Cari colleghi,
nell’ambito del programma di Visiting Professors della Laurea Magistrale in Stochastics and Data Science dell’Università di Torino (alla pagina https://www.master-sds.unito.it/go/visiting https://www.master-sds.unito.it/go/visiting il programma completo per il presente a.a.), con piacere annunciamo il seguente corso:
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Bas KLEIJN (University of Amsterdam)
FREQUENTIST LIMITS FROM BAYESIAN STATISTICS
We look at the role that the posterior can play in frequentist statistics, with special attention for large-sample limits. There exists an intimate relationship between hypothesis testing and concentration of posterior measure, which combines with a notion called remote contiguity to obtain frequentist convergence results from sequences of Bayesian posterior measures. We shall cover frequentist forms of posterior consistent estimation, rates of posterior convergence, as well as asymptotic uncertainty quantification by enlargement of credible sets and hypothesis testing/model selection with Bayes factors.
Plan of the course: eight lectures of 45 minutes each: Lec I - Bayesian Basics (Frequentist/Bayesian formalisms, estimation, coverage, testing) Lec II - The Bernstein-von Mises theorem (Limit shape in smooth parametric models, semi-parametrics) Lec III - Bayes and the Infinite (Consistency, Doob’s theorem, Schwartz’s theorem) Lec IV - Posterior contraction (Barron, Walker, Ghosh-Ghosal-van der Vaart theorems) Lec V - Tests and posteriors (Testing and posterior concentration, Doob’s theorem) Lec VI - Frequentist validity of Bayesian limits (Remote contiguity and frequentist limits) Lec VII - Posterior uncertainty quantification (How confidence sets arise from credible sets) Lec VIII - Uniform and pointwise tests (Which hypotheses are asymptotically testable and which are not?)
Time permitting, we shall also consider
Lec IX - Bayesian tests and posterior model selection (Model selection with posteriors, some examples)
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L'iniziativa è rivolta agli studenti del secondo anno della Laurea Magistrale ma la partecipazione è aperta a tutti gli interessati. Il corso si svolgerà in presenza nell’aula 30, terzo piano, C.so Unione Sovietica 218/bis, 10134, Torino (qui https://www.unito.it/ateneo/gli-speciali/coronavirus-aggiornamenti-la-comuni... https://www.unito.it/ateneo/gli-speciali/coronavirus-aggiornamenti-la-comunita-universitaria/rientri-accesso-alle i requisiti per l’accesso come ingressi occasionali) secondo il seguente calendario:
- mar 30 Novembre, h.14-16 - mer 1 Dicembre, h.14-16 - mar 7 Dicembre, h.14-16 - gio 9 Dicembre, h.11.15-13
e sarà trasmesso in diretta streaming (senza registrazione) tramite la seguente riunione Webex, valida per tutte le lezioni:
https://unito.webex.com/unito/j.php?MTID=m508322b370362bfd0618d768e4772ac0 https://unito.webex.com/unito/j.php?MTID=m508322b370362bfd0618d768e4772ac0 Numero riunione: 2733 233 8719 Password: 9ahN5DGFRU3
Cordiali saluti, Matteo Ruggiero
--- Matteo Ruggiero University of Torino and Collegio Carlo Alberto www.matteoruggiero.it http://www.matteoruggiero.it/