deerlab.UQResult

class UQResult(uqtype, data=None, covmat=None, lb=None, ub=None, threshold=None, profiles=None, noiselvl=None)

Represents the uncertainty quantification of fit results.

This class provides methods for performing uncertainty analysis on fit results. The uncertainty analysis can be performed using moment-based, bootstrapped, or likelihood profile methods. The type of uncertainty analysis is specified when initializing the object.

Attributes:

typestring

Type of uncertainty analysis performed. Possible values are:

• 'moment' - Moment-based uncertainty analysis

• 'bootstrap' - Bootstrapped uncertainty analysis

• 'profile' - Likelihood profile uncertainty analysis

• 'void' - Empty uncertainty analysis

meanndarray

Mean values of the uncertainty distribution of the parameters.

medianndarray

Median values of the uncertainty distribution of the parameters.

stdndarray

Standard deviations of the uncertainty distribution of the parameters.

covmatndarray

Covariance matrix

nparamint scalar

Number of parameters in the analysis.

samplesndarray

Bootstrap samples of the parameters. Only available for type='bootstrap'.

profilendarray

Likelihood profile of the parameters. Only available for type='profile'.

thresholdscalar

Treshold value used for the profile method. Only available for type='profile'.

Methods table

__init__(uqtype[, data, covmat, lb, ub, ...])	Initializes the UQResult object.
ci(coverage)	Compute the confidence intervals for the parameters.
join(*args)	Combine multiple uncertainty quantification instances.
pardist([n])	Generate the uncertainty distribution of the n-th parameter
percentile(p)	Compute the p-th percentiles of the parameters uncertainty distributions
propagate(model[, lb, ub, samples])	Uncertainty propagation.

Methods

UQResult.__init__(uqtype, data=None, covmat=None, lb=None, ub=None, threshold=None, profiles=None, noiselvl=None)

Initializes the UQResult object.

Parameters:

uqtypestr

Type of uncertainty analysis to perform. Possible values are: 'moment', 'bootstrap', 'profile', 'void'.

datandarray

Data to be used for the uncertainty analysis. The format of this parameter depends on the value of uqtype:

• If uqtype='moment', data should be an array of parameter estimates.

• If uqtype='bootstrap', data should be a 2-dimensional array of bootstrap samples, where each row corresponds to a sample and each column corresponds to a parameter.

• If uqtype='profile', data should be an array of parameter estimates.

• If uqtype='void', data should not be provided.

covmatndarray

Covariance matrix of the parameter estimates. Only applicable if uqtype='moment'.

lbndarray

Lower bounds of the parameter estimates. Only applicable if uqtype='moment'.

ubndarray

Upper bounds of the parameter estimates. Only applicable if uqtype='moment'.

thresholdfloat

Threshold value used for the likelihood profile method. Only applicable if uqtype='profile'.

profileslist

List of likelihood profiles for each parameter. Each element of the list should be a tuple of arrays (x, y), where x represents the values of the parameter and y represents the corresponding likelihoods. Only applicable if uqtype='profile'.

noiselvlfloat

Noise level used for the likelihood profile method. Only applicable if uqtype='profile'.

UQResult.ci(coverage)

Compute the confidence intervals for the parameters.

This method computes confidence intervals for the parameters of the fitted distribution, based on the method used to compute the parameter estimates (moment estimation, bootstrapping, or likelihood profile).

Parameters:

coveragefloat scalar

Coverage (confidence level) of the confidence intervals (a value between 0-100)

Returns:

cindarray

A 2D array containing the lower and upper confidence intervals for the parameters. The first column of the array holds the lower confidence intervals, and the second column holds the upper confidence intervals.

• ci[:,0] - Lower confidence intervals

• ci[:,1] - Upper confidence intervals

The array has shape (nparam, 2), where nparam is the number of fitted parameters.

Raises:

ValueError

If the coverage argument is outside the range 0-100.

Notes

The method used to compute the confidence intervals depends on the method used to compute the parameter estimates. If the parameter estimates were computed using moment estimation, the confidence intervals are computed based on the estimated standard errors of the parameters. If the parameter estimates were computed using bootstrapping, the confidence intervals are computed based on the empirical distribution of the bootstrapped samples. If the parameter estimates were computed using likelihood profile, the confidence intervals are computed by finding the parameter values at the edges of the likelihood profile that correspond to the specified coverage.

Examples

Compute 95% confidence intervals for the fitted parameters:

ci = param.ci(95)

UQResult.join(*args)

Combine multiple uncertainty quantification instances.

This method concatenates the parameter vectors of the object calling the method with the parameter vectors of any number of other uncertainty quantification objects.

Parameters:

uqany number of deerlab.UQResult

Uncertainty quantification objects with N1,N2,...,Nn parameters to be joined to the object calling the method with M parameters.

Returns:

uq_joineddeerlab.UQResult

Joined uncertainty quantification object with a total of M + N1 + N2 + ... + Nn parameters. The parameter vectors are concatenated on the order they are passed.

Raises:

TypeError

If any of the input objects is not a deerlab.UQResult instance or if the types of the input objects do not match.

TypeError

If an attempt is made to join an instance of deerlab.UQResult with type 'void'.

UQResult.pardist(n=0)

Generate the uncertainty distribution of the n-th parameter

This method generates the probability density function of the uncertainty of the n-th parameter of the model. The distribution is evaluated at a range of values where the parameter is most likely to be. The range is determined based on the type of uncertainty quantification method used.

Parameters:

nint scalar

Index of the parameter

Returns:

axndarray

Parameter values at which the distribution is evaluated

pdfndarray

Probability density function of the parameter uncertainty.

UQResult.percentile(p)

Compute the p-th percentiles of the parameters uncertainty distributions

Parameters:

pfloat scalar

Percentile (a value between 0-100)

Returns:

prctilesndarray

Percentile values of all parameters

Raises:

ValueError

If is not a number between 0 and 100.

UQResult.propagate(model, lb=None, ub=None, samples=None)

Uncertainty propagation.

The method performs uncertainty propagation on the model by applying the uncertainty analysis of the input parameters to the model. The output is a new uncertainty quantification analysis for the model outputs. The method returns a new UQResult object containing the uncertainty information of the model outputs. If the input type is 'moment', the returned object will be of type 'moment'. Otherwise, if the type is 'bootstrap', the returned object will be of type 'bootstrap'.

Parameters:

modelcallable

A callable function that takes an array of parameters as input and returns a model output.

lbmndarray

Lower bounds of the values returned by model, by default assumed unconstrained.

ubmndarray

Upper bounds of the values returned by model, by default assumed unconstrained.

samplesint, optional

Number of samples to use when propagating uncertainty. If not provided, default value is 1000.

Returns:

modeluqdeerlab.UQResult

New uncertainty quantification analysis for the outputs of model.

Inherited Methods