## a paradox in decision-theoretic interval estimation (solved)

Posted in pictures, Statistics, Travel, University life with tags , , , , , , , , , , , 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

$\text{length}(C) - k \mathbb{I}_C(\theta)$

(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 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

$\dfrac{\text{length}(C)}{\sigma} - k \mathbb{I}_C(\theta)$

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.

## AMSI Lectures #8-10

Posted in Statistics, Travel with tags , , , , , , , , , on August 21, 2012 by xi'an

This is the last series of lectures for my AMSI Lecture tour: in Brisbane, I gave the Rao-Blackwellisation talk this afternoon at the University of Queensland and will give tomorrow both the public lecture (for the second time) and the ABC for model choice at QUT. This will then see the end to this (almost) exhaustive if exhausting tour of Eastern Australian university towns… Brisbane has this great feature of connecting QUT with UQ by a fast boat, which meant I could work with Kerrie Mengersen on the revision of our ABCel paper in the morning and be at UQ ½ an hour later. A good thing as there are only three days left till I leave Australia after this seven week visit… (I am afraid there is no free time left for sampling the Brisbane dumplings!)

## AMSI Lectures #6 & #7

Posted in Statistics, Travel with tags , , , , on August 13, 2012 by xi'an

After this fairly long break stretching from southern Australia to northern Queensland, I am back on track for the second half of my AMSI Lectures, giving a seminar in Canberra tomorrow and at the University of Wollongong the day after.

## AMSI-SSAI Lecture #1 at University of Adelaide

Posted in pictures, Statistics, Travel, University life with tags , , , , on July 16, 2012 by xi'an

On Friday, I gave my first AMSI Lecture, at the University of Adelaide. The talk attracted a fair number of people, esp. when considering that I had already given a talk on ABC the day before. There also were several interesting questions at the end, mostly related to the (ABC) empirical likelihood part which seems to have a high power of attraction! This talk furthermore gave me the opportunity to visit the superb Ingkarni Wardli building housing math and engineering. This means “house of enquiry” in the local indigenous language, well-suited to a science building indeed! (My next talk is at UNSW on Monday afternoon, the very same talk I gave at the ASC 2012 conference last Thursday.)