{"id":90527,"date":"2026-09-16T09:23:00","date_gmt":"2026-09-16T08:23:00","guid":{"rendered":"https:\/\/www.upjs.sk\/prirodovedecka-fakulta\/?post_type=cpt_podujatia&#038;p=90527"},"modified":"2026-09-16T09:23:38","modified_gmt":"2026-09-16T08:23:38","slug":"halfspace-depth-geometry-of-multivariate-quantiles","status":"publish","type":"cpt_podujatia","link":"https:\/\/www.upjs.sk\/prirodovedecka-fakulta\/events\/halfspace-depth-geometry-of-multivariate-quantiles\/","title":{"rendered":"Halfspace depth: Geometry of multivariate quantiles"},"content":{"rendered":"<style>.kadence-column90527_5e4e12-26 > .kt-inside-inner-col{padding-top:var(--global-kb-spacing-xs, 1rem);padding-right:var(--global-kb-spacing-xs, 1rem);padding-left:var(--global-kb-spacing-xs, 1rem);}.kadence-column90527_5e4e12-26 > .kt-inside-inner-col,.kadence-column90527_5e4e12-26 > .kt-inside-inner-col:before{border-top-left-radius:5px;border-top-right-radius:5px;border-bottom-right-radius:5px;border-bottom-left-radius:5px;}.kadence-column90527_5e4e12-26 > .kt-inside-inner-col{column-gap:var(--global-kb-gap-sm, 1rem);}.kadence-column90527_5e4e12-26 > .kt-inside-inner-col{flex-direction:column;}.kadence-column90527_5e4e12-26 > .kt-inside-inner-col > .aligncenter{width:100%;}.kadence-column90527_5e4e12-26 > .kt-inside-inner-col{background-color:#F4F4F4;}.kadence-column90527_5e4e12-26 > .kt-inside-inner-col:before{opacity:0.3;}.kadence-column90527_5e4e12-26{position:relative;}@media all and (max-width: 1024px){.kadence-column90527_5e4e12-26 > .kt-inside-inner-col{flex-direction:column;justify-content:center;}}@media all and (max-width: 767px){.kadence-column90527_5e4e12-26 > .kt-inside-inner-col{flex-direction:column;justify-content:center;}}<\/style>\n<div class=\"wp-block-kadence-column kadence-column90527_5e4e12-26\"><div class=\"kt-inside-inner-col\">\n<p class=\"wp-block-paragraph\">Abstract<br>Statistical depth is a non-parametric tool applicable to multivariate and non-Euclidean data, whose goal is a reasonable generalisation of quantiles to multivariate and more exotic datasets. We discuss the halfspace depth, the most classical depth in statistics. J. W. Tukey proposed that depth in 1975; its rigorous investigation started in the 1990s, and still, an abundance of open problems stimulates research in the area.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">We present surprising links of the halfspace depth with well-studied concepts from convex geometry. Using these relations, we partially resolve several open problems concerning depth. In particular, we resolve the 30-year-old characterisation conjecture, asking whether two different measures can correspond to the same halfspace depth.&nbsp;<\/p>\n<\/div><\/div>\n","protected":false},"excerpt":{"rendered":"<p>Hos\u0165:  doc. Mgr. Stanislav Nagy, Ph.D., Matematicko-fyzik\u00e1lna fakulta Univerzity Karlovej<\/p>\n","protected":false},"author":25,"featured_media":90528,"menu_order":0,"template":"","meta":{"_acf_changed":true,"rs_blank_template":"","rs_page_bg_color":"","slide_template_v7":""},"categories":[],"tags":[],"tax_aktuality":[],"class_list":["post-90527","cpt_podujatia","type-cpt_podujatia","status-publish","has-post-thumbnail","hentry"],"acf":{"acf_link_na_externy_obsah":"","cpt_udalost_datum_konania":"20260923","cpt_udalost_datum_koniec":"20260923","cpt_udalost_miesto_konania":"VKM","cpt_udalost_cas_konania":"14:30:00"},"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v28.6 - https:\/\/yoast.com\/product\/yoast-seo-wordpress\/ -->\n<title>Halfspace depth: Geometry of multivariate quantiles - Pr\u00edrodovedeck\u00e1 fakulta | UPJ\u0160<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/www.upjs.sk\/prirodovedecka-fakulta\/events\/halfspace-depth-geometry-of-multivariate-quantiles\/\" \/>\n<meta property=\"og:locale\" content=\"sk_SK\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Halfspace depth: Geometry of multivariate quantiles - Pr\u00edrodovedeck\u00e1 fakulta | UPJ\u0160\" \/>\n<meta property=\"og:description\" content=\"Hos\u0165: doc. 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