This section will contain a description of my recent research interests. It is not yet complete.
The Hamiltonian or Hybrid Monte Carlo method
In many situations one requires to numerically generate samples of a given probability distribution in Rd; Bayesian statistics is a field where those situations arise constantly. Markov Chain Monte Carlo (MCMC) methods make it possible to obtain those samples even if d is large. HMC (Hybrid or Hamiltonian Monte Carlo) algorithms are widely used MCMC samplers which often outperform alternative techniques. In HMC each sample is obtained by integrating numerically a Hamiltonian system of differential equations with d degrees of freedom; there is then a clear connection between HMC and all my work on numerical Hamiltonian problems (to be completed).