Abstract

Work with S.Bhattacharyya,T.Li,E.Levina,S.Mukherjee,P.Sarkar Networks are a complex type of structure presenting itself in many applications . They are usually represented by a graph ,with possibly weighted edges plus additional covariates (such as directions).Block models have been studied for some time as basic approximations to ergodic stationary probability models for single graphs.A huge number of fitting methods have been developed for these models some of which we will touch on. The mean field method in which an increasing number of parameters must be fitted is used not only for multiple membership block models but also in applications such as LDA .if the graph is too large poor behaviour of the method can be seen.. We have developed what we call “patch methods ” for fitting which help both computationally and inferentially in such situations bur much further analysis is needed. It is intuitively clear but mathematically unclear how knowledge of the model having nested scales helps in fitting large scale as opposed to small scale parameters.We will discuss this issue through an example,