Lamnisos, Demetris, Griffin, Jim E. and Steel, Mark F. J.. (2009) Transdimensional sampling algorithms for Bayesian variable selection in classification problems with many more variables than observations. Journal of Computational and Graphical Statistics, Vol.18 (No.3). pp. 592-612. ISSN 1061-8600

Full text not available from this repository.

Abstract

Model search in probit regression is often conducted by simultaneously exploring the model and parameter space, using a reversible jump MCMC sampler. Standard samplers often have low model acceptance probabilities when there are many more regressors than observations. Implementing recent suggestions in the literature leads to much higher acceptance rates. However, high acceptance rates are often associated with poor mixing of chains. Thus, we design a more general model proposal that allows us to propose models "further" front our current model. This proposal can be tuned to achieve a suitable acceptance rate for good mixing. The effectiveness of this proposal is linked to the form of the marginalization scheme when updating the model and we propose a new efficient implementation of the automatic generic transdimensional algorithm of Green (2003). We also implement other previously proposed samplers and compare the efficiency of all methods on some gene expression datasets. Finally, the results of these applications lead us to propose guidelines for choosing between samplers. Relevant code and datasets are posted as an online supplement.

Item Type:	Journal Article
Subjects:	Q Science > QA Mathematics
Divisions:	Faculty of Science > Statistics
Library of Congress Subject Headings (LCSH):	Sampling (Statistics), Probits, Markov processes, Gene expression -- Statistical methods
Journal or Publication Title:	Journal of Computational and Graphical Statistics
Publisher:	American Statistical Association
ISSN:	1061-8600
Date:	September 2009
Volume:	Vol.18
Number:	No.3
Number of Pages:	21
Page Range:	pp. 592-612
Identification Number:	10.1198/jcgs.2009.08027
Status:	Peer Reviewed
Publication Status:	Published
Access rights to Published version:	Restricted or Subscription Access
Funder:	University of Warwick. Centre for Research in Statistical Methodology
Version or Related Resource:	Lamnisos, D., Griffin, J.E. and Steel, M.F.J. (2008). Transdimensional sampling algorithms for Bayesian variable selection in classification problems with many more variables than observations. [Coventry] : University of Warwick. Centre for Research in Statistical Methodology. (Working papers, no.08-08). http://wrap.warwick.ac.uk/id/eprint/35484
Related URLs:	Related item in WRAP
References:	Albert, J., and Chib, S. (1993), “Bayesian Analysis of Binary and Polychotomous Response Data,” Journal of the American Statistical Association, 88, 669–679. Alon, U., Barkai, N., Notterman, D. A., Gish, K., Ybarra, D., Mack, D., and Levine, A. J. (1999), “Broad Patterns of Gene Expression Revealed by Clustering Analysis of Tumor and Normal Colon Tissues Probe by Oligonucleotide Array,” Proceedings of the National Academy of Sciences of the USA, 96, 6745–6750. Armstrong, S. A., Staunton, J. E., Silverman, L. B., Pieters, R., den Boer, M. L., Minden, M. D., Sallan, S. E., Lander, E. S., Golub, T. R., and Korsmeyer, S. J. (2002), “MLL Translocations Specify a Distinct Gene Expression Profile That Distinguishes a Unique Leukemia,” Nature Genetics, 30, 41–47. Atchadé, Y. F., and Rosenthal, J. S. (2005), “On Adaptive Markov Chain Monte Carlo Algorithms,” Bernoulli, 5, 815–828. Brooks, S. P., Giudici, P., and Roberts, G. O. (2003), “Efficient Construction of Reversible Jump Markov Chain Monte Carlo Proposal Distributions,” Journal of the Royal Statistical Society, Ser. B, 65, 3–55. Brown, P. J., Vannucci, M., and Fearn, T. (1998a), “Multivariate Bayesian Variable Selection and Prediction,” Journal of the Royal Statistical Society, Ser. B, 60, 627–641. (1998b), “Bayesian Wavelength Selection in Multicomponent Analysis,” Journal of Chemometrics, 12, 173–182. Chipman, H., George, E. I., and McCulloch, R. E. (2001), “The Practical Implementation of Bayesian Model Selection,” in Model Selection, ed. P. Lahiri, Hayward, CA: IMS, pp. 67–134. Dudoit, S., Fridlyand, J., and Speed, T. P. (2002), “Comparison of Discrimination Methods for the Classification of Tumors Using Gene Expression Data,” Journal of the American Statistical Association, 97, 77–87. Fernández, C., Ley, E., and Steel, M. F. J. (2001), “Benchmark Priors for Bayesian Model Averaging,” Journal of Econometrics, 100, 381–427. Gamerman, D. (1997), “Sampling From the Posterior Distribution in Generalized Linear Mixed Models,” Statistics and Computing, 7, 57–68. Geyer, C. J. (1992), “Practical Markov Chain Monte Carlo,” Statistical Science, 7, 473–511. Green, P. J. (1995), “Reversible Jump Markov Chain Monte Carlo Computation and Bayesian Model Determination,” Biometrika, 82, 711–732. (2003), “Trans-Dimensional Markov Chain Monte Carlo,” in Highly Structured Stochastic Systems, eds. P. J. Green, N. L. Hjord, and S. Richardson, Oxford, U.K.: Oxford University Press, pp. 179–198. Hans, C., Dobra, A., and West, M. (2007), “Shotgun Stochastic Search for “Large p” Regression,” Journal of the American Statistical Association, 102, 507–516. Holmes, C. C., and Held, L. (2006), “Bayesian Auxiliary Variable Models for Binary and Multinomial Regression,” Bayesian Analysis, 1, 145–168. Lee, K. E., Sha, N., Dougherty, R., Vannucci, M., and Mallick, B. K. (2003), “Gene Selection: A Bayesian Variable Selection Approach,” Bioinformatics, 19, 90–97. Madigan, D., and York, J. (1995), “Bayesian Graphical Models for Discrete Data,” International Statistical Review, 63, 215–232. Mitchell, T. J., and Beauchamp, J. J. (1988), “Bayesian Variable Selection in Linear Regression,” Journal of the American Statistical Association, 83, 1023–1032. Raftery, A. E., Madigan, D., and Hoeting, J. A. (1997), “Bayesian Model Averaging for Linear Regression Models,” Journal of the American Statistical Assocation, 92, 179–191. Roberts, G. O., and Rosenthal, J. S. (2001), “Optimal Scaling of Various Metropolis–Hastings Algorithms,” Statistical Science, 16, 351–367. Sha, N., Vannucci,M., Brown, P. J., Trower, M., and Amphlett, G. (2003), “Gene Selection in Arthritis ClassificationWith Large-ScaleMicroarray Expression Profiles,” Comparative and Functional Genomics, 4, 171–181. Sha, N., Vannucci, M., Tadesse, M. G., Brown, P. J., Dragoni, I., Davies, N., Roberts, T. C., Contestabile, A., Salmon, M., Buckley, C., and Falciani, F. (2004), “Bayesian Variable Selection inMultinomial ProbitModels to Identify Molecular Signatures of Disease Stage,” Biometrics, 60, 812–819. Singh, D., Febbo, P. G., Ross, K., Jackson, D., Manola, J., Ladd, C., Tamayo, P., Renshaw, A., D’Amico, A. V., Richie, J. P., Lander, E. S., Loda, M., Kantoff, P., Golub, T., and Sellers, W. (2002), “Gene Expression Correlates of Clinical Prostate Cancer Behaviour,” Cancer Cell, 1, 203–209. Sisson, S. (2005), “Transdimensional Markov Chains: A Decade of Progress and Future Perspectives,” Journal of the American Statistical Association, 100, 1077–1089. Yeung, K. Y., Bumgarner, R. E., and Raftery, A. E. (2005), “Bayesian Model Averaging: Development of an Improved Multi-Class Gene Selection and Classification Tool for Microarray Data,” Bioinformatics, 21, 2394– 2402.
URI:	http://wrap.warwick.ac.uk/id/eprint/17215

Data sourced from Thomson Reuters' Web of Knowledge

Request changes to a record

Actions (login required)

View Item