derivkit.likelihoods.gaussian module#

Gaussian likelihoods function module.

derivkit.likelihoods.gaussian.build_gaussian_likelihood(data: ArrayLike, model_parameters: ArrayLike, cov: ArrayLike, return_log: bool = True) → tuple[tuple[ndarray[tuple[Any, ...], dtype[float64]], ...], ndarray[tuple[Any, ...], dtype[float64]]]#

Constructs the Gaussian likelihoods function.

Parameters:

  • data – a 1D or 2D array representing the given data values. It is expected that axis 0 represents different samples of data while axis 1 represents the data values.

  • model_parameters – a 1D array representing the theoretical values of the model parameters.

  • cov – covariance matrix. May be a scalar, a 1D vector of diagonal variances, or a full 2D covariance matrix. It will be symmetrised and normalized internally to ensure compatibility with the data and model_parameters.

  • return_log – when set to True, return the log-likelihoods instead of the probability density function.

Returns:

  • coordinate_grids: tuple of 1D arrays giving the evaluation coordinates for each dimension (one array per dimension), ordered consistently with the first axis of data.

  • probability_density: ndarray with the values of the multivariate Gaussian probability density function evaluated on the Cartesian product of those coordinates.

Return type:

A tuple

Raises:

ValueError – raised if - data is not 1D or 2D, - model_parameters is not 1D, - the number of samples in data does not match the number of model parameters, - model_parameters contain non-finite values, - cov cannot be normalized to a valid covariance matrix.

Examples

A 1D Gaussian likelihoods:
>>> import numpy as np
>>> import matplotlib.pyplot as plt
>>> from derivkit.likelihoods.gaussian import build_gaussian_likelihood
>>> data = np.linspace(-10, 10, 100)[np.newaxis, :]
>>> model_parameters = np.array([1.0])
>>> cov = np.array([[2.0]])
>>> x_grid, pdf = build_gaussian_likelihood(data, model_parameters, cov)
>>> plt.plot(x_grid[0], pdf[0])
A 2D Gaussian likelihoods:
>>> import numpy as np
>>> import matplotlib.pyplot as plt
>>> data = np.asarray((np.linspace(-10, 10, 30), np.linspace(3, 6, 30)))
>>> model_parameters = np.array([0.0, 4.0])
>>> cov = np.array([[1.0, 0.2], [0.2, 0.3]])
>>> # Build coordinate arrays and evaluate the probability density on their
>>> # Cartesian product. The indexing ensures the coordinate order matches
>>> # the order in ``data``.
>>> grid, probability_density = build_gaussian_likelihood(data, model_parameters, cov)
>>> plt.contour(*grid, probability_density)