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Syntax overview

This is an overview over the low-level functionality in the CausalityTools.jl package and its subpackages.

Discretization

• RectangularBinning. Instructions for using rectangular partitions.
• TriangulationBinning. Instructions for using triangulated partitions.

Transfer operator estimation

• transferoperator(points, binning_scheme::RectangularBinning)
• transferoperator(pts, ϵ::TriangulationBinning, simplex_intersection_type::ExactIntersection)
• transferoperator(pts, ϵ::TriangulationBinning, simplex_intersection_type::ApproximateIntersection)

Invariant measure estimation

• invariantmeasure(points, binning_scheme::RectangularBinning)
• invariantmeasure(pts, ϵ::TriangulationBinning, simplex_intersection_type::ExactIntersection)
• invariantmeasure(pts, ϵ::TriangulationBinning, simplex_intersection_type::ApproximateIntersection)

Transfer entropy estimation

There are two estimators that compute transfer entropy by rectangular partitions.

• transferentropy(pts, vars::TEVars, ϵ::RectangularBinning, estimator::VisitationFrequency; b = 2)
• transferentropy(pts, vars::TEVars, ϵ::RectangularBinning, estimator::TransferOperatorGrid; b = 2)

To compute transfer entropy over triangulated partitions, the invariant measure over the triangulation must be precomputed, using either

• invariantmeasure(pts, ϵ::TriangulationBinning, simplex_intersection_type::ExactIntersection) or
• invariantmeasure(pts, ϵ::TriangulationBinning, simplex_intersection_type::ApproximateIntersection)).

Then we can superimpose rectangular grid over the triangulation and compute the transfer entropy.

• transferentropy(μ::AbstractTriangulationInvariantMeasure, vars::TEVars, binning_scheme::RectangularBinning; estimator = VisitationFrequency(), n::Int = 10000, b = 2).

Cross mappings

• crossmap.
• convergentcrossmap.

Joint distance distribution

• joint_distance_distribution