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

All examples in this documentation make use of UniformPrior. Examples using GaussianPrior include: