Likelihood classes

The inference.likelihoods module provides tools for constructing likelihood functions. Example code demonstrating their use can be found in the Gaussian fitting jupyter notebook demo.

GaussianLikelihood

class inference.likelihoods.GaussianLikelihood(y_data: ndarray, sigma: ndarray, forward_model: callable, forward_model_jacobian: callable = None)

A class for constructing a Gaussian likelihood function.

Parameters:

• y_data – The measured data as a 1D array.

• sigma – The standard deviations corresponding to each element in y_data as a 1D array.

• forward_model (callable) – A callable which returns a prediction of the y_data values when passed an array of model parameter values.

• forward_model_jacobian (callable) – A callable which returns the Jacobian of the forward-model when passed an array of model parameter values. The Jacobian is a 2D array containing the derivative of the predictions of each y_data value with respect to each model parameter, such that element (i,j) of the Jacobian corresponds to the derivative of the i’th y_data value prediction with respect to the j’th model parameter.

__call__(theta: ndarray) → float

Returns the log-likelihood value for the given set of model parameters.

Parameters:

theta – The model parameters as a 1D numpy.ndarray.

Returns:

The log-likelihood value.

gradient(theta: ndarray) → ndarray

Returns the gradient of the log-likelihood with respect to model parameters.

Using this method requires that the forward_model_jacobian keyword argument was specified when the instance of the class was created.

Parameters:

theta – The model parameters as a 1D numpy.ndarray.

Returns:

The gradient of the log-likelihood as a 1D numpy.ndarray.

CauchyLikelihood

class inference.likelihoods.CauchyLikelihood(y_data: ndarray, gamma: ndarray, forward_model: callable, forward_model_jacobian: callable = None)

A class for constructing a Cauchy likelihood function.

Parameters:

• y_data – The measured data as a 1D array.

• gamma – The uncertainties corresponding to each element in y_data as a 1D array.

• forward_model (callable) – A callable which returns a prediction of the y_data values when passed an array of model parameter values.

• forward_model_jacobian (callable) – A callable which returns the Jacobian of the forward-model when passed an array of model parameter values. The Jacobian is a 2D array containing the derivative of the predictions of each y_data value with respect to each model parameter, such that element (i,j) of the Jacobian corresponds to the derivative of the i’th y_data value prediction with respect to the j’th model parameter.

__call__(theta: ndarray) → float

Returns the log-likelihood value for the given set of model parameters.

Parameters:

theta – The model parameters as a 1D numpy.ndarray.

Returns:

The log-likelihood value.

gradient(theta: ndarray) → ndarray

Returns the gradient of the log-likelihood with respect to model parameters.

Using this method requires that the forward_model_jacobian keyword argument was specified when the instance of the class was created.

Parameters:

theta – The model parameters as a 1D numpy.ndarray.

Returns:

The gradient of the log-likelihood as a 1D numpy.ndarray.

LogisticLikelihood

class inference.likelihoods.LogisticLikelihood(y_data: ndarray, sigma: ndarray, forward_model: callable, forward_model_jacobian: callable = None)

A class for constructing a Logistic likelihood function.

Parameters:

• y_data – The measured data as a 1D array.

• sigma – The uncertainties corresponding to each element in y_data as a 1D array.

• forward_model (callable) – A callable which returns a prediction of the y_data values when passed an array of model parameter values.

• forward_model_jacobian (callable) – A callable which returns the Jacobian of the forward-model when passed an array of model parameter values. The Jacobian is a 2D array containing the derivative of the predictions of each y_data value with respect to each model parameter, such that element (i,j) of the Jacobian corresponds to the derivative of the i’th y_data value prediction with respect to the j’th model parameter.

__call__(theta: ndarray) → float

Returns the log-likelihood value for the given set of model parameters.

Parameters:

theta – The model parameters as a 1D numpy.ndarray.

Returns:

The log-likelihood value.

gradient(theta: ndarray) → ndarray

Returns the gradient of the log-likelihood with respect to model parameters.

Using this method requires that the forward_model_jacobian keyword argument was specified when the instance of the class was created.

Parameters:

theta – The model parameters as a 1D numpy.ndarray.

Returns:

The gradient of the log-likelihood as a 1D numpy.ndarray.