Space distribution

Probability distribution of design and environment parameters defined by distribution functions and constraints. The definition of the parameter distribution can have several effects:

In a call to the method get_statistics of the driver interface the value of interest is averaged over samples drawn from the space distribution.
In a call to the method run_mcmc of the driver interface the space distribution acts as a prior distribution.
In a call to the method get_sobol_indices of the driver interface the space distribution acts as a weighting factor for determining expectation values.
In an ActiveLearning driver, one can access the value of the log-probability density (up to an additive constant) by the name 'log_prob' in any expression, e.g. in Expression variable, Linear combination variable.

include_study_constraints (bool)

If true, the constraints defined when creating the study are included in the distribution.

Default: false

distributions (cell{struct})

List of distributions for all or a subset of design and environment parameters. If not specified, the distributions are uniform over the specified domains.

Default: {}
Example

A multivariate normal distribution over two parameters 'x1', 'x2' and a uniform distribution over a third parameter 'x3'.
{struct('type', "mvn", 'parameters', {"x1","x2"}, 'mean', {0.0,0.0}, 'covariance', {{1.0,0.4},...
 {0.4,2.0}}),...
 struct('type', "uniform", 'parameter', "x2", 'domain', {-2.0,2.0})}
Each element of the list must be a struct. The struct entry type specifies the type of the element. The remaining entries specify its properties. In the following, all possible list element types are described:

Uniform distribution (type "uniform"): Uniform distribution in a specific domain.

See uniform configuration for details.

Normal distribution (type "normal"): Normal distribution of specified mean and standard deviation.

See normal configuration for details.

Gamma distribution (type "gamma"): Gamma distribution defined by rate and shape parameter.

See gamma configuration for details.

Distribution over discrete values (type "discrete"): Distribution over discrete values of a discrete or categorial parameter.

See discrete configuration for details.

Multivariate normal distribution (type "mvn"): Multivariate normal defined my mean vector and covariance matrix.

See mvn configuration for details.

constraints (cell{struct})

List of constraints on parameters.

Default: {}
Example

Constrain probability distribution to values \(\sqrt{x_1^2 + x_2^2} \leq 3\).
{struct('name', "x1_constraint", 'expression', "sqrt(x1^2 + x2^2) <= 3")}
Each element of the list must be a struct. In the following, the list elements are described:

Inequality constraint on design end environment parameters.

See constraint configuration for details.