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Effect of Mixture Prior in Case of Poorly Specified Prior

Author Affiliations

  • 1Department of Statistics, University of Peshawar, Peshawar, PAKISTAN
  • 2Department of Statistics, Government Post Graduate College of Science, Faisalabad, PAKISTAN

Res. J. Recent Sci., Volume 3, Issue (2), Pages 26-30, February,2 (2014)

Abstract

The Shifted exponential distribution is appropriate for modeling the distribution of the time to failure of systems under constant failure rate condition. In this regard, the parameter is related to the mean life plus shifted parameter. In this research paper we present shifted exponential as likelihood function and conjugate inverted gamma prior for making Bayesian inference comparatively robust against a prior density poorly specified. Making use of a mixture of conjugate Square root inverted gamma priors assists us to make robust inference against misspecified prior. In case of having a very different likelihood than what will be expected for the given prior density, a large posterior probability of misspecification is obtained, and our posterior distribution will lean heavily on the likelihood.

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