.. _`topic-variable_support`:
Variable Support
================
Different nondeterministic methods have differing support for
uncertain variable distributions. :numref:`table:variable_support_part_1`,
:numref:`table:variable_support_part_2`, and :numref:`table:variable_support_part_3`
summarize the uncertain variables that are available for use by the different methods, where a "-"
indicates that the distribution is not supported by the method, a "U"
means the uncertain input variables of this type must be uncorrelated,
a "C" denotes that correlations are supported involving uncertain
input variables of this type, and an "A" means the appropriate
variables must be specified as active in the variables
specification block. For example, if one wants to support
sampling or a stochastic expansion method over both
continuous uncertain and continuous state variables, the
specification :dakkw:`active all <variables-active-all>` must be listed in the variables
specification block.
Additional notes include:
- we have four variants for stochastic expansions (SE), listed as
Wiener, Askey, Extended, and Piecewise which draw from different
sets of basis polynomials. The term stochastic expansion indicates
polynomial chaos and stochastic collocation collectively, although
the Piecewise option is only currently supported for stochastic
collocation. Refer to :dakkw:`method-polynomial_chaos` and
:dakkw:`method-stoch_collocation` for additional information on these three options.
- methods supporting the epistemic interval distributions have differing
approaches:
- :dakkw:`method-sampling` and :dakkw:`global_interval_est lhs <method-global_interval_est-lhs>`
model the interval basic probability assignments (BPAs) as continuous histogram
bin distributions for purposes of generating samples;
- :dakkw:`method-local_interval_est` and :dakkw:`global_interval_est ego <method-global_interval_est-ego>`
ignore the BPA details and models these variables as simple bounded regions defined by the cell extremes;
- and :dakkw:`method-local_evidence` and :dakkw:`method-global_evidence` model the interval
specifications as true BPAs.
.. table:: Part I: Continuous Aleatory Types
:name: table:variable_support_part_1
=========================== =========== ==================== ===================== ============ =========== ============== =============== ================= ================== ================= =================
Distribution Type Sampling Local Reliability Global Reliability Wiener SE Askey SE Extended SE Piecewise SE Local Interval Global Interval Local Evidence Global Evidence
=========================== =========== ==================== ===================== ============ =========== ============== =============== ================= ================== ================= =================
Normal C C C C C C \- \- \- \- \-
Bounded Normal C U U U U U U \- \- \- \-
Lognormal C C C C C U \- \- \- \- \-
Bounded Lognormal C U U U U U U \- \- \- \-
Uniform C C C C U U U \- \- \- \-
Loguniform C U U U U U U \- \- \- \-
Triangular C U U U U U U \- \- \- \-
Exponential C C C C U U \- \- \- \- \-
Beta C U U U U U U \- \- \- \-
Gamma C C C C U U \- \- \- \- \-
Gumbel C C C C C U \- \- \- \- \-
Frechet C C C C C U \- \- \- \- \-
Weibull C C C C C U \- \- \- \- \-
Continuous Histogram Bin C U U U U U U \- \- \- \-
=========================== =========== ==================== ===================== ============ =========== ============== =============== ================= ================== ================= =================
.. table:: Part II: Discrete Aleatory Types
:name: table:variable_support_part_2
=========================== =========== ==================== ===================== ============ =========== ============== =============== ================= ================== ================= =================
Distribution Type Sampling Local Reliability Global Reliability Wiener SE Askey SE Extended SE Piecewise SE Local Interval Global Interval Local Evidence Global Evidence
=========================== =========== ==================== ===================== ============ =========== ============== =============== ================= ================== ================= =================
Poisson C \- \- \- \- \- \- \- \- \- \-
Binomial C \- \- \- \- \- \- \- \- \- \-
Negative Binomial C \- \- \- \- \- \- \- \- \- \-
Geometric C \- \- \- \- \- \- \- \- \- \-
Hypergeometric C \- \- \- \- \- \- \- \- \- \-
Discrete Histogram Point C \- \- \- \- \- \- \- \- \- \-
=========================== =========== ==================== ===================== ============ =========== ============== =============== ================= ================== ================= =================
.. table:: Part III: Epistemic, Design, and State Types
:name: table:variable_support_part_3
=========================================== =========== ==================== ===================== ============ =========== ============== =============== ================= ================== ================= =================
Distribution Type Sampling Local Reliability Global Reliability Wiener SE Askey SE Extended SE Piecewise SE Local Interval Global Interval Local Evidence Global Evidence
=========================================== =========== ==================== ===================== ============ =========== ============== =============== ================= ================== ================= =================
Interval U \- U,A U,A U,A U,A U,A U U U U
Continuous Design U,A \- U,A U,A U,A U,A U,A \- \- \- \-
Discrete Design Range, Int Set, Real Set U,A \- \- \- \- \- \- \- \- \- \-
Continuous State U,A \- U,A U,A U,A U,A U,A \- \- \- \-
Discrete State Range, Int Set, Real Set U,A \- \- \- \- \- \- \- \- \- \-
=========================================== =========== ==================== ===================== ============ =========== ============== =============== ================= ================== ================= =================