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DTSTAMP:20251122T072802Z
DESCRIPTION:Title: Max-linear Graphical Models for Extreme Risk Modelling.
 \n\n\n	Abstract:\n\n\nGraphical models can represent multivariate distribut
 ions in an intuitive way and\, hence\, facilitate statistical analysis of 
 high-dimensional data. Such models are usually modular so that high-dimens
 ional distributions can be described and handled by careful combination of
  lower dimensional factors. Furthermore\, graphs are natural data structur
 es for algorithmic treatment. Moreover\, graphical models can allow for ca
 usal interpretation\, often provided through a recursive system on a direc
 ted acyclic graph (DAG) and the max-linear Bayesian network we introduced 
 in [1] is a specific example. This talk contributes to the recently emerge
 d topic of graphical models for extremes\, in particular to max-linear Bay
 esian networks\, which are max-linear graphical models on DAGs. Generalize
 d MLEs are derived in [2]. In this context\, the Latent River Problem has 
 emerged as a flagship problem for causal discovery in extreme value statis
 tics. In [3] we provide a simple and efficient algorithm QTree to solve th
 e Latent River Problem. QTree returns a directed graph and achieves almost
  perfect recovery on the Upper Danube\, the existing benchmark dataset\, a
 s well as on new data from the Lower Colorado River in Texas. It can handl
 e missing data\, and has an automated parameter tuning procedure. In our p
 aper\, we also show that\, under a max-linear Bayesian network model for e
 xtreme values with propagating noise\, the QTree algorithm returns asympto
 tically a.s. the correct tree. Here we use the fact that the non-noisy mod
 el has a left-sided atom for every bivariate marginal distribution\, when 
 there is a directed edge between the the nodes.\n\nReferences:\n\n[1] Giss
 ibl\, N. and Klüppelberg\, C. (2018) Max-linear models on directed acyclic
  graphs. Bernoulli 24(4A)\, 2693-2720.\n\n[2] Gissibl\, N. \, Klüppelberg\
 , C. and Lauritzen\, S. (2021) Identifiability and estimation of recursive
  max-linear models. Scandinavian Journal of Statistics 48(1)\, 188-211.\n
 \n[3] Ngoc\, M.T.\, Buck\, J.\, and Klüppelberg\, C. (2021) Estimating a l
 atent tree for extremes. Submitted\, arXiv:2102.06197.\n\n\n	Speaker\n\n\nC
 laudia Klüppelberg is a mathematical statistician and applied probability 
 theorist\, known for her work in risk assessment and statistical finance. 
 She is a professor emerita of mathematical statistics at the Technical Uni
 versity of Munich. Klüppelberg was awarded the Order of Merit of the Feder
 al Republic of Germany and the Bavarian state order Pro meritis scientiae 
 et litterarum in 2001. She is a Fellow of the Institute of Mathematical St
 atistics\, and was a Medallion Lecturer of the Institute of Mathematical S
 tatistics in 2009.\n\nɬÀï·¬ Statistics Seminar schedule: https://mcgillst
 at.github.io/\n\nIn-person: Burnside 1104\n\nZoom:\n\nhttps://mcgill.zoom.
 us/j/83436686293?pwd=b0RmWmlXRXE3OWR6NlNIcWF5d0dJQT09\n\nMeeting ID: 834 3
 668 6293\n\nPasscode: 12345\n\n \n
DTSTART:20221104T193000Z
DTEND:20221104T203000Z
LOCATION:Room 1104\, Burnside Hall\, CA\, QC\, Montreal\, H3A 0B9\, 805 rue
  Sherbrooke Ouest
SUMMARY:Claudia Klüppelberg (Technical University of Munich)
URL:/mathstat/channels/event/claudia-kluppelberg-techn
 ical-university-munich-343295
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