A generalized Isserlis theorem for location mixtures of Gaussian random vectors

2011/07/12 by Christophe Vignat, C. Vignat, Vignat, C. · 2 citations
Computer Science · Mathematics · #Advanced Statistical Methods and Models #Applied mathematics #Bayesian Methods and Mixture Models #Bernoulli's principle #Computer science #Extension (predicate logic) #FOS: Mathematics #Gaussian #Gaussian function #Gaussian random field #Mathematical analysis #Mathematics #Mixture model #Physics #Probability (math.PR) #Scale (ratio) #Statistical physics #Statistics #math.PR

paper · pdf · doi:10.48550/arxiv.1107.2309

published in arXiv (Cornell University) (Cornell University)

arxiv created 2011/07/12 · openalex publication_date 2011/07/12 · arxiv updated 2011/07/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In a recent paper, Michalowicz et al. provide an extension of Isserlis theorem to the case of a Bernoulli location mixture of a Gaussian vector. We extend here this result to the case of any location mixture of Gaussian vector; we also provide an example of the Isserlis theorem for a "scale location" mixture of Gaussian, namely the d-dimensional generalized hyperbolic distribution.

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