Resolution of singularities and stochastic complexity of complete bipartite graph-type spin model in Bayesian estimation

Abstract

In this paper, we obtain the main term of the average stochastic complexity for certain complete bipartite graph-type spin models in Bayesian estimation. We study the Kullback function of the spin model by using a new method of eigenvalue analysis first and use a recursive blowing up process for obtaining the maximum pole of the zeta function which is defined by using the Kullback function. The papers [1,2] showed that the maximum pole of the zeta function gives the main term of the average stochastic complexity of the hierarchical learning model. © Springer-Verlag Berlin Heidelberg 2007.