pybop.parameters.distributions#

Classes#

`BaseDistribution`	A base class for defining parameter distributions.
`Distribution`	A base class for distributions based on a scipy.stats distribution.
`Exponential`	Represents an exponential distribution with a specified scale parameter.
`Gaussian`	Represents a Gaussian (normal) distribution with a given mean and standard deviation.
`JointDistribution`	Represents a joint distribution composed of multiple distributions.
`LogNormal`	Represents a log-normal distribution corresponding to a Gaussian distribution for
`LogUniform`	Represents a log-uniform distribution over a specified interval.
`Unbounded`	Represents an unbounded distribution with either zero or one finite bound.
`Uniform`	Represents a uniform distribution over a specified interval.

Module Contents#

class pybop.parameters.distributions.BaseDistribution(properties: dict | None = None, n_parameters: int = 1)[source]#

A base class for defining parameter distributions.

This class provides a foundation for implementing various distributions. It includes methods for calculating the probability density function (PDF), log probability density function (log PDF), and generating random variates from the distribution.

properties#

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

Type:: dict

n_parameters#

The number of dimensions (default: 1).

Type:: int

__repr__() → str[source]#

_dlogpdf_dx(x)[source]#

Evaluates the first derivative of the log distribution at x.

Overwrite this function in a subclass to improve upon this generic finite difference approximation.

Parameters:: x (float) – The point(s) at which to evaluate the first derivative.
Returns:: The value(s) of the first derivative at x.
Return type:: float

_transform(transform: pybop.transformation.base_transformation.Transformation)[source]#: Get the transformed distribution in the search space.

abstractmethod 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

get_transformed_distribution(transform: pybop.transformation.base_transformation.Transformation)[source]#: Get the transformed distribution in the search space.

abstractmethod icdf(q)[source]#

Calculates the inverse cumulative distribution function (CDF) of the distribution at q.

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

abstractmethod logpdf(x)[source]#

Calculates the logarithm of the probability density function of the distribution at x.

Parameters:: x (float) – The point(s) at which to evaluate the log pdf.
Returns:: The logarithm of the probability density function value at x.
Return type:: float

logpdfS1(x)[source]#

Evaluates the first derivative of the distribution at x.

Parameters:: x (float) – The point(s) at which to evaluate the first derivative.
Returns:: The value(s) of the first derivative at x.
Return type:: float

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

abstractmethod pdf(x)[source]#

Calculates the probability density function (PDF) of the distribution at x.

Parameters:: x (float) – The point(s) at which to evaluate the pdf.
Returns:: The probability density function value at x.
Return type:: float

abstractmethod rvs(size: int = 1, random_state: int | None = None)[source]#

Generates random variates from the distribution.

Parameters:

size (int) – The number of random variates to generate.
random_state (int, optional) – The random state seed for reproducibility. Default is None.

Returns:

An array of random variates from the distribution.

Return type:

array_like

Raises:

ValueError – If the size parameter is negative.

abstractmethod std() → float[source]#: Get the standard deviation of the distribution.

support() → tuple[float][source]#: Returns the support of the distribution, to be overwritten by child classes.

verify(x) → numpy.ndarray[source]#: Verifies that the input is a numpy array and converts it if necessary.

_n_parameters = 1#

property name#

properties#

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

Bases: BaseDistribution

A base class for distributions based on a scipy.stats distribution.

This class provides a foundation for implementing various distributions. It includes methods for calculating the probability density function (PDF), log probability density function (log PDF), and generating random variates from the distribution.

Additional Attributes#

distributionscipy.stats.distributions.rv_frozen: The underlying continuous random variable distribution.

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

icdf(q)[source]#

Calculates the inverse cumulative distribution function (CDF) of the distribution at q.

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

logpdf(x)[source]#

Calculates the logarithm of the probability density function of the distribution at x.

Parameters:: x (float) – The point(s) at which to evaluate the log pdf.
Returns:: The logarithm of the probability density function value at x.
Return type:: float

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

pdf(x)[source]#

Calculates the probability density function (PDF) of the distribution at x.

Parameters:: x (float) – The point(s) at which to evaluate the pdf.
Returns:: The probability density function value at x.
Return type:: float

rvs(size: int = 1, random_state: int | None = None)[source]#

Generates random variates from the distribution.

Parameters:

size (int) – The number of random variates to generate.
random_state (int, optional) – The random state seed for reproducibility. Default is None.

Returns:

An array of random variates from the distribution.

Return type:

array_like

Raises:

ValueError – If the size parameter is negative.

std() → float[source]#: Get the standard deviation of the distribution.

support() → tuple[float][source]#: Returns the support of the distribution, to be overwritten by child classes.

distribution#

class pybop.parameters.distributions.Exponential(scale: float, loc: float = 0)[source]#

Bases: Distribution

Represents an exponential distribution with a specified scale parameter.

Parameters:: scale (float) – The scale parameter (lambda) of the exponential distribution.

_dlogpdf_dx(x)[source]#: Evaluates the first derivative of the log exponential distribution at x.

class pybop.parameters.distributions.Gaussian(mean: float, sigma: float, truncated_at: list[float] | None = None)[source]#

Bases: Distribution

Represents a Gaussian (normal) distribution with a given mean and standard deviation.

Parameters:

mean (float) – The mean (mu) of the Gaussian distribution.
sigma (float) – The standard deviation (sigma) of the Gaussian distribution.
truncated_at (list[float], optional) – If provided, the distribution becomes a truncated normal distribution.

_dlogpdf_dx(x)[source]#: Evaluates the first derivative of the log Gaussian distribution at x.

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

class pybop.parameters.distributions.JointDistribution(*distributions: BaseDistribution)[source]#

Bases: BaseDistribution

Represents a joint distribution composed of multiple distributions.

Parameters:: distributions (BaseDistribution) – One or more distributions to combine into a joint distribution.

__repr__() → str[source]#

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

cov()[source]#

logpdf(x: float | numpy.ndarray) → float[source]#

Evaluates the log of the joint distribution at a given point.

Parameters:: x (float | np.ndarray) – The point(s) at which to evaluate the distribution. The length of x should match the total number of parameters in the joint distribution.
Returns:: The joint log-probability density of the distribution at x.
Return type:: float

logpdfS1(x: float | numpy.ndarray) → tuple[float, numpy.ndarray][source]#

Evaluates the first derivative of the log of the joint distribution at a given point.

Parameters:: x (float | np.ndarray) – The point(s) at which to evaluate the first derivative. The length of x should match the total number of parameters in the joint distribution.
Returns:: A tuple containing the log-probability density and its first derivative at x.
Return type:: Tuple[float, np.ndarray]

marginal(position: int)[source]#

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

rvs(size: int = 1, random_state: int | None = None)[source]#: Sample each distribution individually and then compile.

std()[source]#: Get the standard deviation of the distribution.

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

_distributions_list: list[BaseDistribution] = []#

_n_parameters = 0#

class pybop.parameters.distributions.LogNormal(mean_log_x: float, sigma: float)[source]#

Bases: Distribution

Represents a log-normal distribution corresponding to a Gaussian distribution for log(x) with a given mean and standard deviation.

Parameters:

mean_log_x (float) – The mean (mu) of the Gaussian distribution of log(x).
sigma (float) – The standard deviation (sigma) of the Gaussian distribution of log(x).

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

class pybop.parameters.distributions.LogUniform(lower: float, upper: float)[source]#

Bases: Distribution

Represents a log-uniform distribution over a specified interval.

Parameters:

lower (float) – The lower bound of the distribution.
upper (float) – The upper bound of the distribution.

__repr__() → str[source]#

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

class pybop.parameters.distributions.Unbounded(initial_value: float = 1.0, lower: float = -np.inf, upper: float = np.inf)[source]#

Bases: BaseDistribution

Represents an unbounded distribution with either zero or one finite bound.

Parameters:

lower (float) – The lower bound of the distribution.
upper (float) – The upper bound of the distribution.

__repr__() → str[source]#

_dlogpdf_dx(x)[source]#: Evaluates the first derivative of the log uniform distribution at x.

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

mean() → float[source]#: Returns an estimate for the mean of the distribution.

std() → float[source]#: Returns an estimate for the standard deivation of the distribution.

support() → tuple[float][source]#: Returns the support of the distribution, to be overwritten by child classes.

initial_value = None#

lower#

upper#

class pybop.parameters.distributions.Uniform(lower: float, upper: float)[source]#

Bases: Distribution

Represents a uniform distribution over a specified interval.

Parameters:

lower (float) – The lower bound of the distribution.
upper (float) – The upper bound of the distribution.

__repr__() → str[source]#

_dlogpdf_dx(x)[source]#: Evaluates the first derivative of the log uniform distribution at x.

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

mean() → float[source]#: Returns the mean of the distribution.