This paper gives sharp rates of convergence to stationarity for a Markov chain generating Bose-Einstein configurations of n balls in k boxes. The analysis leads to curious identities for the arc sine distribution. 0. On a Personal Note In 1971, as a beginning graduate student at Harvard’s Department of Statistics, I badly wanted to learn “real” probability. Someone told me that the deepest, bes...

In this paper we develop tools for analyzing the rate at which a reversible Markov chain converges to stationarity. Our techniques are useful when the Markov chain can be decomposed into pieces which are themselves easier to analyze. The main theorems relate the spectral gap of the original Markov chains to the spectral gap of the pieces. In the first case the pieces are restrictions of the Mar...

abstract background: identify talented people to donate predisposed a major role in supplying healthy blood. if the time interval between donations decrease, the chance that voluntary of blood donation be a regular donor increase. the aim of this study was to determine factors affecting the interval between blood donations in a sample of first-time blood donors. methods: data of a cross-section...

In this paper, Markov chain is used to model the reproduction of fixed finite population, and use binomial distribution discuss probability gen inheritance between generations population genes establish transfer matrix ,using conditional mathematics expect obtain absorption at 0 2N only depends on initial fraction A gene, also must be a fixation gene , conclusion same as results MATLAB simulati...

Introduction: One major problem in analyzing epidemic data is the lack of data and high dependency among the available data, which is due to the fact that the epidemic process is not directly observable. Methods: One method for epidemic data analysis to estimate the desired epidemic parameters, such as disease transmission rate and recovery rate, is data ...