Accelerating Bayesian Structure Learning in Sparse Gaussian Graphical Models

Autor: Reza Mohammadi, Hélène Massam, Gérard Letac

Publikováno v: Journal of the American Statistical Association. :1-14

Gaussian graphical models are relevant tools to learn conditional independence structure between variables. In this class of models, Bayesian structure learning is often done by search algorithms over the graph space. The conjugate prior for the prec

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::679ac560641db62ebf366deaf8c37f21
https://doi.org/10.1080/01621459.2021.1996377

Duality for real and multivariate exponential families

Autor: Gérard Letac

Consider a measure $\mu$ on $\R^n$ generating a natural exponential family $F(\mu)$ with variance function $V_{F(\mu)}(m)$ and Laplace transform $$ \exp(\ell_{\mu}(s))=\int_{\R^n} \exp(-\)\mu(dx).$$ A dual measure $\mu^*$ satisfies $-\ell'_{\mu^*}(-\

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::7c62f070b688be3339ee3c823452ce4a
http://arxiv.org/abs/2104.05510

The median of an exponential family and the normal law

Autor: Lutz Mattner, Gérard Letac, Mauro Piccioni

Publikováno v: Statistics & Probability Letters. 133:38-41

Let P be a probability on the real line generating a natural exponential family ( P t ) t ∈ R . We show that the property that t is a median of P t for all t characterizes P as the standard Gaussian law N ( 0 , 1 ) .

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::94809a3709fcad7fdafb198c0a136674
https://doi.org/10.1016/j.spl.2017.10.002

Multivariate reciprocal inverse Gaussian distributions from the Sabot–Tarrès–Zeng integral

Autor: Jacek Wesołowski, Gérard Letac

Publikováno v: Journal of Multivariate Analysis
Journal of Multivariate Analysis, Elsevier, 2020, 175, pp.104559-. ⟨10.1016/j.jmva.2019.104559⟩

In Sabot and Tarres (2015), the authors have explicitly computed the integral S T Z n = ∫ exp ( − 〈 x , y 〉 ) ( det M x ) − 1 ∕ 2 d x where M x is a symmetric matrix of order n with fixed non-positive off-diagonal coefficients and with di

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::228f18f47343b5af75f4b29f3e587bf8
https://doi.org/10.1016/j.jmva.2019.104559

Dirichlet curves, convex order and Cauchy distribution

Autor: Gérard Letac, Mauro Piccioni

Publikováno v: Bernoulli
Bernoulli, Bernoulli Society for Mathematical Statistics and Probability, 2018, 24 (1), pp.1-29. ⟨10.3150/15-bej765⟩
Bernoulli 24, no. 1 (2018), 1-29

If $\alpha$ is a probability on $\mathbb{R}^{d}$ and $t>0$, the Dirichlet random probability $P_{t}\sim\mathcal{D}(t\alpha)$ is such that for any measurable partition $(A_{0},\ldots,A_{k})$ of $\mathbb{R}^{d}$ the random variable $(P_{t}(A_{0}),\ldot

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::f1eb2b275a6d0a976a976f99d50a28bd
http://hdl.handle.net/11573/1111442