S u p e r c o u r s e S t a t i s t i c s C o u r s e (18)
Mathematical models are used in science to better understand and make predictions of real world phemenon. Often they may help answer questions that cannot be answered by empirical data or experiments. When the phenomenon has elements of uncertainty, which are governed by probability laws, the model is called a probability or a stochastic model. Stochastic models are often characterized by observing a real world situation over time Examples of stochastic models in the biomedical sciences have been developed for therapeutic and early detection clinical trials, epidemics of infectious diseases, cell growth This course is an introduction to stochastic processes as applied to the biomedical sciences. Among the topics which will be discussed are: epidemiology models for incidence, prevalence and mortality, backward and forward recurrence times and their relationship to length biased sampling, Poisson processes, birth and death processes, Markov chains and semiMarkov processes. 
Instructor. M. Zelen (6174324914 ,617632 3013), Harvard University, USA zelen@hsph.harvard.edu An Introduction to Stochastic Processes in Public Health
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format ( it is necessary to click on "fit 2. Elements of Laplace transforms. (1) 3. Relations between incidence, prevalence and time with disease. Stable disease model, forward and backward recurrence times, models for chronological time and age. (2) Exponential distribution normalized spacings, Campbell’s theorem, random sums of exponential random variables, counting processes and the exponential distribution, superposition of counting processes, splitting and component processes, non – homogeneous Poisson processes.(2) Definitions, asymptotics, renewal function, equilibrium renewal processes (1) Pure birth processes (YuleFurry process), generalization to birth and death processes, relationship to Markov chains, linear birth and death processes.(2) Introduction, ChapmanKolmogorov equations, branching processes, statistical equilibrium, classification of states (2) Master equations, moments, first passage time problems. 
Elements of the Analysis of Discrete
Data July, 2000 This course consists of 8 lectures:
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format ( it is necessary to click on "fit Lectures in Supercourse format 1. Examples and Elements of Theory 3. Independence and Urn Sampling 5. Proportional Hazards Models and Urn sampling 6. Multiple Logistic Regression

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