pybop.parameters.multivariate_distributions#

Classes#

`BaseMultivariateDistribution`	A base class for defining multivariate parameter distributions.
`MarginalDistribution`	Represents a univariate marginal distribution of a pybop.BaseMultivariateDistribution.
`MultivariateGaussian`	Represents a multivariate Gaussian (normal) distribution with a
`MultivariateLogNormal`	Represents a multivariate log-normal distribution with a
`MultivariateNonparametric`	Represents a "freeform" distribution, i.e., one that is defined from
`MultivariateUniform`	Represents a multivariate uniform distribution.

Module Contents#

class pybop.parameters.multivariate_distributions.BaseMultivariateDistribution(distribution: scipy.stats.distributions.rv_frozen, properties: dict | None = None, n_parameters: int = 1)[source]#

Bases: pybop.parameters.distributions.Distribution

A base class for defining multivariate parameter distributions.

This class extends pybop.Distribution with methods that reduce the output of a multivariate distribution to its individual dimensions.

Note that, unlike in pybop.Distribution, distribution attributes are stored in a dictionary, as multivariate distributions in SciPy do not follow the loc/scale convention.

distribution#

The underlying continuous random variable distribution.

Type:: scipy.stats.rv_continuous

properties#

A dictionary with distribution keyword argument names as string keys and their values as float values.

Type:: dict

cdf(x)[source]#

Calculates the cumulative distribution function (CDF) of the distribution at x.

Parameters:: x (float) – The point(s) at which to evaluate the CDF.
Returns:: The cumulative distribution function value at x.
Return type:: float

cdf_marginal(x, position: int)[source]#

Takes the marginal cumulative distribution function (CDF) at x.

Parameters:

x (numpy.ndarray) – The point(s) at which to evaluate the CDF.
position (int) – The dimension to which to reduce the CDF to.

Returns:

The marginal cumulative distribution function value at x.

Return type:

float

check_consistent_transformation(transform: pybop.transformation.base_transformation.Transformation) → None[source]#: Raise an error if a composed transformation contains incompatible types of transformation.

cov()[source]#: Get the covariance matrix.

get_transformed_distribution(transform: pybop.transformation.base_transformation.Transformation) → pybop.parameters.distributions.BaseDistribution | None[source]#: Get the transformed distribution in the search space.

abstractmethod icdf_marginal(q, position: int)[source]#

logpdf(x)[source]#: Calculates the logarithm of the probability density function of the distribution at x.

abstractmethod marginal(position: int)[source]#: Return univariate marginal distribution of parameter with index ‘position’.

pdf(x)[source]#: Calculates the probability density function (PDF) of the distribution at x.

rvs(size: int = 1, random_state: int | None = None)[source]#: Generates random variates from the distribution.

std()[source]#: Get the square root of the covariance matrix.

support() → numpy.ndarray[source]#: Return the support as a numpy array of dimensions (2, n_parameters).

icdf = None#: Multivariate distributions have no invertible CDF.

class pybop.parameters.multivariate_distributions.MarginalDistribution(parent_distribution: BaseMultivariateDistribution, position: int)[source]#

Bases: pybop.parameters.distributions.Distribution

Represents a univariate marginal distribution of a pybop.BaseMultivariateDistribution. Relies on the “marginal” method of the multivariate distribution.

Sub-class of pybop.Distribution with the additional properties “parent_distribution” and “position”

Parameters:

parent_distribution (pybop.BaseMultivariateDistribution) – A multivariate distribution
position (int) – position of the parameter for which to create the marginal distribution

__repr__() → str[source]#

get_transformed_distribution(transform: pybop.transformation.base_transformation.Transformation) → pybop.parameters.distributions.BaseDistribution | None[source]#: Get the transformed distribution in the search space, by first transforming the parent distribution and then fetching the marginal distribution.

_position#

parent_distribution#

property position: int#

class pybop.parameters.multivariate_distributions.MultivariateGaussian(mean: numpy.ndarray, covariance: numpy.ndarray)[source]#

Bases: BaseMultivariateDistribution

Represents a multivariate Gaussian (normal) distribution with a given mean and covariance.

Parameters:

mean (numpy.ndarray) – The mean (µ) of the multivariate Gaussian distribution.
covariance (numpy.ndarray) – The covariance matrix (Σ) of the multivariate Gaussian distribution. Note that what is called σ in 1D would be the square root of Σ here.

_transform(transform: pybop.transformation.base_transformation.Transformation) → pybop.parameters.distributions.BaseDistribution | None[source]#: Get the transformed distribution in the search space.

cov()[source]#: Get the covariance matrix.

marginal(position: int)[source]#: Return univariate marginal distribution of parameter with index ‘position’.

mean()[source]#: Get the mean of the distribution.

support() → numpy.ndarray[source]#: Return the support as a numpy array of dimensions (2, n_parameters).

class pybop.parameters.multivariate_distributions.MultivariateLogNormal(mean_log_x, covariance_log_x)[source]#

Bases: BaseMultivariateDistribution

Represents a multivariate log-normal distribution with a given mean and covariance of the normally distributed log(x).

Parameters:

mean_log_x (numpy.ndarray) – The mean (µ) of the multivariate Gaussian distribution of log(x).
covariance_log_x (numpy.ndarray) – The covariance matrix (Σ) of the multivariate Gaussian distribution of log(x). Note that what is called σ in 1D would be the square root of Σ here.

_get_properties()[source]#: Method to compute the mean and covariance of x given the mean and covariance of log(x).

_transform(transform: pybop.transformation.base_transformation.Transformation) → pybop.parameters.distributions.BaseDistribution | None[source]#: Get the transformed distribution in the search space.

cdf(x)[source]#

Calculates the cumulative distribution function (CDF) of the distribution at x.

Parameters:: x (float) – The point(s) at which to evaluate the CDF.
Returns:: The cumulative distribution function value at x.
Return type:: float

cov()[source]#: Get the covariance matrix.

logpdf(x)[source]#: Calculates the logarithm of the probability density function of the distribution at x.

marginal(position: int)[source]#: Return univariate marginal distribution of parameter with index ‘position’.

mean()[source]#: Get the mean of the distribution.

pdf(x)[source]#: Calculates the probability density function (PDF) of the distribution at x.

rvs(size: int = 1, random_state: int | None = None)[source]#: Generates random variates from the distribution.

support() → numpy.ndarray[source]#: Return the support as a numpy array of dimensions (2, n_parameters).

distribution_log_x#

properties#

properties_log_x#

class pybop.parameters.multivariate_distributions.MultivariateNonparametric(samples: numpy.ndarray)[source]#

Bases: BaseMultivariateDistribution

Represents a “freeform” distribution, i.e., one that is defined from a random sampling and a kernel density estimate on that sampling.

Parameters:: samples (numpy.ndarray) – The random variates to base the distribution on.

marginal(position: int)[source]#: Return univariate marginal distribution of parameter with index ‘position’.

mean()[source]#: Get the mean of the distribution.

rvs(size: int = 1, random_state: int | None = None)[source]#: Generates random variates from the distribution.

std()[source]#: Get the square root of the covariance matrix.

class pybop.parameters.multivariate_distributions.MultivariateUniform(bounds: numpy.ndarray)[source]#

Bases: BaseMultivariateDistribution

Represents a multivariate uniform distribution.

Parameters:: bounds (numpy.ndarray) – The lower and upper bounds for the uniform distribution as an array with dimensions (2, n_parameters).

_transform(transform: pybop.transformation.base_transformation.Transformation) → pybop.parameters.distributions.BaseDistribution | None[source]#: Get the transformed distribution in the search space.

marginal(position: int)[source]#: Return univariate marginal distribution of parameter with index ‘position’.