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Course Criteria
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3.00 Credits
Graphical and quantitative description of spatial data. Kriging, block kriging and cokriging. Common variogram models. Analysis of mean-nonstationary data by median polish and universal kriging. Spatial autoregressive models, estimation and testing. Spatial sampling procedures. Use of existing software with emphasis on analysis of real data from the environmental, geological and agricultural sciences.
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3.00 Credits
Introduction to Bayesian inference; specifying prior distributions; conjugate priors, summarizing posterior information, predictive distributions, hierachical models, asymptotic consistency and asymptotic normality. Markov Chain Monte Carlo (MCMC) methods and the use of exising software(e.g., WinBUGS).
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3.00 Credits
Statistical models and methods for categorical responses including the analysis of contingency tables, logistic and Poisson regression, and generalized linear models. Survey of asymptotic and exact methods and their implementation using standard statistical software.
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3.00 Credits
Statistical methods for analysis of time-to-event data, with application to situations with data subject to right-censoring and staggered entry, including clinical trials. Survival distribution and hazard rate; Kaplan-Meier estimator for survival distribution and Greenwood's formula; log-rank and weighted long-rank tests; design issues in clinical trials. Regression models, including accelerated failure time and proportional hazards; partial likelihood; diagnostics.
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3.00 Credits
Markov chains and Markov processes, Poisson process, birth and death processes, queuing theory, renewal theory, stationary processes, Brownian motion.
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3.00 Credits
Fundamental mathematical results of probabilistic measure theory needed for advanced applications in stochastic processes. Probability measures, sigma-algebras, random variables, Lebesgue integration, expectation and conditional expectations w.r.t.sigma algebras, characteristic functions, notions of convergence of sequences of random variables, weak convergence of measures, Gaussian systems, Poisson processes, mixing properties, discrete-time martingales, continuous-time markov chains.
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3.00 Credits
Theory of stochastic differential equations driven by Drownian motions. Current techniques in filtering and financial mathematics. Construction and properties of Brownian motion, wiener measure, Ito's integrals, martingale representation theorem, stochastic differential equations and diffusion processes, Girsanov's theorem, relation to partial differential equations, the Feynman-Kac formula.
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3.00 Credits
Introduction to principles of estimation of linear regression models, such as ordinary least squares and generalized least squares. Extensions to time series and panel data. Consideration of endogeneity and instrumental variables estimation. Limited dependent variable and sample selection models. Attention to implementation of econometric methods using a statistical package and microeconomic and macroeconomic data sets.
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3.00 Credits
Introduction to important econometric methods of estimation such as Least Squares, instrumentatl Variables, Maximum Likelihood, and Generalized Method of Moments and their application to the estimation of linear models for cross-sectional ecomomic data. Discussion of important concepts in the asymptotic statistical analysis of vector process with application to the inference procedures based on the aforementioned estimation methods.
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3.00 Credits
The characteristics of macroeconomic and financial time series data. Discussion of stationarity and non-stationarity as they relate to economic time series. Linear models for stationary economic time series: autoregressive moving average (ARMA) models; vector autoregressive (VAR) models. Linear models for nonstationary data: deterministic and stochastic trends; cointegration. Methods for capturing volatility of financial time series such as autoregressive conditional heteroscedasticity (ARCH) models. Generalized Method of Moments estimation of nonlinear dynamic models.
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