CMRF

class cuqi.distribution.CMRF(location=None, scale=None, bc_type='zero', **kwargs)

Cauchy distribution on the difference between neighboring nodes.

For 1D the Cauchy difference distribution assumes that

\[x_i-x_{i-1} \sim \mathrm{Cauchy}(0, \gamma),\]

where \(\gamma\) is the scale parameter.

For 2D the differences are defined in both horizontal and vertical directions.

It is possible to define boundary conditions using the bc_type parameter.

The location parameter is a shift of the \(\mathbf{x}\).

Parameters:

• location (scalar or ndarray) – The location parameter of the distribution.

• scale (scalar) – The scale parameter of the distribution.

• bc_type (string) – The boundary conditions of the difference operator.

Example

import cuqi
import numpy as np
prior = cuqi.distribution.CMRF(location=np.zeros(128), scale=0.1)

__init__(location=None, scale=None, bc_type='zero', **kwargs)

Initialize the core properties of the distribution.

Parameters:

• name (str, default None) – Name of distribution.

• geometry (Geometry, default _DefaultGeometry (or None)) – Geometry of distribution.

• is_symmetric (bool, default None) – Indicator if distribution is symmetric.

Methods

__init__([location, scale, bc_type])	Initialize the core properties of the distribution.
disable_FD()	Disable finite difference approximation for logd gradient.
enable_FD([epsilon])	Enable finite difference approximation for logd gradient.
get_conditioning_variables()	Return the conditioning variables of this distribution (if any).
get_mutable_variables()	Return any public variable that is mutable (attribute or property) except those in the ignore_vars list
get_parameter_names()	Returns the names of the parameters that the density can be evaluated at or conditioned on.
gradient(*args, **kwargs)	Returns the gradient of the log density at x.
logd(*args, **kwargs)	Evaluate the un-normalized log density function of the distribution.
logpdf(x)	Evaluate the log probability density function of the distribution.
pdf(x)	Evaluate the log probability density function of the distribution.
sample([N])	Sample from the distribution.
to_likelihood(data)	Convert conditional distribution to a likelihood function given observed data

Attributes

FD_enabled	Returns True if finite difference approximation of the logd gradient is enabled.
FD_epsilon	Spacing for the finite difference approximation of the logd gradient.
dim	Return the dimension of the distribution based on the geometry.
geometry	Return the geometry of the distribution.
is_cond	Returns True if instance (self) is a conditional distribution.
location
name	Name of the random variable associated with the density.