On the Credible Interval Assuming a Mixture Prior in High Dimension

• Activity Number: 74
• Type: Contributed
• Date/Time: Sunday, July 31, 2011 : 4:00 PM to 5:50 PM
• Sponsor: Section on Bayesian Statistical Science
• Author(s): Zhigen Zhao*+
• Companies: Temple University
• Keywords: Decision Bayes ; Loss Function ; Two Groups Model ; Mixture Prior

Abstract

In this paper, we consider the construction of the credible interval under the canonical Bayes model when assuming the parameter of interest follows a prior distribution which is a mixture of zero with probability pi0 and another non-trivial distribution. where pi0 is usually very large. This implies that the posterior probability of the parameter being zero is also large, saying greater than 5% in many cases. The traditional approaches constructing 95% credible intervals, such as the equal-tail credible interval, will always enclose zero, and appear to be statistical useless.

In this paper, we use the decision Bayes approach to guide us constructing a mixture credible interval. When there is overwhelming evidence that the parameter is nonzero, we scrutinize the non-zero component of the posterior distribution and consider the equal-tail credible interval. Otherwise, the interval is the union of such an equal-tail interval and zero. The paper provides a systematic way in deciding when to include zero, guaranteeing the coverage probability.

We have further applied this interval construction to a real data set. Come and see how it works out.