Archive for Canada

Longhand [Pinot Grigio]

Posted in Statistics with tags , , , , , on January 20, 2019 by xi'an

Juno Beach [jatp]

Posted in pictures, Travel with tags , , , , , , , , , , , , , , , , on January 2, 2019 by xi'an

a question from McGill about The Bayesian Choice

Posted in Books, pictures, Running, Statistics, Travel, University life with tags , , , , , , , on December 26, 2018 by xi'an

I received an email from a group of McGill students working on Bayesian statistics and using The Bayesian Choice (although the exercise pictured below is not in the book, the closest being exercise 1.53 inspired from Raiffa and Shlaiffer, 1961, and exercise 5.10 as mentioned in the email):

There was a question that some of us cannot seem to decide what is the correct answer. Here are the issues,

Some people believe that the answer to both is ½, while others believe it is 1. The reasoning for ½ is that since Beta is a continuous distribution, we never could have θ exactly equal to ½. Thus regardless of α, the probability that θ=½ in that case is 0. Hence it is ½. I found a related stack exchange question that seems to indicate this as well.

The other side is that by Markov property and mean of Beta(a,a), as α goes to infinity , we will approach ½ with probability 1. And hence the limit as α goes to infinity for both (a) and (b) is 1. I think this also could make sense in another context, as if you use the Bayes factor representation. This is similar I believe to the questions in the Bayesian Choice, 5.10, and 5.11.

As it happens, the answer is ½ in the first case (a) because π(H⁰) is ½ regardless of α and 1 in the second case (b) because the evidence against H⁰ goes to zero as α goes to zero (watch out!), along with the mass of the prior on any compact of (0,1) since Γ(2α)/Γ(α)². (The limit does not correspond to a proper prior and hence is somewhat meaningless.) However, when α goes to infinity, the evidence against H⁰ goes to infinity and the posterior probability of ½ goes to zero, despite the prior under the alternative being more and more concentrated around ½!

function junction NPA

Posted in Mountains, pictures, Travel, Wines with tags , , , , , on November 20, 2018 by xi'an

end of the Canadian Rockies [jatp]

Posted in Mountains, pictures, Travel with tags , , , , , , , , , on September 16, 2018 by xi'an

two positions at UBC

Posted in pictures, Statistics, Travel, University life with tags , , , , , , , on September 12, 2018 by xi'an

Just to repost an announcement that the Department of Statistics at the University of British Columbia in Vancouver, BC, invites applications from outstanding new investigators for two tenure-track position at the rank of Assistant Professor. Deadline for application is October 17. More information is available there. (The above sculpture is the iconic Raven and the First Men by Billy Reid.)

the kingfisher and the heron [jatp]

Posted in Statistics with tags , , , , , , , , , , on September 8, 2018 by xi'an