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15 November

Jesús María Sanz-Serna (University Carlos III of Madrid) Numerical integrators for the Hamiltonian Monte Carlo method

The Hamiltonian Monte Carlo (aka Hybrid Monte Carlo) method is an extremely popular Markov chain algorithm to obtain samples from a target probability distribution. The computational cost of the algorithm mostly originates from the need to numerically integrate, at each step of the chain, a Hamiltonian system of ordinary differential equations. It is therefore important to carry out those integrations as efficiently as possible. While at present the Stormer/Verlet integrator is the integrator of choice, it is possible to construct special integrators tailored to this task. These alternative integrators, while being as easy to implement as Stormer/Verlet, allow for very substantial reductions of the work required to obtain the samples. The talk will focus on the numerical analysis principles used to construct the new integrators.