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SUMMARY:Universal Copulas - Gery Geenens (University of New South Wales)
DTSTART:20251024T130000Z
DTEND:20251024T140000Z
UID:TALK237499@talks.cam.ac.uk
CONTACT:Qingyuan Zhao
DESCRIPTION:Copulas have emerged over the last decades as primary statisti
 cal tools for modelling dependence between random variables. A copula is c
 lassically understood as a cumulative distribution function on the unit hy
 percube with standard uniform margins – we refer to such distributions a
 s “Sklar’s copulas”\, owing to their central role in the decompositi
 on of multivariate distributions established by the celebrated Sklar's the
 orem.\nA standard argument in favour of copula models is that they separat
 e the dependence structure (encoded by the copula) from the marginal behav
 iour of individual components. However\, this interpretation holds only in
  the continuous case: outside it\, copulas lose their “margin-free” na
 ture\, rendering Sklar’s construction unsuitable for modelling dependenc
 e between non-continuous variables.\nIn this work\, we argue that the noti
 on of a copula need not be confined to Sklar’s framework. We propose an 
 alternative definition -- universal copulas -- based on a more precise cha
 racterisation of dependence. This new definition agrees with Sklar’s cop
 ulas in the continuous case\, but yields distinct and more suitable constr
 uctions in discrete or mixed settings. Universal copulas retain key proper
 ties such as margin-freeness\, making them sound and effective beyond the 
 continuous realm. We illustrate their use through examples involving discr
 ete variables and mixed pairs\, such as one continuous and one Bernoulli v
 ariable.
LOCATION:MR12\, Centre for Mathematical Sciences
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