Jayanta K. Ghosh
	Professor of Statistics
	ghosh@stat.purdue.edu

Office Phone: (765) 494-6041
Fax: (765) 494-0558

Current research interests

Supervision of Graduate Students

An Overview of Work Done

1. My early work is on invariance, sufficiency and applications to sequential analysis. Even though I stopped working on these topics a long time ago, I have occasionally returned to sufficciency (for sample surveys and other undominated problems) as well as sequential analysis.
2. My main work after this and till 1982 had been on higher order asymptotics. This has meant proving validity of various Edgeworth and Edgeworth type expansions (e.g. expansions in x²'s of log likelihood ratio statistics). This has also meant proving higher order optimality theorems.
3. I have been interested in reliability at various points of my career and still work occasionally on reliability problems, specially the problem of a change-point in a hazard rate.
4. Since the mid seventies I have worked with geologists on stochastic modeling of sediment transport using data from river flows as well as experimental data from recirculating flumes. Currently, I am trying to model "bursting of vortices" near the bed by a diffusion with jump boundary condition and its effect in flow velocity and sediment transport.
5. Since the late eighties I have worked on Bayesian asymptotics. I have worked on four kinds of problems. The first related to theorems like posterior normality, necessary and sufficient conditions for a normalized posterior to converge to a non-degenerate distribution, etc. In the second set of problems I try to derive priors for which posterior probabilities are close to frequentist probabilities in various senses. This is relevant for validating non-informative priors or constructing confidence intervals. In the third set of problems I deal with Bayesian analysis of infinite dimensional problems like Bayesian survival analysis, Bayesian density estimation, Bayesian semiparametrics, etc. A major concern here is the consistency of posterior and rate of convergence. In recent years I have made major progress in understanding Bayesian and Empirical Bayes model selection rules in high dimensional problems. I have also been working on Bayes Testing, Model Selection in low dimensional problems and have thrown light on some recent as well as long standing asymptotic problems.
6. Two of my current interests in applications involve public health problems and environmental or ecological statistics. I have also begun new work on ecological data on Western Ghats in India, which is one of the world's leading hot spots for biodiversity. A new project concerns the indigenous knowledge base of Santals, a tribal community in India.
7. In addition to the above major areas, I have worked on many other problems. Some of these are briefly listed: characterization, multiple decision theory, survey sampling, model selection, mixtures, Neyman-Scott problems, U-statistics, Bahadur representation of quantiles. Many of the papers in the above areas solve long standing open problems or pioneer new areas, and have been cited often.

Publications

1. (with Ghosal, S. and Ramamoorthi, R. V.) (1999) Posterior consistency of Dirichlet mixtures in density estimation, Ann. Statist., 27, 143-158.

2. (with Maiti, P., Mukhopadhyay, A. C. and Pal, M.) (1997) Stochastic modeling and forecasting of discovery reserve, and production of hydrocarbon-with an application, has appeared in Sankhy~a Ser B.

3. (with Ghosal, S. and Samanta, T.) (1999) Approximation of the posterior distribution in a change point problem, Ann. of Inst. Statist. Math., 51, 479-497.

4. (with Srikant, K. R. and Ramamoorthi, R. V.) (1999) Posterior consistency for right censored data, Statistics and Probability Letters, 41, 255-265.

5. (with Ghosal, S. and Ramamoorthi, R. V.) (1999) Consistent semiparametric Bayesian inference about a location parameter JSPI , 77, 181-193.

6. (with Joshi, S. N. and Mukhopadhyay, C.) (1998) Inference about sharp changes in hazard rates, Frontiers in Reliability (eds. A. P. Basu, S. K. Basu and S. Mukhopad- hyay) pp. 133-142, World Scientific, Singapore.

7. Bayesian density estimation, has appeared as an invited paper in the proceedings of the International Congress of Mathematics, 1998.

8. (with Ghosal, S. and Ramaoorthi, R. V.) (1999) Consistency issues in Bayesian non- parametrics, in Asymptotics, Nonparametrics and Time Series: A tribute to Madan Lal Puri (ed. S. Ghosh), Marcel Dekker, pp. 639-668.

9. (with R. Mukerjee) Test statistics arising from quasi-likelihood: Bartlett-adjustment and higher order power has appeared in JSPI.

10. (with Maiti, P., Rao, T. J., Sinha, B. K.) (1999) Evolution of Statistics in India, IS Review.

11. (with Ghosal, S. and vander Vaart, H.) (2000) Convergence rates of posterior distribution (Ann. Stat. #2)

12. (with Basu, A. Basu, S., Dewanji, A., Majumder, P. P., Chakvabanty, M.) (1998) Projection of HIV Infection in Calcutta, Indian Journal of Medical Research, 107, pp. 159-172.

13. Discussion of "The Stochastic Control of Process Capability Indices" by N. D. Singpurwallah, Test, 7, 47.

14. Discussion of Andrew Barron's paper in Proceedings of Sixth Valencia Meeting, Oxford University Press, 1997

15. (with J. O. Berger and Nitai Mukhopadhyay) (2003) Approximations and consistency of the Bayes factors as model dimension grows. Journal of Statistical Planning and Inference, 112, pp. 241-258.

16. (with T. Samanta) (2000) Nonsubjective Bayes testing - an Overview (2002) JSPI

17. (with T. Samanta) (October 2001) Discussion of a paper by Berger and Pericchi ( 103, 205-223 in IMS Lecture Notes)

18. (with Peter Hang Ping Zhang) (2000) Sequential estimation in a reliability change point problem, in Perspectives in Statistical Science, (eds. A. K. Basu, J. K. Ghosh, P. K. Sinha and B. K. Sinha) Oxford University Press, New Delhi.

19. (with T. Samanta) (2001) Model Selection-An Overview, Current Science, 80, pp. 1135-1144.

20. (with J. Bhanja etc.) (2001) A Statistical Approach to Geological Mapping, (2002) Mathematical Geology, 34, pp. 505-528.

21. (with T. Samanta)(2002) Towards a Nonsubjective Bayesian Paradigm (in Golden Jubilee volume for Mathematics, I.I.T., Kharagpar, editor J. Misra).

22. (with S. Adhikari etc.) (2001) Group Testing and Optimal Design (in volume for Prof. M. N. Das, editors A. Dey et al).

23. (with J. Wilbur etc.) Variable selection in High-Dimensional Multivariate Binary Data With Application to the Analysis of Microbial Community DNA Fingerprints (2002), Biometrics, 58, pp. 378-386.

24. (with A. A. Messan etc.) Posterior Consistency for Regression Problems, Bernoulli (2003).

25. (with Nitai Mukhopadhyay) (2003) Parametric Empirical Bayes Model Selection - Some Theory Methods and Simulations, in IMS lecture notes in honor of Rabi Bhattacharya, editors K. Athreya et al.

26. (with Arijit Chaudhuri and Mausumi Bose) An Application of Adaptive Sampling to Estimate Highly Localized Population Segments, JSPI (2003).

27. (with Ruma Basu and Rahul Mukerjee) (2003) Empirical Bayes Prediction Intervals in a Normal Regression Model: Higher Order Asmptotics, Statistics and Probalility Letters, 63, pp. 197-203.

28. (with S. Purkayastha and T. Samanta) (2004) Sequential Probability Ratio Tests Based on Improper Priors, Sequential Analysis, Vol. 23, pp. 585-602

29. (with S. Purkayastha and T. Samanta) (2005) Role of P-values and other Measures of Evidence in Bayesian Analysis, to appear in Handbook on Bayesian Analysis, eds D. Dey and C.R. Rao, Elsevier, Amsterdam, pp. 151-170.

30. (with K. Dihidar and T. Samanta) (2004) On Different Clusterings of the Same Data Set, to appear in a volume for B.K. Kale, editors Sushma Bendre et al.

31. Is Göedel's Theorem Relevant in the Mind-Machine Debate? Has appeared in the proceedings of an international conference of scientists and philosophers at Ramakrishna Mission Institute, Kolkata, editor Dr. S. Bhattacharya.

32. (with M. Bogdan and R.W. Doerge) (2004) Modifying the Schwarz Bayesian Information Criterion to Locate Multiple Interacting Quantitative Trait Loci, Genetics, 167, pp. 989-999.

33. (with Chakrabarty, A.) (2006) A Generalization of BIC for the General Exponential Family, JSPI (2006, online), pp. 2847-2872.

34. (with Chakrabarty, A.) (2006) Minimax Estimation with AIC in Gaussian White Noise Problem Ann. Inst. Stat. Math, 2006, Vol. 58, pp. 1-20.

35. (with Berger, J. and Mukhopadhyay) (2005) Some Bayesian Predictive Approaches to Model Selection, Statistics and Probability Letters, 75, pp. 369-379.

36. (with Srinivasa Rao, A. S. R., Basu, S. and Basu, A.) (2005) Parametric models for incubation distribution in the presence of left and right censoring, Indian Journal of Pure and Applied Mathematics, 36, No. 7, pp. 371-384.

37. (with Hjort, N., Messan, A.A., and Ramamoorthi, R.V.) (2006) Bayesian Bivariate Survival Estimation. Journal of Statistical Planning and Inference, Vol. 136, pp. 2297-2308.

38. (with R. DasGupta) (2005) Optimal Assembly Problem of Rotor Blades - a Heuristic Approach, Calcutta Statistical Assoc. Bulletin, Vol. 57, pp. 1-18.

39. (with S. Tokdar) (2007) Posterior Consistency of Logistic Gaussian Process Priors in Density Estimation, JSPI, Vol. 137, pp. 34-42.

40. (with S. Tokdar) (2006) Convergence and consistency of Newton's algorithm for Estimating Mixing Distribution, in The Frontiers in Statistics, Fan, J. and Koul, H. eds, Imperial College Press (a volume for Peter Bickel), pp. 429-443.

41. (with Junyong Park) Persistence of Plug-in Rule in classification of High Dimensional Multivariate Binary Data, to appear in JSPI Vol. 137, pp. 3687-3705.

42. (With M. Bogdan, A. Ochman, S. Tokdar) (2007) On the Empirical Bayes Approach to the Problem of Multiple Testing, Quality and Reliability Engineering International (a Wiley Journal). Vol. 23, pp. 727-739.

43. (With M. Bogdan, S. Tokdar) (2008) A Comparison of the Benjamini-Hochberg Procedure with some Bayesian rules for Multiple Testing, in IMS Lecture Note series, N. Balakrishnan et al eds. IMS Collections, Vol. 1, pp. 211-230.

44. (With A. Chakrabarti) (2007) Some Aspects of Bayesian Model Selection for Prediction (with discussion by David Draper, Avi Behtari, L. Pericchi, and S. Lawritzen) to appear in Bayesian Statistics 9 (Proc. of 8th Valencia Conference), Edited by J.M. Bernardo, M.J. Bayarri, J.O. Berger, A.P. Dawid, D. Heckerman, A.F.M. Smith and M. West, Oxford University Press.

45. (With M. Bogdan, F. Frommlet, P. Biecek. R. Cheng, R. Doerge) (2008) Extending the Modified Bayesian Information Criteria (mBIC) to dense Markers and Multiple Interval Mapping, 1 Biometrics 2008 (to be printed, available online.)

46. (With M. Bogdan, M. Zak-Szatkowska) (2008) Selecting Explanatory Variables with the Modified Version of Bayesian Information Criterion, Quality and Reliability Engineering International (2008, to be printed).

47. (With J. Park, J. Wilbur, C. Nakatsu, C. Ackerman) (2007) Selection of Ginavy Variables and Classification by Boosting, Communications in Statistics: Simulation and Computation, Vol. 36, pp. 855-869.

48. (With R. Martin) (2008) Stochastic Approximation and Newton's Estimate of a Mixing Distribution, Statistical Science (to appear)

49. (With R. Martin) On Two Fast Algorithms for Estimating the Mixing Distribution in Mixture Models, Proc of Frontiers in Applied and Computational Mathematics (to appear)

50. (With S. Tokdar, R. Martin) Consistency of a Recursive Estimate of Mixing Distributions, Annals of Statistics, (to appear)

51. (With M. Bogdan and T. Samanta) (2008) Applied Statistics and Indianness of Indian Data (to appear in Sankhya Ser. B)

Monograph Book

1. Invariance in Testing and Estimation (Lecture Notes), 1967, published by Indian Statistical Institute, Calcutta.

2. Higher Order Asymptotics (based on CBMS-NSF lecture), published jointly by Institute of Mathematical Statistics and American Statistical Association, 1994.

3. (with R.V. Ramamoorthi) Bayesian Nonparametrics (Springer 2003).

4. (with Mohan Delampady and Tapas Samanta) An Introduction to Bayesian Analysis - Theory and Methods, Springer 2006.

Books Edited

1. Selected Papers of D. Basu (Springer, 1988)