While answering a question on X validated on the posterior mean being a weighted sum of the prior mean and of the maximum likelihood estimator, when the weights do not depend on the data, which is true in conjugate natural exponential family settings, I re-read this wonderful 1979 paper of Diaconis & Ylvisaker establishing the converse, namely that when the linear combination holds, the prior need be conjugate! This holds within exponential families, but I cannot think of a reasonable case outside exponential families where the linearity holds (again with constant weights, as otherwise it always holds in dimension one, albeit with weights possibly outside [0,1]).
Archive for Annals of Statistics
linearity, reversed
Posted in Books, Kids with tags Annals of Statistics, cross validated, exponential families, linearity, Persi Diaconis, posterior mean on September 19, 2020 by xi'anXmas tree at UCL, with a special gift
Posted in Books, pictures, Statistics, Travel, University life with tags academic position, Annals of Applied Statistics, Annals of Probability, Annals of Statistics, Britain, Current Index to Statistics, fellowships, IMS, London, Statistics, The BUGS book, UCL, University College London, Xmas on November 26, 2019 by xi'anPh.D. students at UCL Statistics have made this Xmas tree out of bound and unbound volumes of statistics journals, not too hard to spot (especially the Current Indexes which I abandoned when I left my INSEE office a few years ago). An invisible present under the tree is the opening of several positions, namely two permanent lectureships and two three-year research fellowships, all in Statistics or Applied Probability, with the fellowship deadline being the 1st of December 2019!
running after my plane
Posted in Books, Kids, pictures, Running, Travel with tags 10k, Abidjan, Annals of Statistics, Caen, censoring, Kore-Eda Hirokazu, La Rochambelle, Les Courants de la Liberté, Manbiki Kazoku, Normandie Course à Pied, Normandie fort et vert, road races, Shoplifters on June 29, 2019 by xi'anA bit of a hectic trip to Abidjan last Sunday, starting from Caen in the early morning where I was supporting my daughter, wife, mother, and mother-in-law for the annual Rochambelle women-only 5k race on the previous evening! With my daughter managing a fantastic 52nd position and ending up first of her category! As I was driven to the local train station to get back to my 63kg of Annals and my plane, the on-going 10k race kept preventing us from reaching it and I eventually decided 8 minutes before the deadline to leave the car and race to the station, actually running along the 10k racers for one kilometer and managing to enter the train just before it was leaving (too bad I could not finish the race, this start would have made for a great time despite my current injury!). And then when I eventually reached the CDG airport with my 63kg, I was told my bags were not good enough to carry them and that I had to drop some years of these Annals in the bin! So very frustrating… At least the remaining books reached their intended destination.
The plane ride itself was uneventful and above a constant cover of clouds. While catching up with some unread arXivals, I also watched a great 2018 Japanese movie, Shoplifters, which sounded more like a modern tale than a realistic story, so outlying its characters were. With unexpected revelations towards the end and overall a moving and very subtle reflection on what ultimately makes a family. (Reading reviews on the movie later made me realise one scene had been censored for plane audiences…)