Hidden Markov model with application in cell adhesion experiment and Bayesian cubic splines in computer experiments

Abstract

Estimation of the number of hidden states is challenging in hidden Markov models. Motivated by the analysis of a specific type of cell adhesion experiments, a new frame-work based on hidden Markov model and double penalized order selection is proposed. The order selection procedure is shown to be consistent in estimating the number of states. A modified Expectation-Maximization algorithm is introduced to efficiently estimate parameters in the model. Simulations show that the proposed framework outperforms existing methods. Applications of the proposed methodology to real data demonstrate the accuracy of estimating receptor-ligand bond lifetimes and waiting times which are essential in kinetic parameter estimation. The second part of the thesis is concerned with prediction of a deterministic response function y at some untried sites given values of y at a chosen set of design sites. The intended application is to computer experiments in which y is the output from a computer simulation and each design site represents a particular configuration of the input variables. A Bayesian version of the cubic spline method commonly used in numerical analysis is proposed, in which the random function that represents prior uncertainty about y is taken to be a specific stationary Gaussian process. An MCMC procedure is given for updating the prior given the observed y values. Simulation examples and a real data application are given to compare the performance of the Bayesian cubic spline with that of two existing methods.