"""The Student-t likelihood."""
from __future__ import annotations
import numpy as np
from firecrown.likelihood.gaussfamily import GaussFamily
from firecrown.modeling_tools import ModelingTools
from firecrown.likelihood.statistic import Statistic
from firecrown import parameters
[docs]
class StudentT(GaussFamily):
r"""A T-distribution for the log-likelihood.
This distribution is appropriate when the covariance has been obtained
from a finite number of simulations. See Sellentin & Heavens
(2016; arXiv:1511.05969). As the number of simulations increases, the
T-distribution approaches a Gaussian.
"""
def __init__(
self,
statistics: list[Statistic],
nu: None | float = None,
):
"""Initialize a StudentT object.
:param statistics: The statistics to use in the likelihood
:param nu: The degrees of freedom of the T-distribution
"""
super().__init__(statistics)
self.nu = parameters.register_new_updatable_parameter(nu, default_value=3.0)
[docs]
def compute_loglike(self, tools: ModelingTools) -> float:
"""Compute the log-likelihood.
:param tools: The modeling tools used to compute the likelihood.
:return: The log-likelihood.
"""
chi2 = self.compute_chisq(tools)
return -0.5 * self.nu * np.log(1.0 + chi2 / (self.nu - 1.0))