Robust Inference Based On the Complementary Hamiltonian Monte Carlo

Abstract

The article aims to explore certain reliability probability models using a Hamiltonian Monte Carlo (HMC) sampler. There are some concerns with the classic HMC samplers. A notable aspect of the method comes from its acceptance probability whose value is constant, “1,” in theory. One practical problem is the possibility of divergence. A further issue emerges from the simulation trajectory, which essentially traverses on the last principal component. Also, the method is extremely sensitive to run-time parameters. As an improvement, Riemann Manifold HMC can travel along the first principal component. However, its overall accuracy on other components remains unclear. The no-U-turn sampler can adjust the distance traveled, but it may also suffer from excessive simulation steps. To address these concerns, this article proposes: to implement the conservation of energy by virtual collision among particles; to adopt constant simulation steps and adjust the acceptance probability and step size; and to alternate two kinds of trajectories to reconcile all principal components. Experiments show that the proposed algorithm is able to estimate the reliability and remaining useful life of the probability models. To bridge theory and practice, algorithm fragment is demonstrated with Mathematica language.