Coursework at Iowa State University
Stat 500. Statistical Methods. Introduction to methods for analyzing data from experiments and observational data. Design-based and model-based inference. Estimation, hypothesis testing, and model assessment for 2 group and k group studies. Experimental design and the use of pairing/blocking. Analysis of discrete data. Correlation and regression, prediction, model selection and diagnostics. Simple mixed models including nested random effects and split plot experimental designs. Use of the SAS statistical software.
Stat 506. Statistical Methods for Spatial Data. The analysis of spatial data; geostatistical methods and spatial prediction; discrete index random fields and Markkov random field models; models for spatial point processes.
Stat 511. Statistical Methods. Introduction to the general theory of linear models, least squares and maximum likelihood estimation, hypothesis testing, interval estimation and prediction, analysis of unbalanced designs. Models with both fixed and random factors. Introduction to non-linear and generalized linear models, bootstrap estimation, local smoothing methods. Requires use of R statistical software.
Stat 512. Design of Experiments. Basic ideas of experimental design and analysis; completely randomized, randomized complete block, and Latin Square designs; factorial experiments, confounding, fractional replication; split-plot and incomplete block designs.
Stat 534. Ecological Statistics. Statistical methods for non-standard problems, illustrated using questions and data from ecological field studies. Specific topics include: Estimation of abundance and survival from mark-recapture studies. Deterministic and stochastic matrix models of population trends. Estimation of species richness and diversity. Ordination and analysis of complex multivariate data. Statistical methods discussed will include randomization and permutation tests, spatial point processes, bootstrap estimation of standard error, partial likelihood and Empirical Bayes methods.
Stat 542. Theory of Probability and Statistics I. Sample spaces, probability, conditional probability; Random variables, univariate distributions, expectation, median, and other characteristics of distributions, moment generating functions; Joint distributions, conditional distributions and independence, correlation and covariance; Probability laws and transformations; Introduction to the Multivariate Normal distribution; Sampling distributions, order statistics; Convergence concepts, the law of large numbers, the central limit theorem and delta method; Basics of stochastic simulation.
Stat 543. Theory of Probability and Statistics II. Point estimation including method of moments, maximum likelihood estimation, exponential family, Bayes estimators, Loss function and Bayesian optimality, unbiasedness, sufficiency, completeness, Basu s theorem; Interval estimation including confidence intervals, prediction intervals, Bayesian interval estimation; Hypothesis testing including Neyman-Pearson Lemma, uniformly most powerful tests, likelihood ratio tests; Bayesian tests; Nonparametric methods, bootstrap.
Stat 544. Bayesian Statistics. Specification of probability models; subjective, conjugate, and noninformative prior distributions; hierarchical models; analytical and computational techniques for obtaining posterior distributions; model checking, model selection, diagnostics; comparison of Bayesian and traditional methods.
Stat 551. Time Series Analysis. Concepts of trend and dependence in time series data; stationarity and basic model structures for dealing with temporal dependence; moving average and autoregressive error structures; analysis in the time domain and the frequency domain; parameter estimation, prediction and forecasting; identification of appropriate model structure for actual data and model assessment techniques. Possible extended topics include dynamic models and linear filters.
Stat 579. An Introduction to R. An introduction to the logic of programming, numerical algorithms, and graphics. The R statistical programming environment will be used to demonstrate how data can be stored, manipulated, plotted, and analyzed using both built-in functions and user extensions. Concepts of modularization, looping, vectorization, conditional execution, and function construction will be emphasized.
Stat 580. Statistical Computing. Introduction to scientific computing for statistics using tools and concepts in R: programming tools, modern programming methodologies, modularization, design of statistical algorithms. Introduction to C programming for efficiency; interfacing R with C. Building statistical libraries. Use of algorithms in modern subroutine packages, optimization and integration. Implementation of simulation methods; inversion of probability integral transform, rejection sampling, importance sampling. Monte Carlo integration.
Stat 601. Advanced Statistical Methods. Emphasis on the approaches statisticians take toward the statistical formulation of scientific problems. Students should develop an understanding of the way that various concepts of probability are used in problem formulation, analysis, and inference, and the ability to develop one or more appropriate analyses for a variety of problems. Specific methodological topics include permutation procedures and design-based analysis; model building with single and multiple stochastic components; estimation based on least-squares, likelihood functions, modified likelihood functions, sample reuse, and Bayesian analysis; inference in the sample space, parameter space, and belief space. Development of various analyses for real problems, including statistical formulation and necessary computations.
Stat 606. Advanced Spatial Statistics. Consideration of advanced topics in spatial statistics, including areas of current research. Topics may include construction of nonstationary covariance structures including intrinsic random functions, examination of edge effects, general formulation of Markov random field models, spatial subsampling, use of pseudo-likelihood and empirical likelihood concepts in spatial analysis, the applicability of asymptotic frameworks for inference, and a discussion of appropriate measures for point processes.
Stat 611. Theory and Applications of Linear Models. Matrix preliminaries, estimability, theory of least squares and of best linear unbiased estimation, analysis of variance and covariance, distribution of quadratic forms, extension of theory to mixed and random models, inference for variance components.
Stat 642. Advanced Probability Theory. Measure spaces, extension theorem and construction of Lebesgue-Stieljes measures on Euclidean spaces, Lebesgue integration and the basic convergence theorems, Lp-spaces, absolute continuity of measures and the Radon Nikodym theorem, absolute continuity of functions on R and the fundamental theorem of Lebesgue integration, product spaces and Fubini-Tonelli Theorems, convolutions. Fourier series and transforms, probability spaces; Kolmogorov's existence theorem for stochastic processes; expectation; Jensen's inequality and applications, independence, Borel-Cantelli lemmas; weak and strong laws of large numbers and applications, renewal theory.
Stat 643. Advanced Theory of Statistical Inference. Weak convergence; characteristic functions; continuity theorem; Lindberg-Feller central limit theorem and its ramifications; conditional expectation and probability; Martingale central limit theorems; sufficiency, completeness; Elements of decision theory; Statistical information; Neyman-Pearson theory of testing hypotheses. Uniformly most powerful tests, likelihood ratio tests. Goodness of fit tests. Asymptotic theory of maximum likelihood estimation and likelihood ratio tests; Bayesian models; Invariance.
Stat 651. Time Series. Stationary and nonstationary time series models, including ARMA, ARCH, and GARCH. Covariance and spectral representation of time series. Fourier and periodogram analyses. Predictions. CLT for mixing processes. Estimation and distribution theory. Long range dependence.