{"id":1098,"date":"2018-11-06T11:01:47","date_gmt":"2018-11-06T10:01:47","guid":{"rendered":"https:\/\/samovar2022.int-evry.fr\/index.php\/2018\/11\/06\/contributions-aux-methodes-de-monte-carlo-et-leur-application-au-filtrage-statistique\/"},"modified":"2020-09-04T18:45:45","modified_gmt":"2020-09-04T16:45:45","slug":"contributions-aux-methodes-de-monte-carlo-et-leur-application-au-filtrage-statistique","status":"publish","type":"post","link":"https:\/\/samovar.telecom-sudparis.eu\/index.php\/2018\/11\/06\/contributions-aux-methodes-de-monte-carlo-et-leur-application-au-filtrage-statistique\/","title":{"rendered":"Contributions aux m\u00e9thodes de Monte Carlo et leur application au filtrage statistique"},"content":{"rendered":"

AVIS DE SOUTENANCE de Monsieur Roland LAMBERTI<\/strong><\/p>\n

Autoris\u00e9 \u00e0 pr\u00e9senter ses travaux en vue de l\u2019obtention du Doctorat de l’Universit\u00e9 Paris-Saclay, pr\u00e9par\u00e9 \u00e0 T\u00e9l\u00e9com SudParis en :<\/p>\n

Math\u00e9matiques aux interfaces<\/p>\n

\u00ab Contributions aux m\u00e9thodes de Monte Carlo et leur application au filtrage statistique \u00bb<\/p>\n

le JEUDI 22 NOVEMBRE 2018 \u00e0 14h00<\/p>\n

\u00e0 T\u00e9l\u00e9com SudParis – 9 rue Charles Fourier – 91000 EVRY<\/p>\n

Salle C06
\n<\/strong><\/p>\n

Membres du jury :<\/strong><\/p>\n\n\n\n\n\n\n\n\n\n\n
M. Fran\u00e7ois DESBOUVRIES<\/td>\n Professeur, T\u00e9l\u00e9com SudParis, FRANCE – Directeur de th\u00e8se<\/td>\n<\/tr>\n
M. Jean-Yves TOURNERET<\/td>\n Professeur des Universit\u00e9s, INP – ENSEEIHT Toulouse, FRANCE – Rapporteur<\/td>\n<\/tr>\n
Mme Gersende FORT<\/td>\n Directeur de Recherche, Institut de Math\u00e9matiques de Toulouse, FRANCE – Rapporteur<\/td>\n<\/tr>\n
M. Yohan PETETIN<\/td>\n Ma\u00eetre de Conf\u00e9rences, T\u00e9l\u00e9com SudParis, FRANCE – Encadrant de th\u00e8se<\/td>\n<\/tr>\n
M. Fran\u00e7ois SEPTIER<\/td>\n Professeur des Universit\u00e9s, Universit\u00e9 Bretagne Sud, FRANCE – Encadrant de th\u00e8se<\/td>\n<\/tr>\n
M. R\u00e9mi BARDENET<\/td>\n Charg\u00e9 de Recherche, \u00c9cole Centrale de Lille, FRANCE – Examinateur<\/td>\n<\/tr>\n
Mme Audrey GIREMUS<\/td>\n Ma\u00eetre de Conf\u00e9rences, IMS Bordeaux, FRANCE – Examinatrice<\/td>\n<\/tr>\n
M. Randal DOUC<\/td>\n Professeur, T\u00e9l\u00e9com SudParis, FRANCE – Examinateur<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

R\u00e9sum\u00e9 :<\/strong><\/p>\n

Cette th\u00e8se s\u2019int\u00e9resse au probl\u00e8me de l\u2019inf\u00e9rence bay\u00e9sienne dans les mod\u00e8les probabilistes dynamiques. Plus pr\u00e9cis\u00e9ment nous nous focalisons sur les m\u00e9thodes de Monte Carlo pour l\u2019int\u00e9gration. Nous revisitons tout d\u2019abord le m\u00e9canisme d\u2019\u00e9chantillonnage d\u2019importance avec r\u00e9\u00e9chantillonnage, puis son extension au cadre dynamique connue sous le nom de filtrage particulaire, pour enfin conclure nos travaux par une application \u00e0 la poursuite multi-cibles. En premier lieu nous partons du probl\u00e8me de l\u2019estimation d\u2019un moment suivant une loi de probabilit\u00e9, connue \u00e0 une constante pr\u00e8s, par une m\u00e9thode de Monte Carlo. Tout d\u2019abord, nous proposons un nouvel estimateur apparent\u00e9 \u00e0 l\u2019estimateur d\u2019\u00e9chantillonnage d\u2019importance normalis\u00e9 mais utilisant deux lois de proposition diff\u00e9rentes au lieu d\u2019une seule. Ensuite, nous revisitons le m\u00e9canisme d\u2019\u00e9chantillonnage d\u2019importance avec r\u00e9\u00e9chantillonnage dans son ensemble afin de produire des tirages Monte Carlo ind\u00e9pendants, contrairement au m\u00e9canisme usuel, et nous construisons ainsi deux nouveaux estimateurs. Dans un second temps nous nous int\u00e9ressons \u00e0 l\u2019aspect dynamique li\u00e9 au probl\u00e8me d\u2019inf\u00e9rence bay\u00e9sienne s\u00e9quentielle. Nous adaptons alors dans ce contexte notre nouvelle technique de r\u00e9\u00e9chantillonnage ind\u00e9pendant d\u00e9velopp\u00e9e pr\u00e9c\u00e9demment dans un cadre statique. Ceci produit le m\u00e9canisme de filtrage particulaire avec r\u00e9\u00e9chantillonnage ind\u00e9pendant, que nous interpr\u00e9tons comme cas particulier de filtrage particulaire auxiliaire. En raison du co\u00fbt suppl\u00e9mentaire en tirages requis par cette technique, nous proposons ensuite une proc\u00e9dure de r\u00e9\u00e9chantillonnage semi-ind\u00e9pendant permettant de le contr\u00f4ler. En dernier lieu, nous consid\u00e9rons une application de poursuite multi-cibles dans un r\u00e9seau de capteurs utilisant un nouveau mod\u00e8le bay\u00e9sien, et analysons empiriquement les r\u00e9sultats donn\u00e9s dans cette application par notre nouvel algorithme de filtrage particulaire ainsi qu\u2019un algorithme de Monte Carlo par Cha\u00eenes de Markov s\u00e9quentiel.<\/p>\n

Abstract :<\/strong><\/p>\n

This thesis deals with integration calculus in the context of Bayesian inference and Bayesian statistical filtering. More precisely, we focus on Monte Carlo integration methods. We first revisit the importance sampling with resampling mechanism, then its extension to the dynamic setting known as particle filtering, and finally conclude our work with a multi-target tracking application. Firstly, we consider the problem of estimating some moment of a probability density, known up to a constant, via Monte Carlo methodology. We start by proposing a new estimator affiliated with the normalized importance sampling estimator but using two proposition densities rather than a single one. We then revisit the importance sampling with resampling mechanism as a whole in order to produce Monte Carlo samples that are independent, contrary to the classical mechanism, which enables us to develop two new estimators. Secondly, we consider the dynamic aspect in the framework of sequential Bayesian inference. We thus adapt to this framework our new independent resampling technique, previously developed in a static setting. This yields the particle filtering with independent resampling mechanism, which we reinterpret as a special case of auxiliary particle filtering. Because of the increased cost required by this technique, we next propose a semiindependent resampling procedure which enables to control this additional cost. Lastly, we consider an application of multi-target tracking within a sensor network using a new Bayesian model, and empirically analyze the results from our new particle filtering algorithm as well as a sequential Markov Chain Monte Carlo algorithm.<\/p>\n","protected":false},"excerpt":{"rendered":"

AVIS DE SOUTENANCE de Monsieur Roland LAMBERTI Autoris\u00e9 \u00e0 pr\u00e9senter ses travaux en vue de l\u2019obtention du Doctorat de l’Universit\u00e9 Paris-Saclay, pr\u00e9par\u00e9 \u00e0 T\u00e9l\u00e9com SudParis en : Math\u00e9matiques aux interfaces \u00ab Contributions aux m\u00e9thodes de Monte Carlo et leur application au filtrage statistique \u00bb le JEUDI 22 NOVEMBRE 2018 \u00e0 14h00 \u00e0 T\u00e9l\u00e9com SudParis – […]<\/p>\n","protected":false},"author":1,"featured_media":1097,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"ocean_post_layout":"","ocean_both_sidebars_style":"","ocean_both_sidebars_content_width":0,"ocean_both_sidebars_sidebars_width":0,"ocean_sidebar":"","ocean_second_sidebar":"","ocean_disable_margins":"enable","ocean_add_body_class":"","ocean_shortcode_before_top_bar":"","ocean_shortcode_after_top_bar":"","ocean_shortcode_before_header":"","ocean_shortcode_after_header":"","ocean_has_shortcode":"","ocean_shortcode_after_title":"","ocean_shortcode_before_footer_widgets":"","ocean_shortcode_after_footer_widgets":"","ocean_shortcode_before_footer_bottom":"","ocean_shortcode_after_footer_bottom":"","ocean_display_top_bar":"default","ocean_display_header":"default","ocean_header_style":"","ocean_center_header_left_menu":"","ocean_custom_header_template":"","ocean_custom_logo":0,"ocean_custom_retina_logo":0,"ocean_custom_logo_max_width":0,"ocean_custom_logo_tablet_max_width":0,"ocean_custom_logo_mobile_max_width":0,"ocean_custom_logo_max_height":0,"ocean_custom_logo_tablet_max_height":0,"ocean_custom_logo_mobile_max_height":0,"ocean_header_custom_menu":"","ocean_menu_typo_font_family":"","ocean_menu_typo_font_subset":"","ocean_menu_typo_font_size":0,"ocean_menu_typo_font_size_tablet":0,"ocean_menu_typo_font_size_mobile":0,"ocean_menu_typo_font_size_unit":"px","ocean_menu_typo_font_weight":"","ocean_menu_typo_font_weight_tablet":"","ocean_menu_typo_font_weight_mobile":"","ocean_menu_typo_transform":"","ocean_menu_typo_transform_tablet":"","ocean_menu_typo_transform_mobile":"","ocean_menu_typo_line_height":0,"ocean_menu_typo_line_height_tablet":0,"ocean_menu_typo_line_height_mobile":0,"ocean_menu_typo_line_height_unit":"","ocean_menu_typo_spacing":0,"ocean_menu_typo_spacing_tablet":0,"ocean_menu_typo_spacing_mobile":0,"ocean_menu_typo_spacing_unit":"","ocean_menu_link_color":"","ocean_menu_link_color_hover":"","ocean_menu_link_color_active":"","ocean_menu_link_background":"","ocean_menu_link_hover_background":"","ocean_menu_link_active_background":"","ocean_menu_social_links_bg":"","ocean_menu_social_hover_links_bg":"","ocean_menu_social_links_color":"","ocean_menu_social_hover_links_color":"","ocean_disable_title":"default","ocean_disable_heading":"default","ocean_post_title":"","ocean_post_subheading":"","ocean_post_title_style":"","ocean_post_title_background_color":"","ocean_post_title_background":0,"ocean_post_title_bg_image_position":"","ocean_post_title_bg_image_attachment":"","ocean_post_title_bg_image_repeat":"","ocean_post_title_bg_image_size":"","ocean_post_title_height":0,"ocean_post_title_bg_overlay":0.5,"ocean_post_title_bg_overlay_color":"","ocean_disable_breadcrumbs":"default","ocean_breadcrumbs_color":"","ocean_breadcrumbs_separator_color":"","ocean_breadcrumbs_links_color":"","ocean_breadcrumbs_links_hover_color":"","ocean_display_footer_widgets":"default","ocean_display_footer_bottom":"default","ocean_custom_footer_template":"","ocean_post_oembed":"","ocean_post_self_hosted_media":"","ocean_post_video_embed":"","ocean_link_format":"","ocean_link_format_target":"self","ocean_quote_format":"","ocean_quote_format_link":"post","ocean_gallery_link_images":"on","ocean_gallery_id":[],"footnotes":""},"categories":[314],"tags":[],"class_list":["post-1098","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-theses-2018-fr","entry","has-media"],"_links":{"self":[{"href":"https:\/\/samovar.telecom-sudparis.eu\/index.php\/wp-json\/wp\/v2\/posts\/1098","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/samovar.telecom-sudparis.eu\/index.php\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/samovar.telecom-sudparis.eu\/index.php\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/samovar.telecom-sudparis.eu\/index.php\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/samovar.telecom-sudparis.eu\/index.php\/wp-json\/wp\/v2\/comments?post=1098"}],"version-history":[{"count":1,"href":"https:\/\/samovar.telecom-sudparis.eu\/index.php\/wp-json\/wp\/v2\/posts\/1098\/revisions"}],"predecessor-version":[{"id":1503,"href":"https:\/\/samovar.telecom-sudparis.eu\/index.php\/wp-json\/wp\/v2\/posts\/1098\/revisions\/1503"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/samovar.telecom-sudparis.eu\/index.php\/wp-json\/wp\/v2\/media\/1097"}],"wp:attachment":[{"href":"https:\/\/samovar.telecom-sudparis.eu\/index.php\/wp-json\/wp\/v2\/media?parent=1098"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/samovar.telecom-sudparis.eu\/index.php\/wp-json\/wp\/v2\/categories?post=1098"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/samovar.telecom-sudparis.eu\/index.php\/wp-json\/wp\/v2\/tags?post=1098"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}