bayesvalidrox.bayes_inference.discrepancy.Discrepancy¶
- class bayesvalidrox.bayes_inference.discrepancy.Discrepancy(InputDisc='', disc_type='Gaussian', parameters=None)¶
Bases:
objectDiscrepancy class for Bayesian inference method. We define the reference or reality to be equal to what we can model and a descripancy term ( epsilon ). We consider the followin format:
$$textbf{y}_{text{reality}} = mathcal{M}(theta) + epsilon,$$
where ( epsilon in R^{N_{out}} ) represents the the effects of measurement error and model inaccuracy. For simplicity, it can be defined as an additive Gaussian disrepancy with zeromean and given covariance matrix ( Sigma ):
$$epsilon sim mathcal{N}(epsilon|0, Sigma). $$
In the context of model inversion or calibration, an observation point ( textbf{y}_i in mathcal{y} ) is a realization of a Gaussian distribution with mean value of (mathcal{M}(theta) ) and covariance matrix of ( Sigma ).
- $$ p(textbf{y}|theta) = mathcal{N}(textbf{y}|mathcal{M}
(theta))$$
The following options are available:
Option A: With known redidual covariance matrix (Sigma) for
independent measurements.
Option B: With unknown redidual covariance matrix (Sigma),
paramethrized as (Sigma(theta_{epsilon})=sigma^2 textbf{I}_ {N_{out}}) with unknown residual variances (sigma^2). This term will be jointly infered with the uncertain input parameters. For the inversion, you need to define a prior marginal via Input class. Note that (sigma^2) is only a single scalar multiplier for the diagonal entries of the covariance matrix (Sigma).
Attributes¶
- InputDiscobj
Input object. When the (sigma^2) is expected to be inferred jointly with the parameters (Option B).If multiple output groups are defined by Model.Output.names, each model output needs to have. a prior marginal using the Input class. The default is ‘’.
- disc_typestr
Type of the noise definition. ‘Gaussian’ is only supported so far.
- parametersdict or pandas.DataFrame
Known residual variance (sigma^2), i.e. diagonal entry of the covariance matrix of the multivariate normal likelihood in case of Option A.
- __init__(InputDisc='', disc_type='Gaussian', parameters=None)¶
Methods
__init__([InputDisc, disc_type, parameters])get_sample(n_samples)Generate samples for the (sigma^2), i.e. the diagonal entries of the variance-covariance matrix in the multivariate normal distribution.