Prior Distributions on Measure Space

Sibusiso Sibisi and John Skilling

Journal of the Royal Statistical Society Series B, 1997, vol. 59, issue 1, 217-235

Abstract: A measure is the formal representation of the non‐negative additive functions that abound in science. We review and develop the art of assigning Bayesian priors to measures. Where necessary, spatial correlation is delegated to correlating kernels imposed on otherwise uncorrelated priors. The latter must be infinitely divisible (ID) and hence described by the Lévy–Khinchin representation. Thus the fundamental object is the Lévy measure, the choice of which corresponds to different ID process priors. The general case of a Lévy measure comprising a mixture of assigned base measures leads to a prior process comprising a convolution of corresponding processes. Examples involving a single base measure are the gamma process, the Dirichlet process (for the normalized case) and the Poisson process. We also discuss processes that we call the supergamma and super‐Dirichlet processes, which are double base measure generalizations of the gamma and Dirichlet processes. Examples of multiple and continuum base measures are also discussed. We conclude with numerical examples of density estimation.

Date: 1997
References: Add references at CitEc
Citations: View citations in EconPapers (2)

Downloads: (external link)
https://doi.org/10.1111/1467-9868.00065

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:bla:jorssb:v:59:y:1997:i:1:p:217-235

Ordering information: This journal article can be ordered from
http://ordering.onli ... 1111/(ISSN)1467-9868

Access Statistics for this article

Journal of the Royal Statistical Society Series B is currently edited by P. Fryzlewicz and I. Van Keilegom

More articles in Journal of the Royal Statistical Society Series B from Royal Statistical Society Contact information at EDIRC.
Bibliographic data for series maintained by Wiley Content Delivery ().