I am off to New York City for two days, giving a seminar at Columbia tomorrow and visiting Andrew Gelman there. My talk will be about testing as mixture estimation, with slides similar to the Nice ones below if slightly upgraded and augmented during the flight to JFK. Looking at the past seminar speakers, I noticed we were three speakers from Paris in the last fortnight, with Ismael Castillo and Paul Doukhan (in the Applied Probability seminar) preceding me. Is there a significant bias there?!
Archive for Paris
There is an opening at the Statistics School ENSAE for a Statistics associate or full professor position, starting on September 2015. Currently located on the South-West boundary of Paris, the school is soon to move to the mega-campus of Paris Saclay, near École Polytechnique, along with a dozen other schools. See this description of the position. The deadline is very close, March 23!
This morning, in the train to Dauphine (train that was even more delayed than usual!), I read a recent arXival of Brendon Brewer and Courtney Donovan. Entitled Fast Bayesian inference for exoplanet discovery in radial velocity data, the paper suggests to associate Matthew Stephens’ (2000) birth-and-death MCMC approach with nested sampling to infer about the number N of exoplanets in an exoplanetary system. The paper is somewhat sparse in its description of the suggested approach, but states that the birth-date moves involves adding a planet with parameters simulated from the prior and removing a planet at random, both being accepted under a likelihood constraint associated with nested sampling. I actually wonder if this actually is the birth-date version of Peter Green’s (1995) RJMCMC rather than the continuous time birth-and-death process version of Matthew…
“The traditional approach to inferring N also contradicts fundamental ideas in Bayesian computation. Imagine we are trying to compute the posterior distribution for a parameter a in the presence of a nuisance parameter b. This is usually solved by exploring the joint posterior for a and b, and then only looking at the generated values of a. Nobody would suggest the wasteful alternative of using a discrete grid of possible a values and doing an entire Nested Sampling run for each, to get the marginal likelihood as a function of a.”
This criticism is receivable when there is a huge number of possible values of N, even though I see no fundamental contradiction with my ideas about Bayesian computation. However, it is more debatable when there are a few possible values for N, given that the exploration of the augmented space by a RJMCMC algorithm is often very inefficient, in particular when the proposed parameters are generated from the prior. The more when nested sampling is involved and simulations are run under the likelihood constraint! In the astronomy examples given in the paper, N never exceeds 15… Furthermore, by merging all N’s together, it is unclear how the evidences associated with the various values of N can be computed. At least, those are not reported in the paper.
The paper also omits to provide the likelihood function so I do not completely understand where “label switching” occurs therein. My first impression is that this is not a mixture model. However if the observed signal (from an exoplanetary system) is the sum of N signals corresponding to N planets, this makes more sense.
Here is the fifth and last set of slides for my third year statistics course, trying to introduce Bayesian statistics in the most natural way and hence starting with… Rasmus’ socks and ABC!!! This is an interesting experiment as I have no idea how my students will react. Either they will see the point besides the anecdotal story or they’ll miss it (being quite unhappy so far about the lack of mathematical rigour in my course and exercises…). We only have two weeks left so I am afraid the concept will not have time to seep through!
reflections on the probability space induced by moment conditions with implications for Bayesian Inference [slides]Posted in Books, Statistics, University life with tags ABC, Arnold Zellner, Christian Gouriéroux, conference, empirical likelihood, fiducial distribution, measure theory, method of moments, Paris, R.A. Fisher, slides, structural model, Université Paris Dauphine on December 4, 2014 by xi'an
Here are the slides of my incoming discussion of Ron Gallant’s paper, tomorrow.