4,511 research outputs found
Asymptotically minimax Bayes predictive densities
Given a random sample from a distribution with density function that depends
on an unknown parameter , we are interested in accurately estimating
the true parametric density function at a future observation from the same
distribution. The asymptotic risk of Bayes predictive density estimates with
Kullback--Leibler loss function is used to examine various ways of choosing prior
distributions; the principal type of choice studied is minimax. We seek
asymptotically least favorable predictive densities for which the corresponding
asymptotic risk is minimax. A result resembling Stein's paradox for estimating
normal means by the maximum likelihood holds for the uniform prior in the
multivariate location family case: when the dimensionality of the model is at
least three, the Jeffreys prior is minimax, though inadmissible. The Jeffreys
prior is both admissible and minimax for one- and two-dimensional location
problems.Comment: Published at http://dx.doi.org/10.1214/009053606000000885 in the
Annals of Statistics (http://www.imstat.org/aos/) by the Institute of
Mathematical Statistics (http://www.imstat.org
Multiscale autocorrelation function: a new approach to anisotropy studies
We present a novel catalog-independent method, based on a scale dependent
approach, to detect anisotropy signatures in the arrival direction distribution
of the ultra highest energy cosmic rays (UHECR). The method provides a good
discrimination power for both large and small data sets, even in presence of
strong contaminating isotropic background. We present some applications to
simulated data sets of events corresponding to plausible scenarios for charged
particles detected by world-wide surface detector-based observatories, in the
last decades.Comment: 18 pages, 9 figure
Objective prior for the number of degrees of freedom of a t distribution
In this paper, we construct an objective prior for the degrees of freedom of a t distribution, when the parameter is taken to be discrete. This parameter is typically problematic to estimate and a problem in objective Bayesian inference since improper priors lead to improper posteriors, whilst proper priors may dom- inate the data likelihood. We find an objective criterion, based on loss functions, instead of trying to define objective probabilities directly. Truncating the prior on the degrees of freedom is necessary, as the t distribution, above a certain number of degrees of freedom, becomes the normal distribution. The defined prior is tested in simulation scenarios, including linear regression with t-distributed errors, and on real data: the daily returns of the closing Dow Jones index over a period of 98 days
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