Andrea Ottolini (Standford University, USA) (webinar)

“Gibbs sampling in the analysis of priors for almost exchangeable data”

Joint initiative with MIDAS Complex Data Modeling Research Network https://midas.mat.uc.cl/network/

Abstract: Consider a population of N individuals divided into d subgroups (e.g., d=4 and people are divided by sex and smoking habits). A sequence of 0-1 valued experiments on the population with outcomes X_1,…, X_n is called partially exchangeable if the only relevant information in the data is the number of 1’s in each category. de Finetti’s representation result guarantees that the distribution of the X’s (for n<<N) is in bijection with measures pi^{(n)} on [0,1]^d. Natural problems — such as understanding which of the subdivisions are truly meaningful and what is the effect of our initial belief pi^{(0)} — can be addressed if one knows how to sample efficiently from these measures. In the absence of further information about the experiments, de Finetti suggests starting with a class of priors pi^{(0)}_{C,A} indexed by a d-dimensional network (measuring the relative differences among categories) and a positive parameter A (measuring the belief in complete exchangeability). in this talk I will analyze the performance of Gibbs sampling in approximating these measures in the almost exchangeable regime (A>>1). It will be shown that A^2 steps are necessary and sufficient to mix in a certain Wasserstein distance, with constants depending on few spectral parameters of the network C. This is based on joint work with Gerencsér.