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On strong Hellinger consistency of posterior distributions

Taylor & Francis
Publication Date
  • Posterior Distribution
  • Hellinger Consistency
  • Nonparametric Model
  • Mathematics And Statistics
  • Mathematics


We establish a sufficient condition ensuring strong Hellinger consistency of posterior distributions. We also prove a strong Hellinger consistency theorem for the pseudoposterior distributions based on the likelihood ratio with power 0 < alpha < 1, which are introduced by Walker and Hjort 2001 'On Bayesian Consistency', J. R. Statist. Soc., B 63, 811-821. Our result is an extension of their theorem for alpha = 1/2.

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