Mixtures of Self-Modelling Regressions

Abstract

A shape invariant model for functions f 1 ,…,f n specifies that each individual function f i can be related to a common shape function g through the relation f i (x)=a i g(c i x + d i ) + b i . We consider a flexible mixture model that allows multiple shape functions g 1 ,…,g K , where each f i is a shape invariant transformation of one of those g k . We derive an MCMC algorithm for fitting the model using Bayesian Adaptive Regression Splines (BARS), propose a strategy to improve its mixing properties and utilize existing model selection criteria in semiparametric mixtures to select the number of distinct shape functions. We discuss some of the computational difficulties that arise. The method is illustrated using synaptic transmission data, where the groups of functions may indicate different active zones in a synapse.