Robust estimation for differential equations, time series analysis on climate change and MCMC simulation of duration-of-load problem

摘要

Usually we need to estimate the unknown parameters of Ordinary Differential Equations based on given data. We propose a robust method in which the parameters are estimated in two levels of optimization. Simulation studies show that the robust method gives satisfactory results. We also apply the robust method to a real ecological data set.Standard normal homogeneity test and Yao and Davisu27 test are two widely used methods in climate study. We generate data from four models and examine whether these two tests are sensitive to different models. We also apply these methods to the climate data of Barkerville, BC.Duration-of-load problem is of great importance in wood engineering. We present literature reviews of three papers in this field. Then we conduct Markov Chain Monte Carlo simulation to explore the empirical probability densities of the break time of lumbers under different models.