Joint Research Conference
June 24-26, 2014
We present an infinite Bayesian mixture of monotonic regression models for analyzing multiple growth pathways of star-shaped objects growing over time by using non-longitudinal data. A motivating example is the analysis of nanocrystal growth processes. A radius function representation used for the outlines of star-shaped objects allows us to represent an object growth (i.e. expansion of outlines) by an increasing sequence of random radius functions. We propose a monotonic regression model to fit the increasing sequence to non-longitudinal data ensuring that the fitted radius functions always monotonically increase in the sequence. To model the multiple pathways of object growth, we propose the Dirichlet infinite location mixture of multiple monotonic regression models and use a block Gibbs sampler as a numerical solver. We apply the proposed model to non-longitudinal sets of microscopic image data for inferring multiple growth pathways of nanocrystals. Comparing the inference result with real nanocrystal growth trajectories, we conclude that the growth pathways inferred from the non-longitudinal data are consistent with the real nanocrystal growth trajectories. Our implementation of the proposed method in Matlab and example datasets are available online as supplementary materials.