Systematic approaches to generate reversiblizations of Markov chains

Given a target distribution π and an arbitrary Markov infinitesimal generator L on finite state space χ, we develop three structured inter-related approaches to generate new reversiblizations from . The first approach hinges geometric perspective, in which view as projections onto the of π-reversible generators under suitable information divergences such xmlns:xlink="http://www.w3.org/1999/xlink">f -divergences. With different choices functions , not only recover nearly all established but also unravel reversiblizations. Along way, unveil interesting results bisection properties, Pythagorean identities, parallelogram laws chain counterpart arithmetic-geometric-harmonic mean inequality governing these This further serves motivation for introducing notion centroids sequence chains give conditions their existence uniqueness. Building upon approach, generalized means. In this second construct via natural notions means Cauchy or dual mean. third combine recently introduced locally-balanced processes framework convex ∗-conjugate study -divergence. latter offers rich source balancing