris A, McCarthy M, Roddey J, McEvoy L, Desikan R, Dale A. Improved detection of common variants associated with schizophrenia by leveraging pleiotropy with cardiovascular disease risk factors. American Journal of Human Genetics. 2013;92:197–209. - PMC - PubMed
    1. Chan JC, Jeliazkov I. MCMC estimation of restricted covariance matrices. Journal of Computational and Graphical Statistics. 2009;18:457–480.
    1. Chen X, Fan Y, Tsyrennikov V. Efficient estimation of semiparametric multivariate copula models. Journal of the American Statistical Association. 2006;101:1228–1240.
    1. Chib S, Jeliazkov I. Inference in semiparametric dynamic models for binary longitudinal data. Journal of the American Statistical Association. 2006;101:685–700.
    1. Colton C, Manderscheid R. Congruencies in increased mortality rates, years of potential life lost, and causes of death among public mental health clients in eight states. Preventing Chronic Diseases. 2006;3:A42. - PMC - PubMed

Publication types

LinkOut - more resources