Journal ArticleDOI
Seeking efficient data augmentation schemes via conditional and marginal augmentation
Xiao-Li Meng,D. A. Van Dyk +1 more
TLDR
This paper investigates the use of working parameters in the contexts 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 approaches.Abstract:
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.read more
Citations
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Journal ArticleDOI
The Art of Data Augmentation
David A. van Dyk,Xiao-Li Meng +1 more
TL;DR: An effective search strategy is introduced that combines the ideas of marginal augmentation and conditional augmentation, together with a deterministic approximation method for selecting good augmentation schemes to obtain efficient Markov chain Monte Carlo algorithms for posterior sampling.
Journal ArticleDOI
Optimization Transfer Using Surrogate Objective Functions
TL;DR: Because optimization transfer algorithms often exhibit the slow convergence of EM algorithms, two methods of accelerating optimization transfer are discussed and evaluated in the context of specific problems.
Journal ArticleDOI
Parameter Expansion for Data Augmentation
Jun Liu,Ying Nian Wu +1 more
TL;DR: A parameter expanded data augmentation (PX-DA) algorithm is rigorously defined and a new theory for iterative conditional sampling under the tra… to understand the role of the expansion parameter.
Journal ArticleDOI
Efficient construction of reversible jump Markov chain Monte Carlo proposal distributions
TL;DR: In this paper, the authors consider reversible jump Markov chain Monte Carlo methods and propose a Taylor series expansion of the acceptance probability around certain canonical jumps to guide the choice of proposal.
Journal ArticleDOI
Partially collapsed Gibbs samplers: Theory and methods
David A. van Dyk,Taeyoung Park +1 more
TL;DR: Three basic tools (marginalization, permutation, and trimming) are introduced that allow us to transform a Gibbs sampler into a partially collapsed GibbsSampler with known stationary distribution and faster convergence.
References
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