Optimal Thinning of MCMC Output

Abstract The use of heuristics to assess the convergence and compress output Markov chain Monte Carlo can be sub-optimal in terms empirical approximations that are produced. Typically a number initial states attributed ‘burn in’ removed, while remainder is ‘thinned’ if compression also required. In this paper, we consider problem retrospectively selecting subset states, fixed cardinality, from sample path such approximation provided by their distribution close optimal. A novel method proposed, based on greedy minimisation kernel Stein discrepancy, suitable when gradient log-target evaluated using small Theoretical results guarantee consistency its effectiveness demonstrated challenging context parameter inference for ordinary differential equations. Software available Thinning package Python, R MATLAB.