jwspecmcmc.likelihood

Log-likelihood and log-probability for MCMC sampling.

The likelihood uses the same weighted chi-squared as jwspecfit.fitter.fit_lines(), ensuring identical statistical treatment of the data.

Functions

log_likelihood(p_free, spec)

Gaussian log-likelihood for free parameters.

log_probability(p_free, spec, prior_set)

Log-posterior = log-prior + log-likelihood.

Classes

LikelihoodSpec(flam, flam_err, valid, edges, ...)

Cached data needed for likelihood evaluation.
class jwspecmcmc.likelihood.LikelihoodSpec(flam, flam_err, valid, edges, n_lines, constraints, w_pix, n_lya=0, lya_model_fn=None)[source]

Bases: object

Cached data needed for likelihood evaluation.

All arrays are in F_lambda units (erg/s/cm^2/Angstrom).

Parameters:

  • flam (np.ndarray) – Continuum-subtracted flux density.

  • flam_err (np.ndarray) – Flux density errors.

  • valid (np.ndarray) – Boolean mask of valid pixels.

  • edges (np.ndarray) – Pixel-edge wavelengths in Angstroms (length n_pix + 1).

  • n_lines (int) – Number of emission lines.

  • constraints (ConstraintSet) – Parameter constraints.

  • w_pix (np.ndarray) – Pixel weights from jwspecfit.models.pixel_weight().

  • n_lya (int) – Number of extra Lyα parameters appended to the free vector (4 when Lyα is being fit, 0 otherwise).

  • lya_model_fn (callable or None) – Function (p_lya,) -> np.ndarray that evaluates the asymmetric Gaussian Lyα model from a 4-element parameter vector [A_peak, mu, sigma, alpha].

constraints: ConstraintSet
edges: ndarray
flam: ndarray
flam_err: ndarray
lya_model_fn: Callable | None = None
n_lines: int
n_lya: int = 0
valid: ndarray
w_pix: ndarray
jwspecmcmc.likelihood.log_likelihood(p_free, spec)[source]

Gaussian log-likelihood for free parameters.

Mirrors the residual function in jwspecfit.fitter.fit_lines: -0.5 * sum(((flam - model) / flam_err * w_pix)^2).

Parameters:

  • p_free (np.ndarray) – Free parameter vector. When Lyα is being fit, the last spec.n_lya elements are the Lyα parameters.

  • spec (LikelihoodSpec) – Cached data for evaluation.

Returns:

Log-likelihood value.

Return type:

float

jwspecmcmc.likelihood.log_probability(p_free, spec, prior_set)[source]

Log-posterior = log-prior + log-likelihood.

Parameters:

  • p_free (np.ndarray) – Free parameter vector.

  • spec (LikelihoodSpec) – Cached data for evaluation.

  • prior_set (PriorSet) – Prior distributions for free parameters.

Returns:

Log-posterior value (-inf if outside prior support).

Return type:

float