Abstract

Hamiltonian (Hybrid) Monte Carlo (HMC) method, initially proposed for Quantum Field theory problems, has recently become a popular tool for solving complex and otherwise intractable problems of statistical inference.  The HMC replaces the random walk, inherent to standard Markov Chain Monte Carlo (MCMC), by Hamiltonian trajectories. This helps to produce less correlated samples and achieve faster convergence to the target distribution. The HMC is, therefore, more efficient than MCMC when applied to indirect observation models, generalized linear and nonlinear mixed models, and neural networks. Applications of HMC range from modelling of biomolecules, materials and chemical processes to Bayesian parameter estimation.

One serious disadvantage of the HMC is, however, its reversibility, which diminishes the mixing rate of the sampler. The other bottleneck is strong dependence of the HMC’s performance on the choice of parameters associated with an integration method for underlying Hamiltonian equations. To date, this choice remains largely heuristic. 

In this talk we discuss the advantages, over conventional HMC, of two irreversible variants of HMC – the Generalized Hamiltonian Monte Carlo (GHMC) and the Mix & Match Hamiltonian Monte Carlo (MMHMC). We also propose a novel approach (s-AIA) that selects a system-specific splitting integrator, complete with a set of reliable parameters,  most appropriate for use in production simulations. The method automatically avoids the values of the simulation parameters, likely to cause undesired extreme scenarios, such as resonance artefacts, low accuracy or especially poor sampling. 

The sampling efficiency of GHMC and MMHMC combined with s-AIA is assessed by performing Bayesian inference on two popular statistical models, SIR and BLR, applied in the studies of epidemic outbreaks and endocrine therapy resistance in cancer, respectively.