-
Notifications
You must be signed in to change notification settings - Fork 10
Commit
This commit does not belong to any branch on this repository, and may belong to a fork outside of the repository.
- Loading branch information
Showing
2 changed files
with
18 additions
and
2 deletions.
There are no files selected for viewing
This file contains bidirectional Unicode text that may be interpreted or compiled differently than what appears below. To review, open the file in an editor that reveals hidden Unicode characters.
Learn more about bidirectional Unicode characters
This file contains bidirectional Unicode text that may be interpreted or compiled differently than what appears below. To review, open the file in an editor that reveals hidden Unicode characters.
Learn more about bidirectional Unicode characters
Original file line number | Diff line number | Diff line change |
---|---|---|
@@ -1,5 +1,20 @@ | ||
```@meta | ||
CurrentModule = Copulas | ||
``` | ||
|
||
One more noticeable class of copulas are the Vines copulas. These distributions use a graph of conditional distributions to encode the distribution of the random vector. To define such a model, working with conditional densities, and given any ordered partition $\bm i_1,...\bm i_p$ of $1,...d$, we write: | ||
# Vines Copulas | ||
|
||
!!! todo "Not implemented yet!" | ||
Do not hesitate to come talk on [our GitHub](https://github.com/lrnv/Copulas.jl) ! | ||
|
||
One more noticeable class of copulas are the Vines copulas. These distributions use a graph of conditional distributions to encode the distribution of the random vector. To define such a model, working with conditional densities, and given any ordered partition $\bm i_1,...\bm i_p$ of $1,...d$, we write: | ||
|
||
$$f(\bm x) = f(x_{\bm i_1}) \prod\limits_{j=1}^{p-1} f(x_{\bm i_{j+1}} | x_{\bm i_j}).$$ | ||
|
||
Of course, the choice of the partition, of its order, and of the conditional models is left to the practitioner. The goal when dealing with such dependency graphs is to tailor the graph to reduce the error of approximation, which can be a tricky task. There exists simplifying assumptions that help with this matter, and we refer to ~\cite{durante2017a,nagler2016,nagler2018,czado2013,czado2019,graler2014} for a deep dive into the vine theory, along with some nice results and extensions. | ||
Of course, the choice of the partition, of its order, and of the conditional models is left to the practitioner. The goal when dealing with such dependency graphs is to tailor the graph to reduce the error of approximation, which can be a tricky task. There exists simplifying assumptions that help with this matter, and we refer to [durante2017a,nagler2016,nagler2018,czado2013,czado2019,graler2014](@cite) for a deep dive into the vine theory, along with some nice results and extensions. | ||
|
||
|
||
```@bibliography | ||
Pages = ["Liouville.md"] | ||
Canonical = false | ||
``` |