Better covariance estimator for vectorised HMC algorithms

[yebai]

When we run parallel HMC sampling using the vectorised HMC implementation, it is possible to adapt the covariance matrix for momentum variables using all samples from all chains. Furthermore, it is possible to do a position-dependent covariance matrix (an approximation to Riemann manifold HMC), using a distance-weighted formula for the covariance matrix.

Reference

Leimkuhler, B., Matthews, C., & Weare, J. (2018). Ensemble preconditioning for Markov chain Monte Carlo simulation. Statistics and Computing, 28(2), 277–290. https://paperpile.com/app/p/7056c9c3-b754-07e0-ae1a-ac773d86096b Code: https://bitbucket.org/c_matthews/ensembleqn/src/master/

[xukai92]

@torfjelde Just realise that we have an issue for this thing.