Archive for Australia
art brut
Posted in pictures, Travel with tags Australia, Great Ocean Road, limestone, Loch Ard Gorge, Victoria on February 3, 2013 by xi'anrememberance from Oz
Posted in Mountains, pictures, Travel with tags Australia, Kata Tjuta, Mounts Olga, Northern Territory, Uluru on October 21, 2012 by xi'an
Vasse Felix
Posted in Wines with tags Australia, Cabernet, Margaret River, Shiraz, Vasse Felix on October 20, 2012 by xi'an
a paradox in decision-theoretic interval estimation (solved)
Posted in pictures, Statistics, Travel, University life with tags Adelaide, AMSI Lecture, Australia, Bayesian confidence interval, Bayesian decision theory, confidence region, credible set, Elsevier, George Casella, Melbourne, rainbow, t-test on October 4, 2012 by xi'an
In 1993, we wrote a paper [with George Casella and Gene/Juinn Hwang] on the paradoxical consequences of using the loss function
(published in Statistica Sinica, 3, 141-155) since it led to the following property: for the standard normal mean estimation problem, the regular confidence interval is dominated by the modified confidence interval equal to the empty set when s² is too large… This was first pointed out by Jim Berger and the most natural culprit is the artificial loss function where the first part is unbounded while the second part is bounded by k. Recently, Paul Kabaila—whom I met in both Adelaide, where he quite appropriately commented about the abnormal talk at the conference!, and Melbourne, where we met with his students after my seminar at the University of Melbourne—published a paper (first on arXiv then in Statistics and Probability Letters) where he demonstrates that the mere modification of the above loss into
solves the paradox:! For Jeffreys’ non-informative prior, the Bayes (optimal) estimate is the regular confidence interval. besides doing the trick, this nice resolution explains the earlier paradox as being linked to a lack of invariance in the (earlier) loss function. This is somehow satisfactory since Jeffreys’ prior also is the invariant prior in this case.
