gaussian likelihood

A simple single-mode Gaussian likelihood with optional normalization.

This is a simpler alternative to gaussian_mixture for cases where you only need a single Gaussian mode.

Usage

The mean and covariance matrix must be specified with the options mean and cov respectively. The dimensionality of the likelihood is determined from these options.

The normalized parameter (default: True) controls whether to include the full normalization constant. When False, only the chi-squared term is computed, which is useful when only relative likelihoods matter.

The following example defines a 2D Gaussian likelihood:

likelihood:
  gaussian:
    mean: [0.5, 1.0]
    cov: [[0.1, 0.05],
          [0.05, 0.2]]
    normalized: True
    input_params: ['x', 'y']

params:
  x:
    prior:
      min: 0
      max: 1
  y:
    prior:
      min: 0
      max: 2

The option input_params_prefix can be used instead of explicit input_params, similar to gaussian_mixture. The number of parameters must match the dimensionality defined by the mean and covariance.

For 1D cases, scalar values can be used:

likelihood:
  gaussian:
    mean: 0.5
    cov: 0.04
    input_params: ['x']

The default option values for this likelihood are:

# Simple Gaussian likelihood

# Mean vector
mean:
# Covariance matrix
cov:
# Whether to include normalization constant (default: True)
normalized: True
# Prefix of parameter names (if not using explicit input_params)
input_params_prefix: ""

Gaussian likelihood class

Synopsis:

Simple Gaussian likelihood

Author:

Antony Lewis

class likelihoods.gaussian.Gaussian(info=mappingproxy({}), name=None, timing=None, packages_path=None, initialize=True, standalone=True)

Simple Gaussian likelihood.

initialize_with_params()

Initializes the gaussian distribution.

logp(**params_values)

Computes the log-likelihood for a given set of parameters.