UncertaintyQuantification.jl

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Inputs ​

Index ​

Types ​

UncertaintyQuantification.Parameter Type
julia
Parameter(value::Real, name::Symbol)

Defines a parameter value (scalar), with an input value and a name.

Examples

julia
julia> Parameter(3.14, :π)
Parameter(3.14, :π)
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UncertaintyQuantification.Interval Type
julia
Interval(lb::Real, ub::Real)

Represents a closed numeric interval with a lower bound lb and an upper bound ub.

Interval is a data type primarily used for constructing probability boxes (p-boxes) and other uncertainty representations. It is not intended for direct use in simulations for that, see IntervalVariable.

Fields

  • lb::Real: Lower bound of the interval.

  • ub::Real: Upper bound of the interval.

Examples

julia
julia> Interval(0.10, 0.14)
[0.1, 0.14]
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UncertaintyQuantification.ProbabilityBox Type
julia
ProbabilityBox{T}(parameters::Dict{Symbol, Union{Real, Interval}}, lb::Real, ub::Real)

Represents a (optionally truncated) probability box (p-box) for a univariate distribution T, where parameters may be specified as precise values (Real) or intervals (Interval). The support of the distribution is bounded by lb (lower bound) and ub (upper bound).

To use the ProbabilityBox in an analysis it has to be wrapped in a RandomVariable.

Fields

  • parameters::Dict{Symbol, Union{Real, Interval}}: Dictionary mapping parameter names (as symbols) to their values or intervals.

  • lb::Real: Lower bound of the distribution's support.

  • ub::Real: Upper bound of the distribution's support.

Constructors

  • ProbabilityBox{T}(parameters::Dict{Symbol, Union{Real, Interval}}, lb::Real, ub::Real): Specify all parameters and support bounds explicitly.

  • ProbabilityBox{T}(parameters::Dict{Symbol, Union{Real, Interval}}): Support bounds are inferred from the distribution type T.

  • ProbabilityBox{T}(parameter::Interval): For univariate distributions with a single parameter, construct from a single interval.

For convenience the first two constructors can also be called with a Vector{Pair{Symbol,Union{Real,Interval}}} to automatically create the Dict.

Examples

julia
julia> ProbabilityBox{Normal}(Dict(:μ => Interval(0, 1), :σ => Interval(0.1, 1)), 0.0, Inf)
ProbabilityBox{Normal}(Dict{Symbol, Union{Real, Interval}}(:μ => [0, 1], :σ => [0.1, 1]), 0.0, Inf)

julia> ProbabilityBox{Normal}(Dict(:μ => Interval(0, 1), :σ => Interval(0.1, 1)))
ProbabilityBox{Normal}(Dict{Symbol, Union{Real, Interval}}(:μ => [0, 1], :σ => [0.1, 1]), -Inf, Inf)

julia> ProbabilityBox{Exponential}(Interval(0.1, 0.5))
ProbabilityBox{Exponential}(Dict{Symbol, Union{Real, Interval}}(:θ => [0.1, 0.5]), 0.0, Inf)

julia> ProbabilityBox{Normal}([:μ => Interval(0, 1), :σ => Interval(0.1, 1)])
ProbabilityBox{Normal}(Dict{Symbol, Union{Real, Interval}}(:μ => [0, 1], :σ => [0.1, 1]), -Inf, Inf)
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UncertaintyQuantification.RandomVariable Type
julia
RandomVariable(dist::UnivariateDistribution, name::Symbol)

Defines a random variable, with a univariate distribution from Distributions.jl and a name.

Examples

julia
julia> RandomVariable(Normal(), :x)
RandomVariable{Normal{Float64}}(Normal{Float64}(μ=0.0, σ=1.0), :x)

julia> RandomVariable(Exponential(1), :x)
RandomVariable{Exponential{Float64}}(Exponential{Float64}(θ=1.0), :x)
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UncertaintyQuantification.IntervalVariable Type
julia
IntervalVariable(lb::Real, ub::Real, name::Symbol)

Defines an interval variable with a lower bound lb, upper bound ub, and an identifying name.

IntervalVariable can be passed directly to analyses and simulations. For other uses, such as building probability boxes (p-boxes) from interval parameters, use Interval instead.

Fields

  • lb::Real: Lower bound of the interval.

  • ub::Real: Upper bound of the interval.

  • name::Symbol: Name or identifier for the variable.

Examples

julia
julia> IntervalVariable(0.10, 0.14, :x)
x ∈ [0.1, 0.14]
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UncertaintyQuantification.EmpiricalDistribution Type
julia
EmpiricalDistribution(x::Vector{<:Real}, n::Integer=10000)

Creates an empirical distribution from the data given in `x` using kernel density estimation.
The kernel used is Gaussian and the bandwidth is obtained through the Sheather-Jones method.
The support is inferred from the kde using numerical root finding.
The `cdf` and `quantile` functions are linearly interpolated using `n` data points.
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UncertaintyQuantification.JointDistribution Type
julia
JointDistribution{D<:Union{Copula,MultivariateDistribution}, M<:Union{RandomVariable,Symbol}}(d, m)

Represents a joint probability distribution, either via a copula and a vector of marginal random variables, or a multivariate distribution and a vector of variable names.

Constructors

  • JointDistribution(d::Copula, m::Vector{RandomVariable}):

    • Use a copula d to combine the marginal distributions in m into a joint distribution.

    • The copula's dimension must match the length of m.

    • m must be a vector of RandomVariable.

  • JointDistribution(d::MultivariateDistribution, m::Vector{Symbol}):

    • Use a multivariate distribution d with named components specified by m.

    • The distribution's dimension (number of variables) must match the length of m.

    • m must be a vector of Symbol.

Examples

julia
julia> JointDistribution(GaussianCopula([1.0 0.71; 0.71 1.0]), [RandomVariable(Normal(), :x), RandomVariable(Uniform(), :y)])
JointDistribution{Copula, RandomVariable}(GaussianCopula([1.0 0.71; 0.71 1.0]), RandomVariable[RandomVariable{Normal{Float64}}(Normal{Float64}(μ=0.0, σ=1.0), :x), RandomVariable{Uniform{Float64}}(Uniform{Float64}(a=0.0, b=1.0), :y)])
julia
julia> JointDistribution(MultivariateNormal([1.0 0.71; 0.71 1.0]), [:x, :y])
JointDistribution{MultivariateDistribution, Symbol}(ZeroMeanFullNormal(
dim: 2
μ: Zeros(2)
Σ: [1.0 0.71; 0.71 1.0]
)
, [:x, :y])
source

Functions ​

UncertaintyQuantification.sample Function
julia
sample(rv::RandomVariable, n::Integer=1)

Generates n samples from a random variable. Returns a DataFrame.

Examples

See also: RandomVariable

source
UncertaintyQuantification.sample Function
julia
sample(inputs::Vector{<:UQInput}, n::Integer=1)

Generates n correlated samples from a collection of inputs. Returns a DataFrame

See also: RandomVariable, Parameter

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UncertaintyQuantification.GaussianMixtureModel Function
julia
GaussianMixtureModel(
    data::DataFrame,
    number_components::Integer;
    maximum_iterations::Integer=100,
    tolerance::Number=1e-4,
)

Fits a Gaussian mixture model to the given data using the Expectation-Maximization (EM) algorithm.

Arguments

  • data::DataFrame: The input data as a DataFrame, where each column represents a variable.

  • number_components::Integer: The number of Gaussian components to fit.

  • maximum_iterations::Integer=100: (Optional) The maximum number of EM iterations. Default is 100.

  • tolerance::Number=1e-4: (Optional) The convergence tolerance for the EM algorithm. Default is 1e-4.

Returns

  • JointDistribution: A joint distribution object representing the fitted Gaussian mixture model, with variable names corresponding to the columns of data.

See also: JointDistribution

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