On probability matching priors |
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Authors: | Ana‐Maria Staicu Nancy M Reid |
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Institution: | 1. Department of Mathematics, University of Bristol University Walk, Bristol BS8 1TW United Kingdom;2. Department of Statistics, University of Toronto 100 Saint George Street, Toronto, Ontario Canada, M5S 3G3 |
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Abstract: | First‐order probability matching priors are priors for which Bayesian and frequentist inference, in the form of posterior quantiles, or confidence intervals, agree to a second order of approximation. The authors show that the matching priors developed by Peers (1965) and Tibshirani (1989) are readily and uniquely implemented in a third‐order approximation to the posterior marginal density. The authors further show how strong orthogonality of parameters simplifies the arguments. Several examples illustrate their results. |
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Keywords: | Approximate Bayesian inference Laplace approximation orthogonal parameters probability matching prior tail probability approximation |
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