Data-dependent probability matching priors of the second order

Abstract

We consider second-order probability matching priors that ensure frequentist validity of posterior quantiles with margin of error o(n ⁻¹), where n is the sample size. It is well known that there are many models of interest where data-free second-order probability matching priors do not exist. We explore how this problem can be resolved via consideration of data-dependent priors. This is done both in the absence and presence of nuisance parameters.

Keywords:

• frequentist validity
• Jeffreys’ prior
• orthogonal parametrization
• posterior quantile
• shrinkage argument

Acknowledgements

We thank the editor for very constructive suggestions. This work was supported by a grant from the Center for Management and Development Studies, Indian Institute of Management Calcutta.