## 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.