If you need an accessible version of this item please contact JSTOR User Support

Variations of Posterior Expectations for Symmetric Unimodal Priors in a Distribution Band

Sanjib Basu
Sankhyā: The Indian Journal of Statistics, Series A (1961-2002)
Vol. 56, No. 2 (Jun., 1994), pp. 320-334
Published by: Springer on behalf of the Indian Statistical Institute
Stable URL: http://www.jstor.org/stable/25050991
Page Count: 15
  • Download PDF
  • Cite this Item

You are not currently logged in.

Access your personal account or get JSTOR access through your library or other institution:

login

Log in to your personal account or through your institution.

If you need an accessible version of this item please contact JSTOR User Support
Variations of Posterior Expectations for Symmetric Unimodal Priors in a Distribution Band
Preview not available

Abstract

Given a random variable with distribution indexed by a one dimensional parameter θ, we consider the problem of robustness of a given Bayesian posterior criterion when the prior c.d.f lies in the class $\Gamma _{SU}=\{F\colon F_{L}\leq F\leq F_{U}$ and F is symmetric and unimodal}. Such a class includes as special cases well known metric neighborhoods of a fixed c.d.f such as Kolmogorov and Lévy neighborhoods. A general method is described for finding the extremum of posterior expectation of a function h(θ) as the prior varies in $\Gamma _{SU}$. Finally, the method is illustrated with two examples. The use of this family in subjective prior elicitation is also discussed.

Page Thumbnails

  • Thumbnail: Page 
[320]
    [320]
  • Thumbnail: Page 
321
    321
  • Thumbnail: Page 
322
    322
  • Thumbnail: Page 
323
    323
  • Thumbnail: Page 
324
    324
  • Thumbnail: Page 
325
    325
  • Thumbnail: Page 
326
    326
  • Thumbnail: Page 
327
    327
  • Thumbnail: Page 
328
    328
  • Thumbnail: Page 
329
    329
  • Thumbnail: Page 
330
    330
  • Thumbnail: Page 
331
    331
  • Thumbnail: Page 
332
    332
  • Thumbnail: Page 
333
    333
  • Thumbnail: Page 
334
    334