{"id":452,"date":"2013-11-22T14:50:10","date_gmt":"2013-11-22T13:50:10","guid":{"rendered":"https:\/\/samovar2022.int-evry.fr\/index.php\/2013\/11\/22\/algorithmes-de-restauration-bayesienne-mono-et-multiobjets-dans-des-modeles-markoviens\/"},"modified":"2020-09-04T18:46:56","modified_gmt":"2020-09-04T16:46:56","slug":"algorithmes-de-restauration-bayesienne-mono-et-multiobjets-dans-des-modeles-markoviens","status":"publish","type":"post","link":"https:\/\/samovar.telecom-sudparis.eu\/index.php\/2013\/11\/22\/algorithmes-de-restauration-bayesienne-mono-et-multiobjets-dans-des-modeles-markoviens\/","title":{"rendered":"\u00ab\u00a0Algorithmes de restauration Bay\u00e9sienne mono- et multiobjet(s) dans des mod\u00e8les Markoviens\u00a0\u00bb"},"content":{"rendered":"<p>Th\u00e8se de <strong>Yohan PETETIN<\/strong><\/p>\n<p><strong><\/strong><\/p>\n<p>le mercredi <strong>27 novembre<\/strong> 2013 \u00e0 <strong>13h30<\/strong> \u00e0 T\u00e9l\u00e9com SudParis, 9 rue Charles Fourier, 91011 Evry, en <strong>salle C06<\/strong>.<\/p>\n<p><strong>Le jury sera compos\u00e9 de :<\/strong><\/p>\n<ul>\n<li> Pr. Christophe Andrieu, Bristol University, rapporteur<\/li>\n<li> Pr. Nicolas CHOPIN, CREST \/ ENSAE, Rapporteur<\/li>\n<li> Dr. Jacques BLANC-TALON, DGA &#8211; MRIS, Examinateur<\/li>\n<li> Pr. Michel BRONIATOWSKI, Universit\u00e9 de Paris VI, Examinateur<\/li>\n<li> Pr. Emmanuel DUFLOS, \u00c9cole Centrale de Lille, Examinateur<\/li>\n<li> Pr. Fran\u00e7ois ROUEFF, T\u00e9l\u00e9com ParisTech, Examinateur<\/li>\n<li> Pr. Jean-Yves TOURNERET, INP-ENSEEIHT, Examinateur<\/li>\n<li> Pr. Fran\u00e7ois DESBOUVRIES, T\u00e9l\u00e9com SudParis, Directeur de th\u00e8se<\/li>\n<\/ul>\n<p><strong>R\u00e9sum\u00e9 :<\/strong><\/p>\n<p>Cette th\u00e8se est consacr\u00e9e au probl\u00e8me d&rsquo;estimation bay\u00e9sienne pour le<br \/>\nfiltrage statistique, dont l&rsquo;objectif est d&rsquo;estimer r\u00e9cursivement des<br \/>\n\u00e9tats inconnus \u00e0 partir d&rsquo;un historique d&rsquo;observations, dans un mod\u00e8le<br \/>\nstochastique donn\u00e9. Ici, le probl\u00e8me est abord\u00e9 sous sa formeg\u00e9n\u00e9rale<br \/>\ndans la mesure o\u00f9 nous consid\u00e9rons le probl\u00e8me du filtrage mono- et<br \/>\nmulti objet(s), ce dernier \u00e9tant abord\u00e9 sous l&rsquo;angle de la th\u00e9orie des<br \/>\nensembles statistiques finis et du filtre \u00ab Probability Hypothesis<br \/>\nDensity \u00bb.<\/p>\n<p>Tout d\u2019abord, nous nous int\u00e9ressons \u00e0 l&rsquo;importante classe<br \/>\nd&rsquo;approximations que constituent les algorithmes de Monte Carlo<br \/>\ns\u00e9quentiels, qui incluent les algorithmes d&rsquo;\u00e9chantillonnage d&rsquo;importance<br \/>\ns\u00e9quentiel et de filtrage particulaire auxiliaire.<\/p>\n<p>Ensuite, les m\u00e9thodes de r\u00e9duction de variance bas\u00e9es sur le th\u00e9or\u00e8me de<br \/>\nRao-Blackwell sont exploit\u00e9es dans le contexte du filtrage mono- et<br \/>\nmulti-objet(s) et nous nous focalisons \u00e0 la fois sur le caract\u00e8re<br \/>\nspatial et temporel du probl\u00e8me de filtrage.<\/p>\n<p>Enfin, nous abordons l&rsquo;extension des mod\u00e8les probabilistes classiquement<br \/>\nutilis\u00e9s, en consid\u00e9rant d&rsquo;abord les mod\u00e8les de Markov couple et<br \/>\ntriplet. Les techniques de filtrage multi-objets sont d\u2019abord \u00e9tendues<br \/>\npour ces mod\u00e8les. De plus, les propri\u00e9t\u00e9s des mod\u00e8les de Markov triplet<br \/>\nsont utilis\u00e9es pour construire des estimateurs ne reposant sur aucune<br \/>\napproximation particulaire et pouvant \u00eatre calcul\u00e9s rapidement dans des<br \/>\nmod\u00e8les \u00e0 sauts Markoviens.<\/p>\n<p><strong>Abstract<\/strong><\/p>\n<p>This thesis focuses on the Bayesian estimation problem for statistical<br \/>\nfiltering which consists in estimating hidden states from an historic of<br \/>\nobservations over time in a given stochastic model. The filtering<br \/>\nproblem is addressed under a general form, that is to say we consider<br \/>\nthe mono- and multi-object filtering problems. The latter one is<br \/>\naddressed in the Random Finite Sets and Probability Hypothesis Density<br \/>\nframeworks.<\/p>\n<p>First, we focus on the class of particle filtering algorithms, which<br \/>\nmainly include the sequential importance sampling and auxiliary particle<br \/>\nfilter algorithms.<\/p>\n<p>Next, variance reduction methods based on the Rao-Blackwell theorem are<br \/>\nexploited in the mono- and multi-object filtering contexts and we focus<br \/>\non the temporal and spatial aspects of the general filtering problem.<\/p>\n<p>Finally, we discuss on the extension of the classical stochastic models<br \/>\nby considering pairwise and triplet Markov models. The multi-object<br \/>\nfiltering problem is addressed for such models in the random finite sets<br \/>\nframework. Moreover, the statistical properties of the more general<br \/>\ntriplet Markov models are used to build new exact and fast<br \/>\napproximations of the optimal Bayesian estimate (in the sense of the<br \/>\nmean square error) in dynamical models with jumps.<\/p>\n<hr \/>\n","protected":false},"excerpt":{"rendered":"<p>Th\u00e8se de Yohan PETETIN le mercredi 27 novembre 2013 \u00e0 13h30 \u00e0 T\u00e9l\u00e9com SudParis, 9 rue Charles Fourier, 91011 Evry, en salle C06. Le jury sera compos\u00e9 de : Pr. Christophe Andrieu, Bristol University, rapporteur Pr. Nicolas CHOPIN, CREST \/ ENSAE, Rapporteur Dr. Jacques BLANC-TALON, DGA &#8211; MRIS, Examinateur Pr. Michel BRONIATOWSKI, Universit\u00e9 de Paris [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"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":[400],"tags":[],"class_list":["post-452","post","type-post","status-publish","format-standard","hentry","category-theses-2013-fr","entry"],"_links":{"self":[{"href":"https:\/\/samovar.telecom-sudparis.eu\/index.php\/wp-json\/wp\/v2\/posts\/452","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=452"}],"version-history":[{"count":1,"href":"https:\/\/samovar.telecom-sudparis.eu\/index.php\/wp-json\/wp\/v2\/posts\/452\/revisions"}],"predecessor-version":[{"id":1836,"href":"https:\/\/samovar.telecom-sudparis.eu\/index.php\/wp-json\/wp\/v2\/posts\/452\/revisions\/1836"}],"wp:attachment":[{"href":"https:\/\/samovar.telecom-sudparis.eu\/index.php\/wp-json\/wp\/v2\/media?parent=452"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/samovar.telecom-sudparis.eu\/index.php\/wp-json\/wp\/v2\/categories?post=452"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/samovar.telecom-sudparis.eu\/index.php\/wp-json\/wp\/v2\/tags?post=452"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}