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SUMMARY:Probabilistic and Statistical Tools 1 - Christian Soize (Universit
 é Gustave Eiffel)
DTSTART:20230710T150000Z
DTEND:20230710T160000Z
UID:TALK193888@talks.cam.ac.uk
DESCRIPTION:Lecture: Monday 10 July 2023\, 16:00 - 17h00Title: Probabilist
 ic and statistical tools 1Presenter: Christian SOIZE\n1. Types of represen
 tation for stochastic modeling.- Why a probability distribution cannot arb
 itrarily be chosen for a stochastic modeling?- Impact of an arbitrary stoc
 hastic modeling of the uncertain parameter.- What is important in UQ? : th
 e stochastic modeling of uncertainties (step 1).- Direct approach for cons
 tructing the probability measure.- Indirect approach for representing the 
 probability measure.\n2. Maximum Entropy (MaxEnt) principle from Informati
 on Theory as a direct approach for constructing a priorprobability model.-
  Entropy as a measure of uncertainties for a vector-valued random variable
 .- Maximum entropy principle.- Reformulation of the optimization problem b
 y using Lagrange&rsquo\;s multipliers.&nbsp\;- Existence and uniqueness of
  the principle.- Analytical examples of classical probability distribution
 s deduced from the MaxEnt principle.- MaxEnt as a numerical tool for proba
 bility measure in any dimension.\n3. Random Matrix Theory for uncertainty 
 quantification in computational mechanics.- A few words on fundamentals of
  the random matrix theory.- Ensembles of random matrices for uncertainty q
 uantification.- Volume element and probability density function for random
  matrices.- The Shannon entropy as a measure of uncertainties for a symmet
 ric real random matrix and MaxEnt principle.- Ensemble of positive-definit
 e random matrices with a unit mean value.- Ensemble of positive-definite r
 andom matrices with a unit mean value and a positive-definite lower bound.
 - Ensemble of positive-definite random matrices with a given mean value an
 d a positive-definite lower bound.
LOCATION:Seminar Room 1\, Newton Institute
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