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Biometrika 1999 86(2):301-320; doi:10.1093/biomet/86.2.301
© 1999 by Biometrika Trust
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Seeking efficient data augmentation schemes via conditional and marginal augmentation

X-L MengA1 and DA van DykA2

A1 Department of Statistics, The University of Chicago, Chicago, IL 60637, USA E-mail: meng@galton.uchicago.edu A2 Department of Statistics, Harvard University, Cambridge, MA 02138, USA E-mail: vandyk@hustat.harvard.edu

Data augmentation, sometimes known as the method of auxiliary variables, is a powerful tool for constructing optimisation and simulation algorithms. In the context of optimisation, Meng & van Dyk (1997, 1998) reported several successes of the 'working parameter' approach for constructing efficient data-augmentation schemes for fast and simple EM-type algorithms. This paper investigates the use of working parameters in the context of Markov chain Monte Carlo, in particular in the context of Tanner & Wong's (1987) data augmentation algorithm, via a theoretical study of two working-parameter approaches, the conditional augmentation approach and the marginal augmentation approach. Posterior sampling under the univariate t model is used as a running example, which particularly illustrates how the marginal augmentation approach obtains a fast-mixing positive recurrent Markov chain by first constructing a nonpositive recurrent Markov chain in a larger space.

Key Words: Auxiliary variable; EM algorithm; Incomplete data; Markov chain Monte Carlo; PXEM algorithm; Rate of convergence; Working parameter.


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