Statistical Demography by Adrian Raftery [lectures]

Adrian Raftery’s course in Paris

UW Professor and U.S. National Academy of Sciences member Adrian Raftery has received the 2020 FSMP research chair and as a result will be visiting Paris this Fall 2021. He will be located at the MAP5 laboratory at the University of Paris. In particular, he will give a 20-hour Master course on statistical semography. This will be given over four successive Tuesdays, with 5 hours of lectures per week. The course is open to all. Attendance is free of charge but registration is mandatory. (To register, please fill the attached form. Lectures will be given in the salle du conseil, on the 7ft floor of the Saint-Germain-des-Prés campus, 45 rue des Saints-Pères, 75006 Paris.)

Demography aims to estimate and forecast population, fertility, mortality and migration. This is important for government policy-making, private sector planning, and research in the health and social sciences, and also critical for climate science and global health. It has traditionally been done using deterministic mathematical methods, but these ignore uncertainty and measurement error.  In the past decade, modern statistical methods were developed for this by our group at the University of Washington, and these were recently adopted by the  United Nations for their official population forecasts for all countries.  Statistical demography is expanding rapidly,  and this course will teach theory and practice of  methods and models of the field, with a focus on current and potential future research.

The topics will be:

1. Review of basic mathematical demographic methods.

2. Modeling age-specific rates, including model schedules and Lee-Carter method.

3. Statistical modeling and projection of fertility, mortality, migration and population.

4. Reconstructing population and vital rates from imperfect data.

riddle on a circle

The Riddler’s riddle this week provides another opportunity to resort to brute-force simulated annealing!

Given a Markov chain defined on the torus {1,2,…,100} with only moves a drift to the right (modulo 100) and a uniformely random jump, find the optimal transition matrix to reach 42 in a minimum (average) number of moves.

Which I coded in my plane to Seattle, under the assumption that there is nothing to do when the chain is already in 42. And the reasoning that there is not gain (on average) in keeping the choice between right shift and random jump random.

dure=min(c(41:0,99:42),50)
temp=.01
for (t in 1:1e6){
  i=sample((1:100)[-42],1)
  dura=1+mean(dure)
  if (temp*log(runif(1))<dure[i]-dura) dure[i]=dura
  if(temp*log(runif(1))<dure[i]-(dura<-1+dure[i*(i<100)+1])) 
    dure[i]=dura 
  temp=temp/(1+.1e-4*(runif(1)>.99))}

In all instances, the solution is to move at random for any position but those between 29 and 41, for an average 13.64286 number of steps to reach 42. (For values outside the range 29-42.)

ABC-SAEM

In connection with the recent PhD thesis defence of Juliette Chevallier, in which I took a somewhat virtual part for being physically in Warwick, I read a paper she wrote with Stéphanie Allassonnière on stochastic approximation versions of the EM algorithm. Computing the MAP estimator can be done via some adapted for simulated annealing versions of EM, possibly using MCMC as for instance in the Monolix software and its MCMC-SAEM algorithm. Where SA stands sometimes for stochastic approximation and sometimes for simulated annealing, originally developed by Gilles Celeux and Jean Diebolt, then reframed by Marc Lavielle and Eric Moulines [friends and coauthors]. With an MCMC step because the simulation of the latent variables involves an untractable normalising constant. (Contrary to this paper, Umberto Picchini and Adeline Samson proposed in 2015 a genuine ABC version of this approach, paper that I thought I missed—although I now remember discussing it with Adeline at JSM in Seattle—, ABC is used as a substitute for the conditional distribution of the latent variables given data and parameter. To be used as a substitute for the Q step of the (SA)EM algorithm. One more approximation step and one more simulation step and we would reach a form of ABC-Gibbs!) In this version, there are very few assumptions made on the approximation sequence, except that it converges with the iteration index to the true distribution (for a fixed observed sample) if convergence of ABC-SAEM is to happen. The paper takes as an illustrative sequence a collection of tempered versions of the true conditionals, but this is quite formal as I cannot fathom a feasible simulation from the tempered version and not from the untempered one. It is thus much more a version of tempered SAEM than truly connected with ABC (although a genuine ABC-EM version could be envisioned).

Mount Baker in the sky [jatp]