[Forum SIS] Seminario di Stefano Rizzelli - Dipartimento di Scienze statistiche

[Dip. Scienze Statistiche - Mi]

DEPARTMENT OF STATISTICAL SCIENCES

Università Cattolica del Sacro Cuore, Milan

Seminar

Wednesday, May 5, at 11.30 a.m.

Stefano Rizzelli

Università Cattolica del Sacro Cuore - École Polytecnique Fédérale de Lausanne



Data-dependent choice of prior hyperparameters in Bayesian inference: consistency and merging of posterior distributions

 Abstract

The Bayesian inferential paradigm prescribes the specification of a prior distribution on the parameters of the statistical model. For complex models, the subjective elicitation of prior hyper-parameters can be a delicate and difficult task. This is particularly the case for hyper-parameters affecting posterior inference via complexity penalization, shrinkage effects, etc. In absence of sufficient information a priori, a principled specification of a hyper-prior distribution can be difficult too and complicate computations. It is common practice to resort to a data-driven choice of the prior hyper-parameters as a shortcut: this approach is commonly called empirical Bayes (EB). Although not rigorous from a Bayesian standpoint, the traditional folklore of EB analysis is that it provides approximations to genuine Bayesian inference, while enjoying some frequentist asymptotic guarantees. We give a new illustration of EB posterior consistency in a semiparametric estimation problem, involving the analysis of extreme multivariate events. We then drift to parametric models and focus on merging in total variation between EB and Bayesian posterior/predictive distributions, almost surely as the sample size increases. We provide new results refining those in Petrone et al. (2014) and illustrate their applications in the context of variable selection.



________________________________________________________________________________

Microsoft Teams meeting

Join on your computer or mobile app

Click here to join the meeting<https://eur03.safelinks.protection.outlook.com/ap/t-59584e83/?url=https%3A%2F%2Fteams.microsoft.com%2Fl%2Fmeetup-join%2F19%253ameeting_MWIyMTNjYzMtNDVjNy00MDJmLWFjYjAtYzhmN2U5YjlkOTgx%2540thread.v2%2F0%3Fcontext%3D%257b%2522Tid%2522%253a%2522b94f7d74-81ff-44a9-b588-6682acc85779%2522%252c%2522Oid%2522%253a%25220c084bb4-4916-4250-aaa9-caeb923cf81d%2522%257d&data=04%7C01%7Cdip.scienzestatistiche%40unicatt.it%7Ca7be2faf2fe546ad1b3e08d8ed129f38%7Cb94f7d7481ff44a9b5886682acc85779%7C0%7C0%7C637520011528076778%7CUnknown%7CTWFpbGZsb3d8eyJWIjoiMC4wLjAwMDAiLCJQIjoiV2luMzIiLCJBTiI6Ik1haWwiLCJXVCI6Mn0%3D%7C1000&sdata=7%2FbwgLZcmRLeO9t2XL0g2NuFsIgbNaez3bD6S1c3H4M%3D&reserved=0>

[https://static.unicatt.it/ext-portale/logo-centenario-o365.jpg]

Learn more<https://eur03.safelinks.protection.outlook.com/?url=https%3A%2F%2Faka.ms%2FJoinTeamsMeeting&data=04%7C01%7Cdip.scienzestatistiche%40unicatt.it%7Ca7be2faf2fe546ad1b3e08d8ed129f38%7Cb94f7d7481ff44a9b5886682acc85779%7C0%7C0%7C637520011528076778%7CUnknown%7CTWFpbGZsb3d8eyJWIjoiMC4wLjAwMDAiLCJQIjoiV2luMzIiLCJBTiI6Ik1haWwiLCJXVCI6Mn0%3D%7C1000&sdata=SqYW3tz24iw4b24MgZ6mZw5VUqbdh9KhqCbl8hRzoAo%3D&reserved=0> | Meeting options<https://eur03.safelinks.protection.outlook.com/?url=https%3A%2F%2Fteams.microsoft.com%2FmeetingOptions%2F%3ForganizerId%3D0c084bb4-4916-4250-aaa9-caeb923cf81d%26tenantId%3Db94f7d74-81ff-44a9-b588-6682acc85779%26threadId%3D19_meeting_MWIyMTNjYzMtNDVjNy00MDJmLWFjYjAtYzhmN2U5YjlkOTgx%40thread.v2%26messageId%3D0%26language%3Den-GB&data=04%7C01%7Cdip.scienzestatistiche%40unicatt.it%7Ca7be2faf2fe546ad1b3e08d8ed129f38%7Cb94f7d7481ff44a9b5886682acc85779%7C0%7C0%7C637520011528086745%7CUnknown%7CTWFpbGZsb3d8eyJWIjoiMC4wLjAwMDAiLCJQIjoiV2luMzIiLCJBTiI6Ik1haWwiLCJXVCI6Mn0%3D%7C1000&sdata=qgq1xNkceNqy8yohLXH12RjEdVsKav6PZtwyj5ydh18%3D&reserved=0>

________________________________________________________________________________


[http://static.unicatt.it/ext-portale/FirmaOutlook.jpg]<http://www.unicatt.it/>
-------------- next part --------------
An HTML attachment was scrubbed...
URL: <http://www.stat.unipg.it/pipermail/sis/attachments/20210426/2a364109/attachment.html>