Intrinsic effective sample size for manifold-valued Markov chain Monte Carlo via kernel discrepancy

ArXi:2605.03266v1 Announce Type: cross Effective sample size is a standard summary of Marko chain Monte Carlo output, but it is usually attached to scalar or Euclidean summaries chosen by the analyst. For manifold-valued samples this choice is not canonical: coordinate-wise effective sample sizes can change under rotations, chart changes, or alternative embeddings of the same underlying path. We propose an intrinsic effective sample size based on kernel discrepancy.