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2024年12月12日 · We’ll examine its mathematical properties, discuss when to use it instead of the Gaussian copula, and provide a complete implementation in Stan. This post continues the series on copulas in Stan by introducing the Gaussian copula, discussing its properties, applications, and providing examples of how to implement it in Stan.

Modeling with the Gaussian copula can be summarised in a few steps: Each F i (X i | θ i) converts the data, X i, to uniformly distributed variables, u i. More formally, the multivariate CDF of X is written. H (X) = Φ Σ (Φ − 1 (F 1 (X 1 | θ 1)), …, Φ − 1 (F D (X D | θ D)) | Σ) where: F i (X i | θ i) are the marginal CDFs of each variate.

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2024年12月12日 · bggj. blog; about; It was the best of tails, it was the worst of tails: The T-Copula. Copulas in Stan: Episode III. The Gaussian copula’s inability to model tail dependence can be a serious limitation in practice. This post introduces the t-copula, which shares many convenient properties with the Gaussian copula while also capturing the ...