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Estimating Multiple Pathways of Object Growth Using Nonlongitudinal Image Data

Summary: [This abstract is based on the authors' abstract.] This article presents an infinite Bayesian mixture of monotonic regression models for analyzing multiple growth pathways of star-shaped objects growing over time by using nonlongitudinal data. A motivating example is the analysis of nanocrystal growth processes. A radius function representation used for the outlines of star-shaped objects allows the representation of an object growth (i.e., expansion of outlines) by an increasing sequence of random radius functions. The author proposes a monotonic regression model to fit the increasing sequence to nonlongitudinal data, ensuring that the fitted radius functions always monotonically increase in the sequence. To model the multiple pathways of object growth, he proposes the Dirichlet infinite location mixture of multiple monotonic regression models and use a block Gibbs sampler as a numerical solver. The proposed model is applied to nonlongitudinal sets of microscopic image data for inferring multiple growth pathways of nanocrystals. In considering a comparison of the inference result with real nanocrystal growth trajectories, it is concluded that the growth pathways inferred from the nonlongitudinal data are consistent with the real nanocrystal growth trajectories. An implementation of the proposed method in MATLAB and example datasets are available online as supplementary materials.

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  • Topics: Statistics
  • Keywords: Bayesian methods, Isotonic regression, Crystal growing, Growth curves, Probability, Estimation
  • Author: Park, Chiwoo;
  • Journal: Technometrics