Archive for sunrise
I attended an highly unusual workshop while in Warwick last week. Unusual for me, obviously. It was about probabilistic numerics, i.e., the use of probabilistic or stochastic arguments in the numerical resolution of (possibly) deterministic problems. The notion in this approach is fairly Bayesian in that it makes use to prior information or belief about the quantity of interest, e.g., a function, to construct an usually Gaussian process prior and derive both an estimator that is identical to a numerical method (e.g., Runge-Kutta or trapezoidal integration) and uncertainty or variability around this estimator. While I did not grasp much more than the classy introduction talk by Philipp Hennig, this concept sounds fairly interesting, if only because of the Bayesian connection, and I wonder if we will soon see a probability numerics section at ISBA! More seriously, placing priors on functions or functionals is a highly formal perspective (as in Bayesian non-parametrics) and it makes me wonder how much of the data (evaluation of a function at a given set of points) and how much of the prior is reflected in the output [variability]. (Obviously, one could also ask a similar question for statistical analyses!) For instance, issues of singularity arise among those stochastic process priors.
Another question that stemmed from this talk is whether or not more efficient numerical methods can derived that way, in addition to recovering the most classical ones. Somewhat, somehow, given the idealised nature of the prior, it feels like priors could be more easily compared or ranked than in classical statistical problems. Since the aim is to figure out the value of an integral or the solution to an ODE. (Or maybe not, since again almost the same could be said about estimating a normal mean.)
As the sunset the day before had been magnificent [thanks to the current air pollution!], I attempted to catch it from a nice spot and went to the top of the nearby hill. The particles were alas (!) not so numerous that evening and so I only got this standard view of the sun going down. Incidentally, I had read a few days earlier in the plane from Vienna that the time and date when Monet’s Impression, Soleil Levant was painted had been identified by a U.S. astronomer as 7h35 on the 13th of Novembre 1872. In Le Havre, Normandy. An exhibit in the nearby Musée Marmottan retraces this quest…