cofi.utils.BaseLikelihood

class cofi.utils.BaseLikelihood

Base class for a likelihood function

This base class provides a consistent interface for likelihood functions used in Bayesian inverse problems. Concrete implementations should define how to evaluate the log-likelihood and its derivatives.

Basic interface

The basic properties / methods for a likelihood function in cofi.utils include the following:

BaseLikelihood.model_shape	The shape of models that current likelihood function accepts.
BaseLikelihood.model_size	The number of unknowns that current likelihood function accepts.
BaseLikelihood.log_likelihood(model)	Evaluate the log-likelihood function at a given model.
BaseLikelihood.gradient(model)	The gradient of log-likelihood with respect to model parameters.
BaseLikelihood.hessian(model)	The Hessian of log-likelihood with respect to model parameters.
BaseLikelihood.__call__(model)	A class instance itself can also be called as a function.
BaseLikelihood.get_ml_cov(model)	Get maximum likelihood estimate of data covariance (if applicable).

Reference Details

__call__(model: ndarray) → float

A class instance itself can also be called as a function.

It works exactly the same as log_likelihood.

In other words, the following two usages are exactly the same:

>>> my_likelihood = GaussianLikelihood(data, forward_func)
>>> log_p = my_likelihood(np.array([1,2,3]))                    # usage 1
>>> log_p = my_likelihood.log_likelihood(np.array([1,2,3]))     # usage 2

Parameters:

model (np.ndarray) – The model parameters to evaluate

Returns:

The log-likelihood value

Return type:

float

get_ml_cov(model: ndarray) → ndarray | None

Get maximum likelihood estimate of data covariance (if applicable).

This is an optional method that some likelihood implementations may provide to return the maximum likelihood estimate of the data covariance matrix for a given model.

Parameters:

model (np.ndarray) – The model parameters

Returns:

The estimated data covariance matrix, or None if not applicable

Return type:

Optional[np.ndarray]

abstract gradient(model: ndarray) → ndarray

The gradient of log-likelihood with respect to model parameters.

The gradient has shape \((M,)\) where \(M\) is the number of model parameters.

Parameters:

model (np.ndarray) – The model parameters at which to evaluate the gradient

Returns:

The gradient vector of shape (M,)

Return type:

np.ndarray

abstract hessian(model: ndarray) → ndarray

The Hessian of log-likelihood with respect to model parameters.

The Hessian has shape \((M,M)\) where \(M\) is the number of model parameters.

Parameters:

model (np.ndarray) – The model parameters at which to evaluate the Hessian

Returns:

The Hessian matrix of shape (M, M)

Return type:

np.ndarray

abstract log_likelihood(model: ndarray) → float

Evaluate the log-likelihood function at a given model.

Parameters:

model (np.ndarray) – The model parameters at which to evaluate the log-likelihood

Returns:

The log-likelihood value log p(d|m)

Return type:

float

model_shape

The shape of models that current likelihood function accepts.

Returns:

The shape of the model parameter array

Return type:

tuple

model_size

The number of unknowns that current likelihood function accepts.

Returns:

The total number of model parameters

Return type:

Number

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