Showing papers on "Jeffreys prior published in 1999"
TL;DR: The reference prior algorithm is applied to multivariate location-scale models with any regular sampling density, where the irrelevance of the usual assumption of normal sampling if our interest is in either the location or the scale is established as discussed by the authors.
22 citations
TL;DR: In this article, the Bures metric for the displaced squeezed thermal state and the quantum Jeffreys prior and its marginal probability distributions were analyzed for both the displaced and undisplaced situations.
Abstract: It is known that, by extending the equivalence of the Fisher information matrix to its quantum version, the Bures metric, the quantum Jeffreys prior can be determined from the volume element of the Bures metric. We compute the Bures metric for the displaced squeezed thermal state and analyse the quantum Jeffreys prior and its marginal probability distributions. To normalize the marginal probability density function, it is necessary to provide a range of values of the squeezing parameter or the inverse temperature. We find that if the range of the squeezing parameter is kept narrow, there are significant differences in the marginal probability density functions in terms of the squeezing parameters for the displaced and undisplaced situations. However, these differences disappear as the range increases. Furthermore, marginal probability density functions against temperature are very different in the two cases.
12 citations
01 Jan 1999
TL;DR: In this article, it was shown that every sequence of Shannon optimal priors on a sequence of regular iid product experiments converges weakly to Jeffreys' prior under Kullback Leibler risk.
Abstract: In 1979, J.M. Bernardo argued heuristically that in the case of regular product experiments his information theoretic reference prior is equal to Jeffreys' prior. In this context, B.S. Clarke and A.R. Barron showed in 1994, that in the same class of experiments Jeffreys' prior is asymptotically optimal in the sense of Shannon, or, in Bayesian terms, Jeffreys' prior is asymptotically least favorable under Kullback Leibler risk. In the present paper, we prove, based on Clarke and Barron's results, that every sequence of Shannon optimal priors on a sequence of regular iid product experiments converges weakly to Jeffreys' prior. This means that for increasing sample size Kullback Leibler least favorable priors tend to Jeffreys' prior.
5 citations
TL;DR: In this article, a review of matching priors obtained via quantiles and via the distribution function is presented, focusing on a proposal of designing priors matching the true coverage probability as well as the false coverage probability of contiguous alternatives with the respective Bayesian counterparts.
Abstract: In recent years, extensive work has been done concerning the derivation of noninformative prior distributions assuring approximate frequentist validity of Bayesian inferences. This paper provides a review of matching priors obtained via quantiles andvia the distribution function. Various matching criteria are described and discussed. Emphasis is laid on a proposal of designing priors matching the true coverage probability as well as the false coverage probabilities of contiguous alternatives with the respective Bayesian counterparts. The review is not primarily meant to be a comprehensive account on the area, but, rather, to convey the main underlying ideas and point out the relationships between matching priors and other noninformative priors, such as the Jeifreys’ and the reference priors.
4 citations