montecarlo op• Data kinds: none → table (an op determined by its arguments alone — it takes no image or data input)
• Call: import fullseye as fs; fs.ledger.mc_sequential_mean(sampler='pi', tol=0.01, rel_tol=0.0, confidence=0.95, batch=4096, max_samples=4000000, seed=0, on_fail='raise') -> 'dict' (to call the implementation directly, import converge; converge.mc_sequential_mean(sampler='pi', tol=0.01, rel_tol=0.0, confidence=0.95, batch=4096, max_samples=4000000, seed=0, on_fail='raise') -> 'dict'; from the registry, opsconverge.get("mc_sequential_mean"))
Sequential Monte Carlo mean: add samples until the confidence interval is narrower than the tolerance.
sampler(rng, n) returns n i.i.d. samples (a 1-D array) — or the built-in "pi" (4 * [u^2 + v^2 <= 1], mean pi). Batch b is drawn from default_rng((seed, b)), so the result is reproducible and does not depend on how many batches came before.
Stops at the first batch boundary, from the second batch on, where the half-width z * s / sqrt(n) <= tol + rel_tol * |mean| (z from confidence; s the running sample standard deviation). This is the fixed-width sequential interval of Chow & Robbins 1965; never stopping inside the first two batches guards against an early, accidentally small variance (raise batch to guard more) — the actual coverage is checked by the gates, not assumed.
Returns mean, se, ci (lower, upper), half_width, n_samples (used), converged and history (n, mean, se per batch). Refusal: max_samples reached first raises NotConvergedError (on_fail="record" returns the record with mean = None and the running values under last_mean / last_se).
• convergent_computation family guide
• Sample-data catalog (download URLs / licences) — 2-D uses skimage.data (BSD/public domain) plus synthetic images; 3-D lists download URLs for real data sources (Stanford, PDS, …).
• Operator provenance and references — the sources of the research/methods this op family came from.
• The canonical algorithm (author, year) and its uses are named in the family usage guide above.
• (none yet)
table as input)—
montecarlo)*Provenance: converge.py — CONVERGE operator registry. This per-op note is generated by tools/opdocs.py md (do not hand-edit).*
© 2026 Kazufumi Furuse — Fullseye operator documentation. Licensed under Apache-2.0.