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Constrained Monte Carlo Maximum Likelihood for Dependent Data

Geyer, Charles J., Thompson, Elizabeth A.·1992·Journal of the Royal Statistical Society Series B: Statistical Methodology
DOI 10.1111/j.2517-6161.1992.tb01443.x
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Abstract

SUMMARY: Maximum likelihood estimates (MLEs) in autologistic models and other exponential family models for dependent data can be calculated with Markov chain Monte Carlo methods (the Metropolis algorithm or the Gibbs sampler), which simulate ergodic Markov chains having equilibrium distributions in the model. From one realization of such a Markov chain, a Monte Carlo approximant to the whole likelihood function can be constructed. The parameter value (if any) maximizing this function approximates the MLE. When no parameter point in the model maximizes the likelihood, the MLE in the closure of the exponential family may exist and can be calculated by a two-phase algorithm, first finding the support of the MLE by linear programming and then finding the distribution within the family conditioned on the support by maximizing the likelihood for that family. These methods are illustrated by a constrained autologistic model for DNA fingerprint data. MLEs are compared with maximum pseudolikelihood estimates (MPLEs) and with maximum conditional likelihood estimates (MCLEs), neither of which produce acceptable estimates, the MPLE because it overestimates dependence, and the MCLE because conditioning removes the constraints.

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Metadata

Authors
Geyer, C. J., & Thompson, E. A.
Venue
Journal of the Royal Statistical Society Series B: Statistical Methodology
Publisher
Oxford University Press (OUP)
Published
1992-07-01
Volume
54
Issue
3
Pages
657-683
ISSN
  • 1369-7412 (ISSN-L)
  • 1467-9868
DOI
10.1111/j.2517-6161.1992.tb01443.x
OpenAlex
W107938046
Cited by
874
References
2
FWCI
18.83
Type
journal article
Language
en
Open access
closed
Licence
academic.oup.com/journals/pages/open_access/funder_policies/chorus/standard_publication_model (vor)

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Geyer, C. J., & Thompson, E. A. (1992). Constrained Monte Carlo Maximum Likelihood for Dependent Data. Journal of the Royal Statistical Society Series B: Statistical Methodology. https://doi.org/10.1111/j.2517-6161.1992.tb01443.x

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