The following new article has just been published in Population Health Metrics
Small area synthetic estimates of smoking prevalence during pregnancy in England
Szatkowski L, Fahy S, Coleman T, Taylor J, Twigg L, Moon G, Leonardi-Bee J
Population Health Metrics 2015, 13 :34 (9 December 2015)
I found an even better example of the value of Laplace approximation, and its just a small tweak to the example I did a few weeks ago: http://nbviewer.ipython.org/gist/aflaxman/6d0a9ff2441348f3a130
I admit that I’ve been skeptical of the complete rewrite of PyMC that underlies version 3. It seemed to me motivated by an interest in using unproven new step methods that require knowing the derivative of the posterior distribution. But, it is really coming together, and regardless of whether or not the Hamiltonian Monte Carlo stuff pays off, there are some cool tricks you can do when you can get derivatives without a hassle.
Exhibit 1: A Laplace approximation approach to fitting mixed effect models (as described in http://www.seanet.com/~bradbell/tmb.htm)
I’ve got a fun class going this quarter, on “artificial intelligence for health metricians”, and the course content mixed with some of the student interest has got me looking at the options for doing Gaussian process regression in Python. `PyMC2` has some nice stuff, but the `sklearn` version fits with the rest of my course examples more naturally, so I’m using that instead.
But `sklearn` doesn’t have the fanciest of fancy covariance functions implemented, and at IHME we have been down the road of the Matern covariance function for over five years now. It’s in `PyMC`, so I took a crack at mash-up. (Took a mash at a mash-up?) There is some room for improvement, but it is a start. If you need to do non-parametric regression for something that is differentiable more than once, but less than infinity times, you could try starting here: http://nbviewer.ipython.org/gist/aflaxman/af7bdb56987c50f3812b
p.s. Chris Fonnesbeck has some great notes on doing stuff like this and much more here: http://nbviewer.ipython.org/github/fonnesbeck/Bios366/blob/master/notebooks/Section5_1-Gaussian-Processes.ipynb