Bernoulli

  • Bernoulli
  • Volume 15, Number 3 (2009), 736-753.

Discrete chain graph models

Mathias Drton

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Abstract

The statistical literature discusses different types of Markov properties for chain graphs that lead to four possible classes of chain graph Markov models. The different models are rather well understood when the observations are continuous and multivariate normal, and it is also known that one model class, referred to as models of LWF (Lauritzen–Wermuth–Frydenberg) or block concentration type, yields discrete models for categorical data that are smooth. This paper considers the structural properties of the discrete models based on the three alternative Markov properties. It is shown by example that two of the alternative Markov properties can lead to non-smooth models. The remaining model class, which can be viewed as a discrete version of multivariate regressions, is proven to comprise only smooth models. The proof employs a simple change of coordinates that also reveals that the model’s likelihood function is unimodal if the chain components of the graph are complete sets.

Article information

Source
Bernoulli Volume 15, Number 3 (2009), 736-753.

Dates
First available in Project Euclid: 28 August 2009

Permanent link to this document
http://projecteuclid.org/euclid.bj/1251463279

Digital Object Identifier
doi:10.3150/08-BEJ172

Mathematical Reviews number (MathSciNet)
MR2555197

Zentralblatt MATH identifier
1153.65309

Keywords
algebraic statistics categorical data conditional independence graphical model Markov property path diagram

Citation

Drton, Mathias. Discrete chain graph models. Bernoulli 15 (2009), no. 3, 736--753. doi:10.3150/08-BEJ172. http://projecteuclid.org/euclid.bj/1251463279.


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