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Bayesian Statistics 9$
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José M. Bernardo, M. J. Bayarri, James O. Berger, A. P. Dawid, David Heckerman, Adrian F. M. Smith, and Mike West

Print publication date: 2011

Print ISBN-13: 9780199694587

Published to Oxford Scholarship Online: January 2012

DOI: 10.1093/acprof:oso/9780199694587.001.0001

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PRINTED FROM OXFORD SCHOLARSHIP ONLINE (oxford.universitypressscholarship.com). (c) Copyright Oxford University Press, 2021. All Rights Reserved. An individual user may print out a PDF of a single chapter of a monograph in OSO for personal use. date: 23 April 2021

Nonparametric Bayesian Networks *

Nonparametric Bayesian Networks *

(p.283) Nonparametric Bayesian Networks*
Bayesian Statistics 9

Katja Ickstadt

Bjöorn Bornkamp

Marco Grzegorczyk

Jakob Wieczorek

Malik R. Sheriff

Hernáan E. Grecco

Eli Zamir

Oxford University Press

A convenient way of modelling complex interactions is by employing graphs or networks which correspond to conditional independence structures in an underlying statistical model. One main class of models in this regard are Bayesian networks, which have the drawback of making parametric assumptions. Bayesian nonparametric mixture models offer a possibility to overcome this limitation, but have hardly been used in combination with networks. This manuscript bridges this gap by introducing nonparametric Bayesian network models. We review (parametric) Bayesian networks, in particular Gaussian Bayesian networks, from a Bayesian perspective as well as nonparametric Bayesian mixture models. Afterwards these two modelling approaches are combined into nonparametric Bayesian networks. The new models are compared both to Gaussian Bayesian networks and to mixture models in a simulation study, where it turns out that the nonparametric network models perform favourably in non‐Gaussian situations. The new models are also applied to an example from systems biology, namely finding modules within the MAPK cascade.

Keywords:   Gaussian Bayesian networks, Systems Biology, Nonparametric Mixture Models, Species Sampling Models

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