NonnegativeGMRF#

class cuqi.implicitprior.NonnegativeGMRF(mean=None, prec=None, bc_type='zero', order=1, **kwargs)#

Implicit Nonnegative GMRF (Gaussian Markov Random Field).

Defines a so-called implicit prior based on a GMRF distribution with implicit nonnegativity constraints.

Can be used as a prior in a posterior which can be sampled with the RegularizedLinearRTO sampler.

Alias for RegularizedGMRF with only nonnegativity constraints.

For more details on implicit regularized Gaussian see the following paper:

[1] Everink, Jasper M., Yiqiu Dong, and Martin S. Andersen. “Sparse Bayesian inference with regularized Gaussian distributions.” Inverse Problems 39.11 (2023): 115004.

Parameters:

mean – See GMRF for details.
prec – See GMRF for details.
bc_type – See GMRF for details.
order – See GMRF for details.

__init__(mean=None, prec=None, bc_type='zero', order=1, **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__`([mean, prec, bc_type, order])	Initialize the core properties of the distribution.
`constraint_options`()
`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.
`regularization_options`()
`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.
`cov`
`dim`	Return the dimension of the distribution based on the geometry.
`gaussian`
`geometry`	Return the geometry of the distribution.
`is_cond`	Returns True if instance (self) is a conditional distribution.
`mean`
`name`	Name of the random variable associated with the density.
`prec`
`preset`
`proximal`
`sqrtcov`
`sqrtprec`