Chimera
An atlas of regular vines on up to 8 nodes
Oswaldo Morales-Nápoles (TU Delft - Hydraulic Structures and Flood Risk)
Mojtaba Rajabi-Bahaabadi (Yazd University)
Gina Alexandra Torres-Alves (TU Delft - Hydraulic Structures and Flood Risk)
Cornelis Marcel Pieter ’t Hart (Tunnel Engineering Consultants, TU Delft - Hydraulic Structures and Flood Risk)
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Abstract
Vine copulas have become the standard tool for modelling complex probabilistic dependence. It has been shown that the number of regular vines grows extremely quickly with the number of nodes. Chimera is the first attempt to map the vast space of regular vines. Software for operating with regular vines is available for R, matlab and Python. However, no dataset containing all regular vines is available. Our atlas of regular vines, Chimera, comprises all 24 4 × 4 matrices representing regular vines on 4 nodes, 480 5 × 5 matrices representing regular vines on 5 nodes, 23,040 6 × 6 matrices representing regular vines on 6 nodes, 2,580,480 7 × 7 matrices representing regular vines on 7 nodes and 660,602,880 8 × 8 matrices representing regular vines on 8 nodes. Regular vines in Chimera are classified according to their tree-equivalence class. We fit all regular vines to synthetic data to demonstrate the potential of Chimera. Chimera provides thus a tool for researchers to navigate this vast space in an orderly fashion.
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