| In this thesis, we use the model-based clustering procedure to cluster fifteen Zernike coefficients into groups. Quantile regressions are considered to describe the relationship between Zernike coefficients and pupil size. We employ Gibbs sampler and adaptive rejection Metropolis sampling to infer the parameters for each cluster. Bayesian information criterion (BIC) combined with a measure of uncertainty are used to determine the number of clusters. A comparison of likelihoods between the unclustered and the clustered Zernike coefficients is implemented to determine the quantile at which population heterogeneity is the most significant. We illustrate the performance of the proposed method using both simulated and real data sets. In the ophthalmology data application, at quantile tau=0.65, the population are most heterogeneous and divided into two clusters. |
