Fix test_lowrank_multivariate_normal_moments via larger sample#4419
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Fix test_lowrank_multivariate_normal_moments via larger sample#4419PatrykWilczewski wants to merge 4 commits into
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Problem: test_lowrank_multivariate_normal_moments fails with "Tensor-likes are not close!" Root cause: underpowered test - N=100 000, atol=0.01 -> worst 3-sigma spread ~0.0168 > 0.01; Fix: Override sample count 100 000 -> 500 000 Fixes: intel#4253
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Problem: test_lowrank_multivariate_normal_moments fails with "Tensor-likes are not close!"
Root cause: underpowered test - N=100 000, atol=0.01 -> worst 3-sigma spread ~0.0168 > 0.01;
The upstream test draws only 100 000 samples and checks the empirical mean against the analytic mean with atol=0.01, rtol=0. For this fixture the worst per-element variance is ~3.15, so the standard error of the empirical mean is sqrt(3.15 / 100 000) ~= 0.0056 and its 3-sigma spread ~= 0.0168 already exceeds the 0.01 tolerance. The test is therefore statistically underpowered; it only appeared to "pass" on XPU because the exact seed-0 draws happened to land under the threshold, until PR #3725 (std::log -> sycl::log in the Box-Muller transform) legitimately perturbed those draws.
Fix: Raise the sample count to 500 000 shrinks the 3-sigma mean spread to ~0.0075 (< 0.01) and the variance spread comfortably under 0.02, making the check robust across seeds without weakening the tolerance.
Fixes: #4253