Exchangeable measure-valued Pólya sequences

Vortrag von Prof. Dr. Mladen Savov

Sprecher eingeladen von: Prof. Dr. Jean Bertoin

Datum: 03.06.26  Zeit: 17.15 - 18.45  Raum: Y27H12

Measure-valued Pólya sequences (MVPS) are stochastic processes 
whose dynamics are governed by generalized Pólya urn schemes 
with infinitely many colors. Assuming a general reinforcement 
rule, MVPSs can be viewed as extensions of Blackwell and 
MacQueen’s Pólya sequence, which characterizes an exchangeable 
sequence with a Dirichlet process (DP) prior distribution.

In this talk, we give a complete account of the class of 
exchangeable MVPSs in terms of their prior distributions. 
First, we show that under exchangeability, an MVPS is 
necessarily balanced and its reinforcement kernel is, after 
normalization, a regular conditional distribution.

As a result, its prior distribution is that of a DP mixture 
with respect to a latent parameter, which is associated with 
the conditioning sigma-algebra. Furthermore, we examine the 
effects of relaxing exchangeability to conditional identity 
in distribution and find that the two are equivalent for 
balanced MVPSs.

In the second part of the talk, we study Hoeffding 
decomposability under exchangeability and provide a complete 
characterization of the class of exchangeable 
Hoeffding-decomposable sequences. In particular, we show that 
there exists a random parameter, conditional on which an 
exchangeable Hoeffding-decomposable sequence is an MVPS.

Joint work with Chorbadzhiyska, Y., Sariev, H. and Gerdjikov, S.