A shape invariant model for functions f1,...,fn specifies that each individual function fi can be related to a common shape function g through the relation fi(x) = aig(cix + di) + bi. We consider a flexible mixture model that allows multiple shape functions g1,...,gK, where each fi is a shape invariant transformation of one of those gK. 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.

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Published in Journal of Biometrics & Biostatistics, special issue S12, 003, p. 1-8.

© 2014 Szczesniak RD, et al.

This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.

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This research was supported by NCRR(NIH) Grant P20 RR16481.