Bayesian Analysis of Simple Random Densities

DOI: 10.4236/ojs.2014.45037   PDF   HTML     2,925 Downloads   3,325 Views  

Abstract

A tractable nonparametric prior over densities is introduced which is closed under sampling and exhibits proper posterior asymptotics.

Share and Cite:

F., P. and Pereira, C. (2014) Bayesian Analysis of Simple Random Densities. Open Journal of Statistics, 4, 377-390. doi: 10.4236/ojs.2014.45037.

Conflicts of Interest

The authors declare no conflicts of interest.

References

[1] Ferguson, T. (1973) A Bayesian Analysis of Some Nonparametric Problems. The Annals of Statistics, 1, 209-230.
http://dx.doi.org/10.1214/aos/1176342360
[2] Blackwell, D. (1973) Discreteness of Ferguson Selections. The Annals of Statistics, 1, 356-358.
http://dx.doi.org/10.1214/aos/1176342373
[3] Gosh, J.K. and Ramamoorthi, R.V. (2002) Bayesian Nonparametrics. Springer, New York.
[4] Thorburn, D. (1986) A Bayesian Approach to Density Estimation. Biometrika, 73, 65-75.
http://dx.doi.org/10.2307/2336272
[5] Lenk, P.J. (1988) The Logistic Normal Distribution for Bayesian, Nonparametric, Predictive Densities. Journal of the American Statistical Association, 83, 509-516.
http://dx.doi.org/10.1080/01621459.1988.10478625
[6] Robert, C.P. and Casella, G. (2004) Monte Carlo Statistical Methods. 2nd Edition, Springer, New York.
http://dx.doi.org/10.1007/978-1-4757-4145-2
[7] Billingsley, P. (1995) Probability and Measure. 3rd Edition, Wiley-Interscience, New Jersey.
[8] Ash, R.B. (2000) Probability and Measure Theory. 3rd Edition, Harcourt/Academic Press, Massa- chusetts.
[9] Schervish, M.J. (1995) Theory of Statistics. Springer, New York.
http://dx.doi.org/10.1007/978-1-4612-4250-5
[10] Bazaraa, M.S. and Shetty, C.M. (2006) Nonlinear Programming: Theory and Algorithms. 3rd Edition, Wiley-Interscience, New Jersey.

  
comments powered by Disqus

Copyright © 2020 by authors and Scientific Research Publishing Inc.

Creative Commons License

This work and the related PDF file are licensed under a Creative Commons Attribution 4.0 International License.