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Weighted (nested) populations

Weighted populations

The UncertainScalarPopulation type allows representation of an uncertain scalar represented by a population of values who will be sampled according to a vector of explicitly provided probabilities. Think of it as an explicit kernel density estimate.

Generic constructor

# UncertainData.UncertainValues.UncertainValue — Method.

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UncertainValue(values::Vector, probs::Union{Vector, AbstractWeights})

Construct a population whose members are given by values and whose sampling probabilities are given by probs. The elements of values can be either numeric or uncertain values of any type.

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Type documentation

# UncertainData.UncertainValues.UncertainScalarPopulation — Type.

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UncertainScalarPopulation(values, probs)
UncertainScalarPopulation(values, probs::Vector{Number})
UncertainScalarPopulation(values, probs::Statsbase.AbstractWeights)

An UncertainScalarPopulation, which consists of some population members (values) and some weights (probs) that indicate the relative importance of the population members (for example during resampling).

Fields

  • values: The members of the population. Can be either numerical values, any type of uncertain value defined in this package (including populations), and Measurement instances from Measurements.jl.
  • probs: The probabilities of sampling each member of the population.

Constructors

  • If values contains only scalar numeric values, then the values field will be of type Vector{Number}.
  • If values contains one or more uncertain values, then the values field will be of type Vector{AbstractUncertainValue}

Example

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# Uncertain population consisting of CertainValues (scalars get promoted to 
# CertainValue), theoretical distributions and KDE distributions
pop1 = UncertainScalarPopulation(
    [3.0, UncertainValue(Normal, 0, 1), UncertainValue(Gamma, 2, 3), 
    UncertainValue(Uniform, rand(1000))], [0.5, 0.5, 0.5, 0.5])

# Uncertain population consisting of scalar values
pop2 = UncertainScalarPopulation([1, 2, 3], rand(3))
pop3 = UncertainScalarPopulation([1, 2, 3], Weights(rand(3)))

# Uncertain population consisting of uncertain populations
pop4 = UncertainScalarPopulation([pop1, pop2], [0.1, 0.5])

# Uncertain population consisting of uncertain populations, a scalar and 
# a normal distribution. Assign random weights.
vals = [pop1, pop2, 2, UncertainValue(Normal, 0.3, 0.014)]
pop5 = UncertainScalarPopulation(vals, Weights(rand(4)))

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