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Course Criteria
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3.00 Credits
Advanced Stochastic Processes. (3-0). Credit 3. Conditional expectation; stopping times; discrete Markov processes; birth-death processes; queuing models; discrete semi-Markov processes; Brownian motion; diffusion processes, Ito integrals, theorem and limit distributions; differential statistical functions and their limit distributions; M-,L-,R-estimation. Prerequisite: STAT 614 or STAT 615.
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3.00 Credits
Statistical Methods for Chemistry. (3-0). Credit 3. Chemometrics topics of process optimization, precision and accuracy; curve fitting; chi-squared tests; multivariate calibration; errors in calibration standards; statistics of instrumentation. Prerequisite: STAT 601, 641 or 652 or approval of instructor.
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3.00 Credits
Methods in Time Series Analysis. (3-0). Credit 3. Introduction to statistical time series analysis; autocorrelation and spectral characteristics of univariate, autoregressive, moving average models; identification, estimation and forecasting. Prerequisite: STAT 601 or 642 or approval of instructor.
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3.00 Credits
Nonparametric Function Estimation. (3-0). Credit 3. Nonparametric function estimation; kernel, local polynomials, Fourier series and spline methods; automated smoothing methods including cross-validation; large sample distributional properties of estimators; recent advances in function estimation. Prerequisite: STAT 611.
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3.00 Credits
Overview of Mathematical Statistics. (3-0). Credit 3. Basic probability theory including distributions of random variables and expectations. Introduction to the theory of statistical inference from the likelihood point of view including maximum likelihood estimation, confidence intervals, and likelihood ratio tests. Introduction to Bayesian methods. Prerequisites: MATH 221, 251, and 253.
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3.00 Credits
Statistical Methods in Finance. (3-0). Credit 3. Regression and the capital asset pricing model, statistics for portfolio analysis, resampling, time series models, volatility models, option pricing and Monte Carlo methods, copulas, extreme value theory, value at risk, spline smoothing of term structure. Prerequisites: STAT 610, 611, 608.
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3.00 Credits
Statistical Methodology II-Bayesian Modeling and Inference. (3-0). Credit 3. Decision theory; fundamentals of Bayesian inference; single and multi-parameter models; Gaussian model; linear and generalized linear models; Bayesian computations; asymptotic methods; non-iterative MC; MCMC; hierarchical models; nonlinear models; random effect models; survival analysis; spatial models. Prerequisite: STAT 613.
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3.00 Credits
Advanced Bayesian Modeling and Computation. (3-0). Credit 3. Bayesian methods in their research; methodology, and applications of Bayesian methods in bioinformatics, biostatistics, signal processing, machine learning, and related fields. Prerequisite: STAT 608, 613, 632.
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3.00 Credits
Response Surface Design and Analysis. (3-0). Credit 3. Definition of response surface and relation to multiple regression; ridge analysis; first, second and third order designs for response surface estimation; optimization of response surface designs for various criteria; the Box-Draper theory and EVOP. Prerequisite: STAT 608.
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3.00 Credits
Application of Stochastic Processes to the Natural Sciences. (3-0). Credit 3. Basic concepts, Random walks, Markov chains, branching processes, Markov processes in continuous time, homogeneous and nonhomogeneous processes, multi-dimensional processes, queuing processes, epidemic processes, competition and predation, diffusion and non-Markovian processes. Prerequisite: STAT 610 or approval of instructor.
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