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On some recent advances on high dimensional Bayesian statistics
Nicolas Chopin1 ; Sébastien Gadat2 ; Benjamin Guedj3 ; Arnaud Guyader4 ; Elodie Vernet5
1ENSAE, Malakoff, France,
2Toulouse School of Economics (Université Toulouse I Capitole), Toulouse, France,
3MODAL project-team, Inria Lille - Nord Europe, Villeneuve d’Ascq, France,
4LSTA, Université Pierre et Marie Curie, Paris, France & Projet ASPI, Inria, Rennes, France,
5Université Paris-Sud, Orsay, France,
ESAIM. Proceedings, Tome 51 (2015), pp. 293-319
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This paper proposes to review some recent developments in Bayesian statistics for high dimensional data. After giving some brief motivations in a short introduction, we describe new advances in the understanding of Bayes posterior computation as well as theoretical contributions in non parametric and high dimensional Bayesian approaches. From an applied point of view, we describe the so-called sqmc particle method to compute posterior Bayesian law, and provide a nonparametric analysis of the widespread abc method. On the theoretical side, we describe some recent advances in Bayesian consistency for a nonparametric hidden Markov model as well as new pac-Bayesian results for different models of high dimensional regression.
DOI : 10.1051/proc/201551016

Nicolas Chopin  1   ; Sébastien Gadat  2   ; Benjamin Guedj  3   ; Arnaud Guyader  4   ; Elodie Vernet  5

1 ENSAE, Malakoff, France,
2 Toulouse School of Economics (Université Toulouse I Capitole), Toulouse, France,
3 MODAL project-team, Inria Lille - Nord Europe, Villeneuve d’Ascq, France,
4 LSTA, Université Pierre et Marie Curie, Paris, France & Projet ASPI, Inria, Rennes, France,
5 Université Paris-Sud, Orsay, France, 
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     title = {On some recent advances on high dimensional {Bayesian} statistics},
     journal = {ESAIM. Proceedings},
     pages = {293--319},
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     doi = {10.1051/proc/201551016},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1051/proc/201551016/}
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Nicolas Chopin; Sébastien Gadat; Benjamin Guedj; Arnaud Guyader; Elodie Vernet. On some recent advances on high dimensional Bayesian statistics. ESAIM. Proceedings, Tome 51 (2015), pp. 293-319. doi: 10.1051/proc/201551016

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