The variation of the posterior variance and Bayesian sample size determination
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We investigate a new criterion for Bayesian sample size determination that is designed to limit the fluctuations of the posterior variance under repeated sampling. Instead of taking the approach to bound the variance of the posterior variance we present a modified object that has an intuitive interpretation and matches closer the asymptotic behavior of the fluctuations as well as frequentist analogues. Our approach can be derived in the context of decision theory using a suitable loss function. Computations and explicit formulas are presented for several standard choices of likelihoods and their conjugate priors.
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