Archive for the pictures Category
Second day at the Indo-French Centre for Applied Mathematics and the workshop. Maybe not the most exciting day in terms of talks (as I missed the first two plenary sessions by (a) oversleeping and (b) running across the campus!). However I had a neat talk with another conference participant that led to [what I think are] interesting questions… (And a very good meal in a local restaurant as the guest house had not booked me for dinner!)
To wit: given a target like
the simulation of λ can be demarginalised into the simulation of
where z is a latent (and artificial) variable. This means a Gibbs sampler simulating λ given z and z given λ can produce an outcome from the target (*). Interestingly, another completion is to consider that the zi‘s are U(0,yi) and to see the quantity
as an unbiased estimator of the target. What’s quite intriguing is that the quantity remains the same but with different motivations: (a) demarginalisation versus unbiasedness and (b) zi ∼ Exp(λ) versus zi ∼ U(0,yi). The stationary is the same, as shown by the graph below, the core distributions are [formally] the same, … but the reasoning deeply differs.
Obviously, since unbiased estimators of the likelihood can be justified by auxiliary variable arguments, this is not in fine a big surprise. Still, I had not thought of the analogy between demarginalisation and unbiased likelihood estimation previously. Continue reading
First day at the Indo-French Centre for Applied Mathematics and the get-together (or speed-dating!) workshop. The campus of the Indian Institute of Science of Bangalore where we all stay is very pleasant with plenty of greenery in the middle of a very busy city. Plus, being at about 1000m means the temperature remains tolerable for me, to the point of letting me run in the morning.Plus, staying in a guest house in the campus also means genuine and enjoyable south Indian food.
The workshop is a mix of statisticians and of mathematicians of neurosciences, from both India and France, and we are few enough to have a lot of opportunities for discussion and potential joint projects. I gave the first talk this morning (hence a fairly short run!) on ABC model choice with random forests and, given the mixed audience, may have launched too quickly into the technicalities of the forests. Even though I think I kept the statisticians on-board for most of the talk. While the mathematical biology talks mostly went over my head (esp. when I could not resist dozing!), I enjoyed the presentation of Francis Bach of a fast stochastic gradient algorithm, where the stochastic average is only updated one term at a time, for apparently much faster convergence results. This is related with a joint work with Éric Moulines that both Éric and Francis presented in the past month. And makes me wonder at the intuition behind the major speed-up. Shrinkage to the mean maybe?