The Library
On the Bayesian analysis of species sampling mixture models for density estimation
Tools
Griffin, Jim E. (2006) On the Bayesian analysis of species sampling mixture models for density estimation. Working Paper. University of Warwick. Centre for Research in Statistical Methodology, Coventry.
|
PDF
WRAP_Griffin_06-13w.pdf - Published Version - Requires a PDF viewer such as GSview, Xpdf or Adobe Acrobat Reader Download (1153Kb) |
Official URL: http://www2.warwick.ac.uk/fac/sci/statistics/crism...
Abstract
The mixture of normals model has been extensively applied to density estimation problems. This paper proposes an alternative parameterisation that naturally leads to new forms of prior distribution. The parameters can be interpreted as the location, scale and smoothness of the density. Priors on these parameters are often easier to specify. Alternatively, improper and default choices lead to automatic Bayesian density estimation. The ideas are extended to multivariate density estimation.
| Item Type: | Working or Discussion Paper (Working Paper) |
|---|---|
| Subjects: | Q Science > QA Mathematics |
| Divisions: | Faculty of Science > Statistics |
| Library of Congress Subject Headings (LCSH): | Mixture distributions (Probability theory) |
| Series Name: | Working papers |
| Publisher: | University of Warwick. Centre for Research in Statistical Methodology |
| Place of Publication: | Coventry |
| Date: | 2006 |
| Volume: | Vol.2006 |
| Number: | No.13 |
| Number of Pages: | 21 |
| Status: | Not Peer Reviewed |
| Access rights to Published version: | Open Access |
| References: | Blackwell, D. and MacQueen, J.B. (1973): “Ferguson distributions via P´olya urn schemes,” Annals of Statistics, 1, 353-355. Bowman, A. W. and A. Azzalini (1997): “Applied Smoothing Techniques for Data Analysis,” Oxford: Oxford University Press. Bush, C. A. and S. N. MacEachern (1996): “A Semiparametric Bayesian Model for Randomised Block Designs,” Biometrika, 83, 275-285. Escobar, M. D. and West, M. (1995): “Bayesian density-estimation and inference using mixtures,” Journal of the American Statistical Association, 90, 577-588 . Ferguson, T. S. (1973): “A Bayesian Analysis of Some Nonparametric Problems,” The Annals of Statistics, 1, 209-230. Ferguson, T. S. (1983): “Bayesian Density Estimation by Mixtures of Normal Distribution,” in Recent Advances In Statistics: Papers in Honor of Herman Chernoff on His Sixtieth Birthday, eds: M. H. Rizvi, J. Rustagi and D. Siegmund, Academic Press: New York. Gelfand, A. E. and A. Kottas (2002): “A Computational Approach for Full Nonparametric Bayesian Inference under Dirichlet Proces Mixture Models,” Journal of Computational and Graphical Statistics, 11, 289-305. Ishwaran, H. and James, L. (2001): “Gibbs Sampling Methods for Stick-Breaking Priors,” Journal of the American Statistical Association, 96, 161-73. Ishwaran, H. and James, L. F. (2002): “Approximate Dirichlet Process Computing in Finite Normal Mixtures: Smoothing and Prior Information,” Journal of Computational and Graphical Statistics, 11, 1-26. Jain, S. and R. M. Neal (2005): “Splitting and merging components of a nonconjugate Dirichlet process mixture model,” Technical Report 0507, Department of Statistics, University of Toronto. James, L. F. (2006): “Spatial neutral to the right species sampling mixture models,” prepared for “Festschrift for Kjell Doksum”. Lijoi, A., R. H. Mena, and I. Pr¨unster (2005): “Hierarchical mixture modelling with normalized inverse-Gaussian priors,” Journal of the American Statistical Association, 100, 1278-1291./par Lo, A. Y. (1984): “On a Class of Bayesian Nonparametric Estimates: I. Density Estimates,” The Annals of Statistics, 12, 351-357. MacEachern, S. N. andM¨uller, P. (1998): “Estimating mixture of Dirichlet process models,” Journal of Computational and Graphical Statistics, 7, 223-238. Marin, J.-M., K. Mengersen and C. P. Robert (2006): “Bayesian Modelling and Inference on Mixtures of Distributions,” Handbook of Statistics 25, (eds: D. Dey and C.R. Rao). Mengersen, K. and C. Robert (1996): “Testing for mixtures: A Bayesian entropic approach (with dicussion),” in Bayesian Statistics 5, eds: J. Berger, J. Bernardo, A. Dawid, D. Lindley and A. Smith, Oxford University Press : Oxford. M¨uller, P. and Quintana, F. (2004): “Nonparametric Bayesian Data Analysis,” Statistical Science, 19, 95-110. M¨uller, P. and Rosner, G. (1997): “A Bayesian population model with hierarchical mixture priors applied to blood count data,” Journal of the American Statistical Association, 92, 1279-1292. Neal, R. M. (2000): “Markov chain sampling methods for Dirichlet process mixture models,” Journal of COmputational and Graphical Statistics, 9, 249-265. Nietro-Barajas, L. E., I Pr¨unster and S. G. Walker (2004): “Normalized random measures driven by increasing additive processes,” Annals of Statistics, 32, 2343-2360. Papaspiliopoulos, O. and Roberts, G. (2004): “Retrospective MCMC for Dirichlet process hierarchical models,” technical report, University of Lancaster. Pitman, J. (1996): “Some Developments of the Blackwell-MacQueen Urn Scheme,” in Statistics, Probability and Game Theory: Papers in Honor of David Blackwell, eds: T. S. Ferguson, L. S. Shapley and J. B. MacQueen, Institue of Mathematical Statistics Lecture Notes. Richardson, S. and P. J. Green (1997): “On Bayesian analysis of mixtures with unknown number of components (With discussion,” Journal of the Royal Statistical Society B, 731-792. Robert, C. and M. Titterington (1998): “Reparameterisation strategies for hidden Markov models and Bayesian approaches to maximum likelihood estimation,” Statistics and Computing, 4, 327-355. Roeder, K. (1990): “Density Estation with Confidence Sets Exemplified by Superclusters and Voids in the Galaxies,” Journal of the American Statistical Assocation, 85, 617- 624. Roeder, K. (1994): “A Graphical Technique for Deteremining the Number of Components in a Mixture of Normals,” Journal of the American Statistical Assocation, 89, 487-495. Roeder, K. and L. Wasserman (1997): “Practical Bayesian Density Estimation Using Mixtures of Normals,” Journal of the American Statistical Association, 92, 894-902. Walker, S. G., Damien, P., Laud, P.W. and Smith, A. F. M. (1999): “Bayesian nonparametric inference for random distributions and related functions,” (with discussion) Journal of the Royal Statistical Society B, 61, 485-527. |
| URI: | http://wrap.warwick.ac.uk/id/eprint/35572 |
Actions (login required)
![]() |
View Item |
Tools
Tools

