Prior

This module facilitates the definition of prior probabilities for model parameters within Bayesian inversion problems. It offers out-of-the-box support for free parameters described by uniform, Gaussian, and Laplace probability distributions, along with high-level functionalities for custom prior definitions. When used in conjunction with a discretized spatial domain (see Discretization), these prior distributions can also be tailored to vary as a function of position within the domain.

graph TD; Prior-->UniformPrior; Prior-->GaussianPrior; Prior-->LaplacePrior; Prior-->CustomPrior;

bayesbay.prior.Prior	Base class for defining the prior probability associated with a free parameter in the inference problem
bayesbay.prior.UniformPrior	Class for defining the prior probability of a free parameter distributed according to a uniform probability distribution
bayesbay.prior.GaussianPrior	Class for defining the prior probability of a free parameter distributed according to a Gaussian distribution, \(\mathcal{N}(\mu, \sigma)\), where \(\mu\) denotes the mean and \(\sigma\) the standard deviation
bayesbay.prior.LaplacePrior	Class for defining the prior probability of a free parameter distributed according to a Laplace distribution, with probability density function \(p(v) = \frac{1}{2b} \exp \Big \lbrace -\frac{|v - \mu|}{b} \Big \rbrace\), where \(\mu\) denotes the mean and \(b\) the scale.
bayesbay.prior.CustomPrior	Class enabling the definition of an arbitrary prior for a free parameter