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 (list[dict])

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'.

[{'type': 'mvn', 'parameters': ['x1','x2'], 'mean': [0.0,0.0], 'covariance': [[1.0,0.4],
 [0.4,2.0]]},
 {'type': 'uniform', 'parameter': 'x2', 'domain': [-2.0,2.0]}]

Each element of the list must be a dict. The dict 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 (list[dict])

List of constraints on parameters.

Default: []

Example

Constrain probability distribution to values \(\sqrt{x_1^2 + x_2^2} \leq 3\).

[{'name': 'x1_constraint', 'expression': 'sqrt(x1^2 + x2^2) <= 3'}]

Each element of the list must be a dict. In the following, the list elements are described:

Inequality constraint on design end environment parameters.

See constraint configuration for details.