期刊
JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
卷 106, 期 496, 页码 1361-1370出版社
AMER STATISTICAL ASSOC
DOI: 10.1198/jasa.2011.tm10747
关键词
Curved exponential family; Markov chain Monte Carlo; Social network; Statistical exponential family; Undirected graphical model
资金
- Netherlands Organisation for Scientific Research [446-06-029]
- National Institute of Health [1R01HD052887-01A2]
- Office of Naval Research [N00014-08-1-1015]
A number of discrete exponential family models for dependent data, first and foremost relational data, have turned out to be near-degenerate and problematic in terms of Markov chain Monte Carlo (MCMC) simulation and statistical inference. I introduce the notion of instability with an eye to characterize, detect, and penalize discrete exponential family models that are near-degenerate and problematic in terms of MCMC simulation and statistical inference. I show that unstable discrete exponential family models are characterized by excessive sensitivity and near-degeneracy. In special cases, the subset of the natural parameter space corresponding to nondegenerate distributions and mean-value parameters far from the boundary of the mean-value parameter space turns out to be a lower-dimensional subspace of the natural parameter space. These characteristics of unstable discrete exponential family models tend to obstruct MCMC simulation and statistical inference. In applications to relational data, I show that discrete exponential family models with Markov dependence tend to be unstable, and that the parameter space of some curved exponential families contains unstable subsets.
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