Bayesian outlier detection with dirichlet process mixtures

Bayesian Analysis

Volumn 6, Issue 4, 2011, Pages 665-690

  Shotwell, Matthew S ^a   Slate, Elizabeth H ^b  

^a VANDERBILT UNIVERSITY   (United States)

^b MEDICAL UNIVERSITY OF SOUTH CAROLINA   (United States)

Author keywords

Bayes factor; Optimization; Partition

Indexed keywords

EID: 84860856946     PISSN: 19360975     EISSN: 19316690     Source Type: Journal    
DOI: 10.1214/11-BA625     Document Type: Article

References (53)

1. Al-Zoubi, M. (2009). "An Effective Clustering-Based Approach for Outlier Detection." European Journal of Scientific Research, 28: 310-316.
2. Antoniak, C. E. (1974). "Mixtures of Dirichlet Processes with Applications to Bayesian Nonparametric Problems." The Annals of Statistics, 2: 1152-1174.
3. Bayarri, M. J. and Morales, J. (2003). "Bayesian measures of surprise for outlier detec-tion." Journal of Statistical Planning and Inference, 111(1-2): 3 - 22.
4. Bell, E. T. (1934). "Exponential Numbers." The American Mathematical Monthly, 41: 411-419.
5. Ben-Gal, I. (2005). "Outlier Detection." In Maimon, O. and Rockach, L. (eds.), Data Mining and Knowledge Discovery Handbook: A Complete Guide for Practitioners and Researchers". Kulwer Academic Publishers.
6. Berger, J. O. (1985). Statistical Decision Theory and Bayesian Analysis. Springer-Verlag New York Inc., 2 edition.
7. Bernardo, J. and Smith, A. (1994). Bayesian theory. Wiley series in probability and mathematical statistics: Probability and mathematical statistics. Wiley.
8. Blackwell, D. and MacQueen, J. B. (1973). "Ferguson Distributions Via Polya Urn Schemes." The Annals of Statistics, 1(2): 353-355.
9. Blei, D. and Jordan, M. (2006). "Variational Inference for Dirichlet Process Mixtures." Bayesian Analysis, 1(1): 121-144.
10. Box, G. E. P. and Tiao, G. C. (1968). "A Bayesian Approach to Some Outlier Problems." Biometrika, 55: 119-129.
11. Bush, C. A., Lee, J., and MacEachern, S. N. (2010). "Minimally informative prior distributions for non-parametric Bayesian analysis." Journal of the Royal Statistical Society, Series B, 72: 253-268.
12. Bush, C. A. and MacEachern, S. N. (1996). "A Semiparametric Bayesian Model for Randomised Block Designs." Biometrika, 83: 275-285.
13. Dahl, D. B. (2009). "Modal Clustering in a Class of Product Partition Models." Bayesian Analysis, 4: 243-264.
14. Efron, B. and Gous, A. (2001). "Scales of Evidence for Model Selection: Fisher versus Jeffreys." In Lahiri, P. (ed.), Model Selection: Lecture Notes-Monograph Series, volume 38, 208-246. Institute of Mathematical Statistics, Beachwood, OH.
15. Escobar, M. D. and West, M. (1995). "Bayesian Density Estimation and Inference Using Mixtures." Journal of the American Statistical Association, 90(430): 577-588.
16. Ferguson, T. S. (1961). "Rules for Rejection of Outliers." Review of the International Statistical Institute, 29(3): 29-43.
17. Ferguson, T. S. (1973). "A Bayesian Analysis of Some Nonparametric Problems." The Annals of Statistics, 1(2): 209-230.
18. Fraley, C. and Raftery, A. E. (2002). "Model-Based Clustering, Descriminant Analysis, and Density Estimation." Journal of the American Statistical Association, 97: 611- 631.
19. Geisser, S. (1980). "Discussion of 'Sampling and Bayes Inference in Scientific Modeling and Robustness', by G.E.P. Box." Journal of the Royal Statistical Society, Ser. A, 143: 416-417.
20. Green, P. J. and Richardson, S. (2001). "Modelling Heterogeneity With and Without the Dirichlet Process." Scandinavian Journal of Statistics, 28: 355-375.
21. Hartigan, J. A. (1990). "Partition Models." Communications in Statistics, Theory and Methods, 19: 2745-2756.
22. Hautamaki, V., Karkkainen, I., and Franti, P. (2004). "Outlier Detection Using K-nearest Neighbor Graph." In Proceedings of the 17th International Conference on Pattern Recognition, 430-433.
23. Heard, N. A., Holmes, C. C., and Stephens, D. A. (2006). "A Quantitative Study of Gene Regulation Involved in the Immune Response of Anopheline Mosquitoes: An Application of Bayesian Hierarchical Clustering of Curves." Journal of the American Statistical Association, 101(473): 18-28.
24. Heller, K. A. and Ghahramani, Z. (2005). "Bayesian Hierarchical Clustering." In Twenty-second International Conference on Machine Learning.
25. Hoeting, J., Raftery, A. E., and Madigan, D. (1996). "A method for simultaneous vari-able selection and outlier identification in linear regression." Computational Statistics & Data Analysis, 22(3): 251 - 270.
26. Hogg, R. V., McKean, J. W., and Craig, A. T. (2005). Introduction to Mathematical Statistics. Pearson Prentice Hall, 6 edition.
27. Ishwaran, H. and James, L. F. (2001). "Gibbs Sampling Methods for Stick-breaking Priors." Journal of the American Statistical Association, 96: 161-174.
28. Jain, S. and Neal, R. M. (2004). "A Split-Merge Markov Chain Monte Carlo Procedure for the Dirichlet Process Mixture Model." Journal of Computational and Graphical Statistics, 13(1): 158-182.
29. Jain, S. (2007). "Splitting and Merging Components of a Nonconjugate Dirichlet Process Mixture Model." Bayesian Analysis, 2(3): 445-472.
30. Jeffreys, H. (1961). Theory of Probability. Oxford, UK: Oxford University Press, 3 edition.
31. Kaufman, L. and Rousseeuw, P. (1990). Finding Groups in Data: An Introduction to Cluster Analysis. John Wiley & Sons.
32. Kirkpatrick, S., Gelatt, C. D., and Vecchi, M. P. (1983). "Optimization by Simulated Annealing." Science, 220: 671-680.
33. Lau, J. W. and Green, P. J. (2007). "Bayesian Model Based Clustering Procedures." Journal of Computational and Graphical Statistics, 16: 526-558.
34. Laursen, P. S. (1993). "Simple Approaches to Parallel Branch and Bound." Parallel Computing, 19: 143-152.
35. Luan, Y. and Li, H. (2003). "Clustering of Time-course Gene Expression Data Using a Mixed-effects Model with B-splines." Bioinformatics, 19: 474-482.
36. MacEachern, S. N. (1994). "Estimating Normal Means with a Conjugate Style Dirichlet Process Prior." Communications in Statistics B, 23: 727-741.
37. MacEachern, S. N., Clyde, M., and Liu, J. S. (1999). "Sequential Importance Sam-pling for Nonparametric Bayes Models: The Next Generation." Canadian Journal of Statistics, 27: 251-267.
38. MacEachern, S. N. and Guha, S. (2011). "Parametric and semiparametric hypotheses in the linear model." The Canadian Journal of Statistics, 39: 165-180.
39. MacEachern, S. N. and Müller, P. (1998). "Estimating Mixture of Dirichlet Process Models." Journal of Computational and Graphical Statistics, 7: 223-238.
40. Newton, M. A. (2002). "On a Nonparametric Recursive Estimator of the Mixing Dis-tribution." Sankhyā, Series A, 64: 306-322.
41. Ng, S., McLachlan, G., Wang, K., Ben-Tovim Jones, L., and Ng, S. (2006). "A Mixture Model with Random-effects Components for Clustering Correlated Gene-expression Profiles." Bioinformatics, 22: 1745-1752.
42. Petit, L. I. (1992). "Bayes Factors for Outlier Models using the Device of Imaginary Observations." Journal of the American Statistical Association, 87: 541-545.
43. Quintana, F. A. (2004). "A Predictive View of Bayesian Clustering." Journal of Statis-tical Planning and Inference, 136: 2407-2429.
44. Quintana, F. A. and Iglesias, P. L. (2003). "Bayesian Clustering and Product Partition Models." Journal of the Royal Statistical Society, Series B, 65: 557-574.
45. R Development Core Team (2011). R: A Language and Environment for Statistical Computing. R Foundation for Statistical Computing, Vienna, Austria. ISBN 3-900051-07-0. URL http://www.R-project.org/
46. Rand, W. M. (1971). "Objective Criteria for the Evaluation of Clustering Methods." Journal of the American Statistical Association, 66: 846-850.
47. Ray, S. and Mallick, B. (2006). "Functional Clustering by Bayesian Wavelet Methods." Journal of the Royal Statistical Society, Series B, 68: 305-332.
48. Rota, G. (1964). "The Number of Partitions of a Set." The American Mathematical Monthly, 71: 498-504.
49. Spellman, P. T., Sherlock, G., Zhang, M. Q., Iyer, V. R., Anders, K., Eisen, M. B., Brown, P. O., Botstein, D., and Futcher, B. (1998). "Comprehensive Identification of Cell Cycle-regulated Genes of the Yeast Saccharomyces cerevisiae by Microarray Hybridization." Molecular Biology of the Cell, 9: 3273-3297.
50. Wang, L. and Dunson, D. B. (2011). "Fast Bayesian Inference in Dirichlet Process Mixture Models." Journal of Computational and Graphical Statistics, 20: 196-216.
51. Ward, J. H. (1963). "Hierarchical Grouping to Optimize an Objective Function." Jour-nal of the American Statistical Association, 58(301): 236-244.
52. Wilkinson, L. (2008). "The Future of Statistical Computing." Technometrics, 50(4): 418-435.
53. Xu, Y., Heller, K. A., and Ghahramani, Z. (2009). "Tree-Based Inference for Dirich-let Process Mixtures." In Proceedings of the Twelfth International Conference on Artificial Intelligence and Statistics, 615-622.