Glossary

Pull — a residual divided by its standard uncertainty, $z_i=(d_i-m_i)/\sigma_i$, with data value $d_i$, model prediction $m_i$, and standard uncertainty $\sigma_i$. Under a correct model, pulls scatter around zero with scale one. With a non-diagonal covariance the reported pulls are whitened residuals (see Whitening); they keep the scale-one property but no longer refer to individual data points.

Whitening — re-expressing the residual vector $r$, whose covariance is $V$, as $z=L^{-1}r$ with $V=LL^T$, so that $\chi^2=z^Tz$. It changes coordinates, not the data or the model.

Effective variance — the propagated per-point variance $\sigma_{y,i}^2+(\partial f/\partial x)^2|_{x_i}\,\sigma_{x,i}^2$, where $f$ is the model curve evaluated at the current parameters; it turns x uncertainty into a parameter-dependent y covariance.

ndf — degrees of freedom: observations (including Gaussian priors and constraints, which count as extra observations) minus free parameters. Reduced statistics and p-values require $\mathrm{ndf}>0$.

Deviance — the Poisson likelihood-ratio statistic against the saturated model, the reference model with one free expectation per count that reproduces every observation exactly; it fills the chi-square fields for count fits and shares their asymptotic calibration.

Profile — the cost minimized over all remaining parameters (the nuisance parameters) at each fixed value of one parameter of interest. Freezing the others at their best-fit values (a slice) yields intervals that are too narrow; the re-minimization at each fixed value is what defines the profile.

Profile interval — the parameter range where the profiled cost exceeds the cost at the global minimum by at most the threshold, $\Delta C = C_\mathrm{profile} - C_\mathrm{min} \le$ threshold. threshold=1 corresponds to 68.27% asymptotically for one parameter; $\Delta C$ is divided by the same covariance scale as param_stderr, so both report matching uncertainties.

Confidence band — the pointwise 68.27% (at nsigma=1) interval for the fitted mean curve from the parameter covariance.

Prediction band — the confidence band widened by the observation uncertainty: where a new measurement would plausibly land.

Covariance scaling — multiplying the parameter covariance by $\chi^2/\mathrm{ndf}$ when no y or x uncertainties were supplied, so the residual scale is estimated from the data (scale_covariance=:auto); profiles and contours follow the same scale.

Finding — one structured diagnostic (severity, stable code, evidence, recommendation) produced by diagnose; the dashboard aggregates findings into ok/review/stop.