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SUMMARY: &quot\;Symmetry and sufficiency&quot\; - Peter Orbanz (University
  of Cambridge)
DTSTART:20120308T140000Z
DTEND:20120308T153000Z
UID:TALK36931@talks.cam.ac.uk
CONTACT:Konstantina Palla
DESCRIPTION:Suppose we represent observational data as a sequence of rando
 m variables. If the distribution of this sequence does not \ndepend on the
  order of the variables\, the sequence is conditionally independent given 
 a random probability measure. \nThis result is de Finetti's theorem\, whic
 h forms the formal basis of Bayesian statistics and also plays a pivotal r
 ole in \napplied probability. Various generalizations exist\, both to othe
 r types of invariances than exchangeability\, and to other \nrandom struct
 ures than sequences. A beautiful theorem of Lauritzen provides a common fr
 amework for these results \nand directly links them to statistics\, by for
 malizing invariance by means of a sufficient statistic.\n\nI will discuss 
 the relation between symmetry and sufficiency\, sketch the general theorem
 \, and discuss how it can be used \nto determine the fundamental independe
 nce structure of Bayesian models when the data is not an exchangeable sequ
 ence\, \nbut rather some other exchangeable random structure -- the exampl
 es I will consider in the talk are random partitions and \nrandom graphs. 
 The theorem can also be used to derive parametric exponential family model
 s as a special case.\n\n\nWith this talk\, I will stand in for a cancelled
  RCC on short notice\, and I will use a talk I recently gave in the Statis
 tical Laboratory\; \nthis talk has evolved from an RCC titled "Exchangeabi
 lity" which I gave last spring. The talks differ quite a bit and there is 
 plenty of \nnew material\, but if you attended my talk last year and thoug
 ht it was boring\, this one is bound to be worse.
LOCATION:Engineering Department\, CBL Room 438
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