- Abstract: The use of heuristics to assess the convergence and compress the output of Markov chain Monte Carlo can be sub-optimal in terms of the empirical approximations that are produced. Typically a number of the initial states are attributed to "burn-in" and removed, whilst the remainder of the chain is "thinned" if compression is also required. In this paper, we consider the problem of retrospectively selecting a subset of states, of fixed cardinality, from the sample path such that the approximation provided by their empirical distribution is close to optimal. We present a method based on greedy minimisation of a kernel Stein discrepancy, that is suitable for problems where heavy compression is required. Theoretical results guarantee consistency of the method and its effectiveness is demonstrated in the challenging context of parameter inference for ordinary differential equations.