global_evidence

Evidence theory with evidence measures computed with global optimization methods

Topics

epistemic_uncertainty_quantification_methods, evidence_theory

Specification

• Alias: nond_global_evidence

• Arguments: None

Child Keywords:

Required/Optional	Description of Group	Dakota Keyword	Dakota Keyword Description
Optional		samples	Number of samples for sampling-based methods
Optional		seed	Seed of the random number generator
Optional (Choose One)	Solution Approach	sbgo	Use the surrogate based optimization method
		ego	Use the Efficient Global Optimization method
		ea	Use an evolutionary algorithm
		lhs	Uses Latin Hypercube Sampling (LHS) to sample variables
Optional		response_levels	Values at which to estimate desired statistics for each response
Optional		probability_levels	Specify probability levels at which to estimate the corresponding response value
Optional		gen_reliability_levels	Specify generalized relability levels at which to estimate the corresponding response value
Optional		distribution	Selection of cumulative or complementary cumulative functions
Optional		rng	Selection of a random number generator
Optional		model_pointer	Identifier for model block to be used by a method

Description

global_evidence allows the user to specify several global approaches for calculating the belief and plausibility functions:

• lhs - note: this takes the minimum and maximum of the samples as the bounds per “interval cell combination.”

• ego - uses Efficient Global Optimization which is based on an adaptive Gaussian process surrogate.

• sbo - uses a Gaussian process surrogate (non-adaptive) within an optimization process.

• ea - uses an evolutionary algorithm. This can be expensive as the ea will be run for each interval cell combination.

Note that to calculate the plausibility and belief cumulative distribution functions, one has to look at all combinations of intervals for the uncertain variables. In terms of implementation, if one is using LHS sampling as outlined above, this method creates a large sample over the response surface, then examines each cell to determine the minimum and maximum sample values within each cell. To do this, one needs to set the number of samples relatively high: the default is 10,000 and we recommend at least that number. If the model you are running is a simulation that is computationally quite expensive, we recommend that you set up a surrogate model within the Dakota input file so that global_evidence performs its sampling and calculations on the surrogate and not on the original model. If one uses optimization methods instead to find the minimum and maximum sample values within each cell, this can also be computationally expensive.

Additional Resources

See the topic page Evidence Theory for important background information and usage notes.

Refer to Variable Support for information on supported variable types.

Theory

The basic idea is that one specifies an “evidence structure” on uncertain inputs and propagates that to obtain belief and plausibility functions on the response functions. The inputs are defined by sets of intervals and Basic Probability Assignments (BPAs). Evidence propagation is computationally expensive, since the minimum and maximum function value must be calculated for each “interval cell combination.” These bounds are aggregated into belief and plausibility.