estimate_uncertainties_from_model

ell1fit.scaling.estimate_uncertainties_from_model(model, parameter_names, observation_length, optimistic=False)[source]

Estimate heuristic 1-sigma scales for selected fit parameters.

This helper derives approximate uncertainty magnitudes from the binary and spin scales of the input model(s), not from covariance propagation or a timing fit. It is intended to provide coarse parameter scales for initialization/tuning.

Parameters:
modellist

List of PINT timing models (one per file). The first model provides orbital parameters PB, PBDOT, A1 and the maximum F0 across models is used in the estimates.

parameter_nameslist of str

Parameter names to estimate. Supported entries are PB, A1, A1DOT, TASC, and frequency-derivative names matching F<n>_<i>.

observation_lengtharray-like

Per-file observation durations in seconds. The maximum value is used.

Returns:
dict

Mapping {parameter_name: estimated_uncertainty}. Returned units follow parameter units used by this module: PB (s), A1 (light-seconds), A1DOT (light-seconds per second), TASC (s, relative to epoch), and F<n>_<i> in the native derivative units.

Notes

The implemented heuristics are:

  • PB: \(\sigma_{PB} \approx \frac{\sqrt{3}}{\pi} \frac{1}{2\pi F0}\frac{PB^2}{A1\,T_{obs}}\)

  • A1: \(\sigma_{A1} \approx \frac{1}{2\pi F0}\)

  • A1DOT: \(\sigma_{\dot{A1}} \approx \sigma_{A1} / T_{span}\), with \(T_{span}\) the spread of the files’ PEPOCH. Omitted when a single epoch leaves no lever arm.

  • TASC: \(\sigma_{TASC} \approx \frac{1}{2\pi F0}\frac{PB}{2\pi A1}\)

  • F_k: \(\sigma_{F_k} \approx \max(A1\,\Omega^{k+1}F0,\;10/T_{obs}^{k+1})\), with \(\Omega=2\pi/PB\).