DIVISION OF STATISTICS
Course Descriptions
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208. BASIC STATISTICS (3). Designed to provide students with an understanding of reasoning involved in the statistician’s approach to a variety of problems. Not open for credit toward the major or minor in mathematical sciences. Not open for credit to students with credit in an upper-division statistics course or in OMIS 324 or UBUS 223. Not used in major or minor GPA calculation for mathematical sciences majors or minors. 301. ELEMENTARY STATISTICS (4). Introduction to basic concepts in statistical methods including probability, theoretical and empirical distributions, estimation, tests of hypotheses, linear regression and correlation, and single classification analysis of variance procedures. Not available for credit toward the major in mathematical sciences. Not used in major GPA calculation for mathematical sciences majors. PRQ: MATH206 or MATH 210 or MATH 211 or MATH 229. 350. INTRODUCTION TO PROBABILITY AND STATISTICS (3). Introduction to the basic ideas and fundamental laws of probability including sample spaces, events, independence, random variables, special probability distributions and elementary statistical inference. PRQ: MATH230. 470. INTRODUCTIOIN TO PROBABILITY THEORY (3). Includes probability spaces, random variables, discrete, continuous, mixed probability distributions, moment generating functions, multivariate distributions, conditional probability, conditional expectation, special distributions, laws of large numbers, and central limit theorem. PRQ: MATH 232 and MATH 240, or consent of division. 471.
PROBABILITY MODELS AND
APPLICATIONS (3). Introduction to elementary stochastic processes and their
applications to various phenomena in engineering, management science, the
physical and social sciences, and operations research. PRQ: STAT 470 or consent of division. 472.
INTRODUCTION TO
MATHEMATICAL STATISTICS (3). Includes
distributions of functions of random variables, interval estimation,
sufficiency, completeness, point estimation, statistical hypotheses, analysis
of variance, and the multivariate normal distribution. PRQ: STAT 470 or consent of division. 473.
STATISTICAL METHODS AND
MODELS I (3). A first course in
statistical methods and models including exploratory data analysis and
graphical techniques, regression analysis, experimental design, and basic
sampling techniques. Extensive use of
statistical computer packages. PRQ:
MATH 211 and STAT 301, or STAT 350, or consent of division. CRQ:
STAT 473A. 473A. STATISTICAL COMPUTING PACKAGES (1). Introduction to statistical computing with the aid of software packages. Data entry, transformations, simple plots, summary statistics, and statistical procedures. No previous computer experience is required. PRQ: MATH 211 and STAT 301, or STAT 350, or consent of division. CRQ: STAT 473 or consent of division. 474.
STATISTICAL METHODS
AND MODELS II (3). Continuation of STAT 473.
Topics include factorial experiments: interactions, nested models, and
randomized block designs. Categorical
response data analysis: ordinal data measures of association,
Cochran-Mantel-Haenszel Test, logistic regression, and measures of agreement.
PRQ: STAT 473 and STAT 473A, or consent of division. 478.
STATISTICAL METHODS OF
FORECASTING (3). Introduction to forecasting including use of regression in
forecasting; removal and estimation of trend and seasonality; exponential
smoothing; stochastic time series models; stochastic difference equations;
autoregressive, moving average and mixed models; model identification and
estimation; diagnostic checking; and the use of time series models in
forecasting. PRQ: STAT 473 or consent
of division.
481.
PROBABILISTIC FOUNDATIONS OF ACTUARIAL SCIENCE (3). Actuarial populations.
Univariate parametric actuarial distributions including Weibull and Pareto.
Multivariate actuarial distributions.
Exact and asymptotic relationships among these distributions.
Mixtures of distributions.
Jointly discrete, continuous, and mixed distributions.
Moment, cumulant, and probability generating functions.
Transformations of variables for multivariate distributions.
Basic theory of individual and collective risk models for aggregate loss from insurance policies.
PRQ: STAT 470 or consent of division.
493. SPECIAL TOPICS IN STATISTICS (1-3). Discussion and study of readings on topics of special interest to 565.
REGRESSION ANALYSIS
(3). Simple and multiple linear regression, estimation, confidence intervals
and tests, and prediction. Diagnostic
methods using residuals, transformations, outliers, and influence analysis. Polynomial regression, stepwise variable
selection, and collinearity. PRQ STAT
474 or consent of division. 566.
DISCRETE MULTIVARIATE
DATA ANALYSIS (3). A first course in the analysis of discrete data including
two-dimensional tables, the log linear model, goodness-of-fit of the model,
measures of dependence, three and higher dimensional tables, hierarchical
models, model selection, ordered categories, logit model, zero frequency
problem, and introduction to Bayesian analysis of categorical data. PRQ:
STAT 472 and STAT 474, or consent of division. 567.
RELIABILITY AND LIFE
TESTING (3). Survival function, failure rate, types of censored data,
estimation for parametric models, accelerated life tests, competing risks,
and Bayesian analysis of survival data.
PRQ: STAT 472 and STAT 474, or consent of division. 568.
METHODS IN
BIOSTATISTICS (3). Survival function, failure rate, types of censored data,
life tables, regression models for life-time data, bioassay, direct assay,
indirect assays with quantitative response, and clinical trials. PRQ: STAT 472 and STAT 474, or consent of
division. 569.
METHODS FOR QUALITY
CONTROL AND IMPROVEMENT (3). Control charts for attributes and variables,
special control charts, process control techniques, acceptance sampling,
process capability, Taguchi’s approach to improving quality of a product and
the philosophy of Deming. PRQ: STAT
472 and STAT 474, or consent of division. 570.
PROBABILITY THEORY (3). Review of measures, measurable functions, and
algebras of events. Random variables and their moments and characteristic
function. Sequences of random variables and various modes of
convergence. Borel-Cantelli Lemma and
Kolmogorov 0-1 law. Weak and strong
laws of large numbers. Convergence in distributions and central limit
theorems. Conditional expectation and martingales. Brownian motion and stochastic processes. PRQ: MATH 530 and
STAT 470, or consent of division. 571.
STOCHASTIC PROCESSES (3). Markov chains and processes. Brownian motion and Gaussian processes.
Point processes and renewal processes. Martingales and weakly dependent
stochastic processes. Convergence of
stochastic processes. PRQ: STAT 570 or consent of division. 572.
THEORY OF STATISTICS (3). Exponential class, elements of decision
theory, unbiased estimation, shrinkage estimators, methods for estimating
standard errors, multiparameter estimation, generalized likelihood ratio
tests, sequential probability ratio test, and linear models. PRQ: STAT 472 or
consent of division. 573.
LINEAR MODELS (3). Theory of linear models with applications to the
analysis of variance and regression and to the design of experiments. PRQ: STAT 472 and STAT 474, or consent of
division. 574.
DESIGN AND ANALYSIS OF EXPERIMENTS (3). Intermediate course in the
design and analysis of experiments including linear models of less than full
rank, distributions of quadratic forms, estimable functions; confounding,
fractional replication; incomplete block, hierarchical, Latin square,
cross-over, split plot, repeated measures and related designs, response
surface methods, covariance analysis. PRQ: STAT 472 and STAT 474, or consent
of division. 575.
MULTIVARIATE METHODS OF STATISTICS (3). Introduction to the techniques
of multivariate analysis including description of multivariate data, reducing
the dimension, principal components, factor analysis, estimation and testing
for the parameters in multinormal populations, and multivariate analysis of
variance. Problems which involve the use
of computers will be treated. PRQ: STAT 472 or STAT 474, or consent of
division. 576.
DISTRIBUTION-FREE STATISTICS (3). Survey of nonparametric statistical
techniques and their logical foundations including the distributions of order
statistics and ranks, tests of hypotheses, confidence intervals and
Hodges-Lehmann estimators for one-sample, two-sample, and paired sample location
problems, the two-sample dispersion problem, analysis of one-way and two-way
layouts, tests of independence, goodness-of-fit tests, linear rank
statistics, and U-statistics. PRQ: STAT 472 or STAT 474, or consent of
division. 577.
SAMPLING TECHNIQUES (3). Introduction to sample survey techniques and
sampling theory including estimation of population parameters based on simple
random sampling, cluster sampling, stratified sampling, and ratio sampling.
Includes a summary of recent advances in sampling theory and discussions of
practical problems and sources of error in surveys. PRQ: STAT 472 or STAT
474, or consent of division. 578.
TIME SERIES ANALYSIS (3). Models for analysis of time series data
including mean and covariance functions of stationary time series, moving
average, autoregressive and mixed models, identification and estimation in
ARMA (p,q) models, asymptotic properties of estimators, periodogram and
spectral analysis, and regression with time series error. PRQ: STAT 472 and
STAT 474, or consent of division. 579.
ADVANCED STATISTICAL METHODS (3). Various topics discussed from the
perspective of modeling and analyzing data. Emphasis on application of
statistical methodology. Data analytic techniques illustrated with several
types of data including categorical data, multivariate data, survival data,
linear and nonlinear regression data, time series data, and data from
designed experiments. Extensive use of modern statistical software. PRQ: STAT
472 and STAT 474, or consent of division.
Recommended: MATH 562. 591.
STATISTICAL CONSULTING (3). Techniques for problem formulation.
Identification of parameters and solutions. Client-consultant interaction
techniques. Ill-posed problems and their formulation. Management of
consulting time, facilities, and personnel. Participation under supervision
in actual consulting projects. PRQ: Consent of division. 593.
GRADUATE READING IN PROBABILITY AND STATISTICS (1-9). May be repeated to a maximum of 9 semester
hours. PRQ: Consent of division. 599.
MASTER’S THESIS (1-6). May be repeated to a maximum of 6 semester
hours. PRQ: Consent of division. 675.
TOPICS IN STATISTICS (3). Content varies; may include courses in
linear models, estimation, hypothesis testing, decision theory, and Bayesian
inference. May be repeated to a maximum of 15 semester hours. PRQ: Consent of division. 690.
SEMINAR IN STATISTICS (1-9). Discussions on topics in advanced
probability and statistics as scheduled. Topics include but are not limited
to probability theory, stochastic processes, statistical inference,
nonparametric statistics, multivariate analysis, linear and nonlinear models,
discrete data analysis, time series. One to 9 semester hours as
scheduled. May be repeated to a
maximum of 24 semester hours, not more than 15 of which may be on a single
topic. PRQ: Consent of division. |
For more information about Statistics courses, please contact the
Director of Undergraduate and Graduate Studies (see below).
Dr. Sanjib Basu, Professor
Director of Undergraduate and
Graduate Studies
Northern Illinois University ¨
Division of Statistics ¨ DuSable Hall 361-F
815-753-6714¨
basu[at]math.niu.edu
This page maintained by Donna Lynn - donna[at]math.niu.edu (last updated 1/13/2008 7:46 PM).