Fix numba CauchyRV loc/scale - #2309
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The numba dispatch computed `(loc + z) / scale` instead of `loc + scale * z`, giving the sampled variable location `loc/scale` and scale `1/scale`. `rng_fn_scipy` and the JAX dispatch are both correct, so only the numba backend was affected -- but it is the default linker. `logp` is untouched, so NUTS posteriors were fine; everything that draws was not, including `sample_prior_predictive` on a `HalfCauchy` prior. The existing `cauchy` case in `test_unaligned_RandomVariable` passed `scale=1.0`, where `(loc + z) / 1` is algebraically identical to `loc + 1 * z`, so both the location and scale errors vanished together. Bumping that to `scale=3.0` makes the Cramer-von Mises check fail on the old code (p = 1.7e-08) and pass on the new. Closes pymc-devs#2308
`test_unaligned_RandomVariable` is the only test that checks these samplers against their distribution, and it has three cases. `cauchy` and `gumbel` both used `scale=1.0`; `t` already passes `scale=np.pi`. `GumbelRV` has a hand-written core too (`loc - scale * np.log(-np.log(U))`) and is correct, but at `scale=1` a `(loc - z) / scale`-style slip would be invisible there for the same algebraic reason. Bumped to `scale=4.0`. Verified by injecting exactly that slip: the test fails at p=7.2e-08 with it and passes without. Audited the other hand-written numba cores (`t`, `halfnormal`, `pareto`, `invgamma`, `gumbel`, `wald`, plus the default-path RVs) against scipy with non-degenerate parameters -- all match, so `cauchy` was the only actual bug.
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Asked whether other distributions share the cauchy blind spot. Two axes checked.
1. Empirical. Every hand-written numba core (StudentT, HalfNormal, Pareto,
InvGamma, Gumbel, Wald, Cauchy) plus the default-path RVs (normal, laplace,
logistic, gamma, exponential, vonmises, weibull) sampled with NON-degenerate
loc/scale/shape and compared to scipy by median, IQR and Cramer-von Mises.
All match. Cauchy was the only real bug.
2. Structural. test_unaligned_RandomVariable is the only test that checks these
samplers against their distribution, and it has exactly three cases. Two used
scale=1.0, where (loc +/- z)/scale is algebraically identical to loc +/- 1*z,
so location and scale errors vanish together:
cauchy scale=1.0 -> 3.0 (catches the actual bug, p=1.7e-08)
gumbel scale=1.0 -> 4.0 (no bug, but equally undetectable)
t scale=np.pi already fine
Gumbel has a hand-written loc-scale core too. Proved the new case works by
injecting the analogous slip into it: fails at p=7.2e-08 with, passes without.
Corrected one of my own readings along the way: I first flagged the t case as
degenerate, but it passes loc=[1,2] and scale=np.pi -- my regex only missed it
because np.e and np.pi are not numeric literals.
PR pymc-devs/pytensor#2309 updated with both. Full file: 84 passed, 2 xfailed.
Co-Authored-By: Claude Opus 5 (1M context) <noreply@anthropic.com>
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Closes #2308.
The numba dispatch computed
(loc + z) / scaleinstead ofloc + scale * z, so the sampled variable had locationloc/scaleand scale1/scale.rng_fn_scipyand the JAX dispatch were already correct, so only numba was affected — but it is the default linker.logpis untouched, so NUTS posteriors were fine; anything that draws was not, includingsample_prior_predictiveon aHalfCauchyprior (HalfCauchyRV.rv_opbuildsabs(cauchy(0, beta))).Tests
test_unaligned_RandomVariableis the only test checking these samplers against their distribution, and it has three cases. Two used a degenerate scale:cauchyscale=1.0scale=3.0gumbelscale=1.0scale=4.0tscale=np.piAt
scale=1,(loc ± z) / 1is algebraically identical toloc ± 1 * z, so both the location and scale errors vanish together and Cramér–von Mises passes.GumbelRVhas a hand-written core too (loc - scale * np.log(-np.log(U))) and is correct, but was equally undetectable. Verified by injecting the analogous slip: the new case fails at p=7.2e-08 with it, passes without.Audit
Checked every hand-written numba core (
t,halfnormal,pareto,invgamma,gumbel,wald) plus the default-path RVs against scipy with non-degenerate parameters. All match —cauchywas the only real bug.tests/link/numba/test_random.py: 84 passed, 2 xfailed.