Population models

Population models for GWPopulation follow a specific syntax which is an extension of the bilby.hyper.model syntax.

Functions

The simplest definition is as function that take as input a dictionary of arrays with sample points named dataset and named hyperparmeters and return an array containing the probability density of the model evaluated at the sample points.

For example, the following function defines a simple power-law mass model:

def power_law_mass_model(dataset, alpha, minimum_mass, maximum_mass):
    mass_1 = dataset["mass_1"]
    normalization = (
        (1 - alpha)
        / (maximum_mass ** (1 - alpha) - minimum_mass ** (1 - alpha))
    )
    in_bounds = (mass_1 >= minimum_mass) & (mass_1 <= maximum_mass)
    return mass_1 ** -alpha * normalization * in_bounds

Classes

The more complex definition is as a class that has an __init__ method that has the same signature. In this case a variable_names attribute or property can be used to avoid having to explicitly name the hyperparameters. For example, the following class defines the same power-law mass model:

class PowerLawMassModel:

    variable_names = ["alpha", "minimum_mass", "maximum_mass"]

    def __init__(self, dataset, **kwargs):
        return power_law_mass_model(
            dataset,
            kwargs["alpha"],
            kwargs["minimum_mass"],
            kwargs["maximum_mass"],
        )

The class definition allows for more complex models to be defined and to cache values that are expensive to compute and don’t depend on the hyperparameters.

We provide a number of pre-defined models along with standard base models that can be extended. See the API documentation for more details on implemented models.