gcfit.probabilities.likelihood_mass_func

gcfit.probabilities.likelihood_mass_func(model, mf, fields, *, hyperparams=False)

Compute the loglikelihood of the cluster’s PDMF.

Computes the log likelihood component of a cluster’s present day mass function (PDMF) distribution of visible stars. Radial profiles of the relative number of stars counted in each mass bin, within each observation’s boundary polygons, are compared against the computed mass function N of the model, given by it’s density profile and integrated over the same field.

A Gaussian likelihood is assumed, with a δN Poisson error accompanying the mass function nuisance parameter F.

Parameters:

modelgcfit.FittableModel

Cluster model used to compute probability distribution.

mfgcfit.core.data.Dataset

Mass function profile dataset used to compute probability distribution and evaluate log likelihood.

fieldsdict

Dictionary of gcfit.util.mass.Field field, as given by gcfit.util.mass.initialize_fields.

hyperparamsbool, optional

Whether to include bayesian hyperparameters.

Returns:

float

Log likelihood value.

See also

util.mass.Field.MC_integrate

Monte Carlo integration method used to integrate the surface density profile.

Notes

The model mass function N is given for each stellar mass bin by the integral of the surface density profile within each radial bin, within the relevant field boundaries:

\[N = \int_{r_0}^{r_1} \Sigma(r) dr\]