{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,24]],"date-time":"2026-02-24T20:14:01Z","timestamp":1771964041372,"version":"3.50.1"},"reference-count":0,"publisher":"TechForum Publishing Group","issue":"1","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Bull. Comput. Data Sci."],"published-print":{"date-parts":[[2021,12,30]]},"abstract":"<jats:p>Effective Sample Size (ESS) is central to diagnosing Markov chain Monte Carlo (MCMC) efficiency, yet standard multivariate ESS definitions either collapse in high dimensions when some coordinates are (near-)deterministic or become numerically unstable under hardware approximations (e.g., fixed-point quantization and probability truncation). We introduce mvESS-Z, a multivariate ESS that (i) is invariant to zero-variance coordinates, (ii) admits finite-sample concentration guarantees, and (iii) is stable under quantization\/truncation commonly used in probabilistic accelerators. mvESS-Z is defined on the signal subspace determined by the posterior covariance and uses pseudo-determinant or spectral aggregation to avoid degeneracy. We prove basic properties, give a practical estimator with automatic rank selection, and show on synthetic and vision-style workloads that mvESS-Z correlates with downstream task error more reliably than per-coordinate ESS and split-^R, enabling quality-constrained tuning of precision and random number generators.<\/jats:p>","DOI":"10.71448\/bcds2121-2","type":"journal-article","created":{"date-parts":[[2026,2,24]],"date-time":"2026-02-24T19:55:41Z","timestamp":1771962941000},"page":"3-16","source":"Crossref","is-referenced-by-count":0,"title":["mvESS-Z: A Robust Multivariate Effective Sample Size for Degenerate and Quantized Markov Chains"],"prefix":"10.71448","volume":"2","author":[{"name":"Chennai Mathematical Institute, Chennai, India","sequence":"first","affiliation":[]},{"given":"Sayan","family":"Mukherjee","sequence":"first","affiliation":[]}],"member":"52394","published-online":{"date-parts":[[2021,12,30]]},"container-title":["Bulletin of Computer and Data Sciences"],"original-title":[],"deposited":{"date-parts":[[2026,2,24]],"date-time":"2026-02-24T19:55:42Z","timestamp":1771962942000},"score":1,"resource":{"primary":{"URL":"https:\/\/bcds.ch\/mvess-z-a-robust-multivariate-effective-sample-size-for-degenerate-and-quantized-markov-chains\/"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,12,30]]},"references-count":0,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2021,12,30]]},"published-print":{"date-parts":[[2021,12,30]]}},"URL":"https:\/\/doi.org\/10.71448\/bcds2121-2","relation":{},"ISSN":["3072-2926"],"issn-type":[{"value":"3072-2926","type":"electronic"}],"subject":[],"published":{"date-parts":[[2021,12,30]]}}}