{"id":1777,"date":"2021-06-07T11:21:11","date_gmt":"2021-06-07T09:21:11","guid":{"rendered":"https:\/\/www.uni.lu\/fstm-fr\/events\/probability-and-statistics-seminar-3\/"},"modified":"2021-06-07T11:21:11","modified_gmt":"2021-06-07T09:21:11","slug":"probability-and-statistics-seminar-3","status":"publish","type":"events","link":"https:\/\/www.uni.lu\/fstm-fr\/events\/probability-and-statistics-seminar-3\/","title":{"rendered":"Probability and Statistics seminar"},"content":{"rendered":"<section class=\"wp-block-unilux-blocks-free-section section\"><div class=\"container xl:max-w-screen-xl\"><p><i>Stein\u2019s density method for multivariate continuous distributions<\/i><\/p><p>We will discuss a general framework for Stein\u2019s density method for multivariate continuous distributions. The approach associates to any probability density function a canonical operator and Stein class, as well as an infinite collection of operators and classes which we call standardizations. These in turn spawn an entire family of Stein identities and characterizations for any continuous distribution on Rd, among which we highlight those based on the score function and the Stein kernel. A feature of these operators is that they do not depend on normalizing constants. A new definition of Stein kernel is introduced and examined; integral formulas are obtained through a connection with mass transport, as well as ready-to-use explicit formulas for elliptical distributions. The flexibility of the kernels is used to compare in Stein discrepancy (and therefore 2-Wasserstein distance) between two normal distributions, Student and normal distributions, as well as two normal-gamma distributions. Upper and lower bounds on the 1-Wasserstein distance between continuous distributions are provided, and computed for a variety of examples: comparison between different normal distri- butions (improving on existing bounds in some regimes), posterior distributions with different priors in a Bayesian setting (including logistic regression), centred Azzalini- Dalla Valle distributions. Finally the notion of weak Stein equation and weak Stein factors is introduced, and new bounds are obtained for Lipschitz test functions if the distribution admits a Poincar\u00e9 constant, which we use to compare in 1-Wasserstein distance between different copulas on the unit square. (arXiv : <a href=\"https:\/\/arxiv.org\/abs\/2101.05079\" target=\"_self\" title=\"\" rel=\"noopener\">https:\/\/arxiv.org\/abs\/2101.05079<\/a>)<\/p><\/div><\/section>","protected":false},"excerpt":{"rendered":"<p>Stein\u2019s density method for multivariate continuous distributions<\/p>\n","protected":false},"author":0,"featured_media":1778,"parent":0,"menu_order":0,"comment_status":"open","ping_status":"closed","template":"","format":"standard","meta":{"featured_image_focal_point":[],"show_featured_caption":false,"ulux_newsletter_groups":"","uluxPostTitle":"","uluxPrePostTitle":"","_trash_the_other_posts":false,"_price":"","_stock":"","_tribe_ticket_header":"","_tribe_default_ticket_provider":"","_tribe_ticket_capacity":"0","_ticket_start_date":"","_ticket_end_date":"","_tribe_ticket_show_description":"","_tribe_ticket_show_not_going":false,"_tribe_ticket_use_global_stock":"","_tribe_ticket_global_stock_level":"","_global_stock_mode":"","_global_stock_cap":"","_tribe_rsvp_for_event":"","_tribe_ticket_going_count":"","_tribe_ticket_not_going_count":"","_tribe_tickets_list":"[]","_tribe_ticket_has_attendee_info_fields":false,"event_start_date":"2021-06-10 13:00:00","event_end_date":"2021-06-10 14:00:00","event_speaker_name":"Yvik Swan from Universit\u00e9 Libre de Bruxelles","event_speaker_link":"","event_is_online":false,"event_location":"","event_street":"","event_location_link":"","event_zip_code":"","event_city":"","event_country":"LU"},"events-topic":[309],"events-type":[],"organisation":[60],"authorship":[],"acf":[],"yoast_head":"<!-- This site is optimized with the Yoast SEO Premium plugin v22.3 (Yoast SEO v22.3) - 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