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Monte Carlo Methods and Applications

Managing Editor: Sabelfeld, Karl K.

Editorial Board: Binder, Kurt / Bouleau, Nicolas / Chorin, Alexandre J. / Dimov, Ivan / Dubus, Alain / Egorov, Alexander D. / Ermakov, Sergei M. / Halton, John H. / Heinrich, Stefan / Kalos, Malvin H. / Lepingle, D. / Makarov, Roman / Mascagni, Michael / Mathe, Peter / Niederreiter, Harald / Platen, Eckhard / Sawford, Brian R. / Schmid, Wolfgang Ch. / Schoenmakers, John / Simonov, Nikolai A. / Sobol, Ilya M. / Spanier, Jerry / Talay, Denis

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1569-3961
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Volume 16, Issue 3-4

Issues

MCMC imputation in autologistic model

Marta Zalewska
  • Department of Environmental Hazards Prevention and Allergology, Medical University of Warsaw, Zwirki i Wigury 61, 02-091 Warszawa, Poland. E-mail:
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/ Wojciech Niemiro
  • Faculty of Mathematics and Computer Science, Nicolaus Copernicus University, Chopina 12/18, 87-100 Toruń, Institute of Applied Mathematics and Mechanics, University of Warsaw, Banacha 2, 02-097 Warszawa, Poland. E-mail:
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/ Bolesław Samoliński
  • Department of Environmental Hazards Prevention and Allergology, Medical University of Warsaw, Zwirki i Wigury 61, 02-091 Warszawa, Poland. E-mail:
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Published Online: 2010-10-20 | DOI: https://doi.org/10.1515/mcma.2010.017

Abstract

We consider statistical inference from incomplete sets of binary data. Our approach is based on the autologistic model, which is very flexible and well suited for medical applications. We propose a Bayesian approach, essentially using Monte Carlo techniques. The method developed in this paper is a special version of Gibbs sampler. We repeat intermittently the following two steps. First, missing values are generated from the predictive distribution. Second, unknown parametes are estimated from the completed data. The Monte Carlo method of computing maximum likelihood estimates due to Geyer and Thompson (J. R. Statist. Soc. B 54: 657–699, 1992) is modified to the Bayesian setting and missing data problems. We include results of some small scale simulation experiments. We artificially introduce missing values in a real data set and then use our algorithm to refill missings. The rate of correct imputations is quite satisfactory.

Keywords.: Missing data; Markov chain Monte Carlo; medical data; Gibbs sampler; generalized linear models; Bayesian imputation

About the article

Received: 2009-11-15

Revised: 2010-09-15

Published Online: 2010-10-20

Published in Print: 2010-12-01


Citation Information: Monte Carlo Methods and Applications, Volume 16, Issue 3-4, Pages 421–438, ISSN (Online) 1569-3961, ISSN (Print) 0929-9629, DOI: https://doi.org/10.1515/mcma.2010.017.

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