Spike-and-Slab Dirichlet Process Mixture Models

DOI: 10.4236/ojs.2012.25066   PDF   HTML     5,602 Downloads   7,884 Views   Citations

Abstract

In this paper, Spike-and-Slab Dirichlet Process (SS-DP) priors are introduced and discussed for non-parametric Bayesian modeling and inference, especially in the mixture models context. Specifying a spike-and-slab base measure for DP priors combines the merits of Dirichlet process and spike-and-slab priors and serves as a flexible approach in Bayesian model selection and averaging. Computationally, Bayesian Expectation-Maximization (BEM) is utilized to obtain MAP estimates. Two simulated examples in mixture modeling and time series analysis contexts demonstrate the models and computational methodology.

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K. Cui and W. Cui, "Spike-and-Slab Dirichlet Process Mixture Models," Open Journal of Statistics, Vol. 2 No. 5, 2012, pp. 512-518. doi: 10.4236/ojs.2012.25066.

Conflicts of Interest

The authors declare no conflicts of interest.

References

[1] J. F. Geweke, “Variable Selection and Model Comparison in Regression,” Working Papers 539, Federal Reserve Bank of Minneapolis, Minneapolis, 1994.
[2] T. J. Mitchell and J. J. Beauchamp, “Bayesian Variable Selection in Linear Regression,” Journal of the American Statistical Association, Vol. 83, No. 404, 1988, pp. 1023- 1032,
[3] E. I. George and R. E. McCulloch, “Variable Selection via Gibbs Sampling,” Journal of the American Statistical Association, Vol. 88, No. 423, 1993, pp. 881-889.
[4] D. B. Dahl and M. A. Newton, “Multiple Hypothesis Testing by Clustering Treatment Effects,” Journal of the American Statistical Association, Vol. 102, No. 478, 2007, pp. 517-526.
[5] D. B. Dahl, Q. Mo and M. Vannucci, “Simultaneous Inference for Multiple Testing and Clustering via a Dirichlet Process Mixture Model,” Statistical Modelling, Vol. 8, No. 1, 2008, pp. 23-29.
[6] S. Kim and D. B. Dahl and M. Vannucci, “Spiked Dirichlet Process Prior for Bayesian Multiple Hypothesis Testing in Random Effects Models,” Bayesian Analysis, Vol. 4, No. 4, 2009, pp. 707-732.
[7] T. S. Ferguson, “A Bayesian Analysis of Some NonParametric Problems,” The Annals of Statistics, Vol. 1, No. 2, 1973, pp. 209-230.
[8] T. S. Ferguson, “Prior Distributions on Spaces of Probability Measures,” Annals of Statistics, Vol. 2, No. 4, 1974, pp. 615-629.
[9] J. Sethuraman, “A Constructive Definition of Dirichlet Priors,” Statistica Sinica, Vol. 4, 1994, pp. 639-650.
[10] E. P. Chan, “Quantitative Trading,” John Wiley and Sons, Hoboken, 2008.
[11] D. A. Dickey and W.A. Fuller, “Distribution of the Estimators for Autoregressive Time Series with a Unit Root,” Journal of the American Statistical Association, Vol. 74, No. 366, 1979, pp. 427-431.

  
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