Noise and calibration

The default likelihood is Gaussian with the uncertainties you pass to each observation. This page lists the terms that change it: error floors and inflated errors, upper limits, and the calibration of a spectrum. The outlier mixture and the Gaussian-process likelihood have their own pages (Outlier model, GP likelihood). GOTCHAS.md (section 5) lists the combinations that are refused.

Fixed terms, set on the observation

• Spectrum(noise_floor=f): a fractional floor, sigma_eff² = sigma² + (f |model|)².
• Photometry(upper_limit=mask): bands where mask is True get a one-sided penalty (only a model above the data is penalised).

Sampled noise terms

Four terms inflate an observation's variance. Each is switched on by giving its parameter a prior (and a free_param_init) in SedModel:

parameter	variance becomes
log_err_scale_<kind>	sigma² exp(2 log_err_scale): a common rescaling of the quoted errors
log_jitter_<kind>	+ exp(log_jitter)², in data units
log_f_calib_<kind>	+ (exp(log_f_calib) |model|)²
log_f_data_<kind>	+ (exp(log_f_data) |data|)²

<kind> is phot, spec or lines. With several observations of one kind, each has its own term, <root>_<kind>_<obs.name> (for example log_jitter_spec_nirspec); the plain name then raises. A constant transform fixes a term at a value. These names are read by fitSED; with run_sampler you build the DiagonalNoiseModel yourself. log_jitter is the natural log of a flux in the observation's units (maggies, cgs F_nu or erg s⁻¹ cm⁻²), so set its prior from the size of your uncertainties.

Calibrating a spectrum

A spectrum's flux calibration rarely matches the photometry. Keep the photometry in the fit: it anchors the absolute level, and without it the continuum shape is degenerate with dust and age. Three ways to model the calibration, one per spectrum:

• Sampled level and shape. spectrum_scaling multiplies the whole Spectrum prediction. spectrum_calib, shape (order,), multiplies it by 1 + sum_k c_k P_k(x), Legendre polynomials of the observed wavelength mapped onto [-1, 1] over all pixels (no P_0 term: the level is spectrum_scaling). With several spectra, use spectrum_scaling_<obs.name> and spectrum_calib_<obs.name>.
• Profiled polynomial. Spectrum(polynomial_order=M) solves for the Chebyshev coefficients c_0..c_M inside the likelihood at every step, as Prospector's PolyOptCal does. The posterior is conditional on the best-fit polynomial: its uncertainty is not propagated.
• Marginalised polynomial. Spectrum(polynomial_order=M, polynomial_mode="marginalize", polynomial_prior_sigma=s) integrates the coefficients out analytically under a Gaussian prior of width s (in units of the fractional response). The calibration uncertainty then reaches the posterior and the evidence, with no extra sampled dimension.

eline_scaling is a different parameter: it scales the model emission lines of a Lines observation only, not the spectrum.