profile-ci-review

name	profile-ci-review
description	Review freqTLS profile-likelihood confidence intervals for correctness, equivariance, chi-square calibration, and honest open/boundary/multimodal handling.

Profile-Likelihood CI Review

Use this skill for any change to R/profile.R, R/confint.R, or R/diagnostics.R, and before any claim about a freqTLS interval. Fisher leads; Noether checks the transform algebra; Curie checks the tests.

The Algorithm Contract

For a scalar target psi: fit the MLE (theta_hat, logLik_hat); fix psi's unconstrained coordinate; re-optimise the other coordinates; form the deviance D = 2 * (logLik_hat - logLik_p); the interval is {psi : D <= qchisq(level, 1)}, found by uniroot on each side; transform endpoints to the natural scale.

Target	Profile on	Transform
z, z:grp	eta_logz[g]	exp
CTmax, CTmax:grp	beta_CT[g]	identity
low	beta_low	plogis
k	beta_logk	exp
phi	log_phi	exp
up	re-root on the native (up, low-fraction)	identity (else Wald/delta)
contrasts dCTmax, dlog_z	reference + contrast recoding	identity (ratio z = exp(dlog_z))

Review Checklist

1. Is |D(MLE)| near zero (about 1e-4) at the fitted optimum?
2. Is profile equivariance enforced? The z-profile must equal exp() of the log_z-profile, so a test asserts ci_z == exp(ci_log_z) to about 1e-6. This is the headline equivariance check.
3. Is the chi-square cutoff qchisq(level, 1) (one degree of freedom per scalar target), and is the confidence level wired through correctly?
4. Is asymmetry allowed and preserved (do not symmetrise the interval)?
5. Open / non-closing profile: does the side that does not cross the cutoff return NA with a warning ("profile did not close; weakly identified -- consider bayesTLS or bootstrap") and a conf.status marker, rather than crashing or fabricating an endpoint (R-PROFILE)?
6. Boundary MLE: when the MLE is on a boundary, is the chi-square calibration flagged as unreliable (warning), not silently trusted?
7. Multimodal / non-monotone profile: is a non-monotone deviance trace detected and reported, not collapsed to a single interval?
8. Inner non-convergence: does an inner re-optimisation failure propagate as NA with a warning, not a misleading finite endpoint?

Tests Of The Tests

• A clean interior fit yields a finite closed interval with ci_z == exp(ci_log_z).
• A deliberately sparse design triggers expect_warning("did not close") and an NA endpoint with no crash.
• The deviance at the MLE is essentially zero.

Record the exact uniroot tolerances and the chi-square level in the after-task report; do not relax a tolerance without inspecting the failure first.