Stereological estimation of the distribution of spherical bodies with constant radius.

Abstract

by Fung Siu-kwong.Thesis (M.Phil.)--Chinese University of Hong Kong, 1995.Includes bibliographical references (leaves 61-62).Chapter 1 --- Introduction --- p.1Chapter 2 --- Independently distributed spheres with constant radius --- p.5Chapter 2.1 --- The method of moment estimator of R --- p.6Chapter 2.2 --- Maximum likelihood estimator of R --- p.7Chapter 2.3 --- Mean squared errors of the estimators of R --- p.7Chapter 2.4 --- Confidence interval of R .。 --- p.14Chapter 3 --- Dependently distributed spheres with the constant radius --- p.17Chapter 3.1 --- Gibbs Sampler --- p.18Chapter 3.2 --- Model based on simulating spatial patterns --- p.20Chapter 3.3 --- Algorithm --- p.23Chapter 3.4 --- Explanation of the algorithm --- p.24Chapter 3.5 --- Posterior distribution of R --- p.28Chapter 3.6 --- The number of spheres is unknown --- p.30Chapter 3.7 --- Boundary Effect --- p.31Chapter 4 --- Simulation Study --- p.32Chapter 4.1 --- Determination of the convergence of the Gibbs sequence --- p.33Chapter 4.2 --- Comparison between Rbay and RadjMLE --- p.35Chapter 4.2.1 --- The number of spheres is known --- p.37Chapter 4.2.2 --- The number of sphere is unknown --- p.41Chapter 4.2.3 --- Boundary effect --- p.45Chapter 5 --- Extension and Conclusion --- p.53Chapter 5.1 --- Extension on the simulation algorithm --- p.53Chapter 5.2 --- Extension to the case of varied radius --- p.56Chapter 5.2.1 --- Modified Algorithm --- p.57Chapter 5.2.2 --- An artificial example --- p.58Bibliography --- p.6