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STAT 500 Statistical Methodology in Archaeometry (3-0)3
Subjects covering statistical methodology in
collectingband analyzing data. Elementary probability
distributions, hypothesis testing, analysis of variance,
analysis of frequencies with emphasis on the use of computers
in processing data. (Open to the students of the Archaeometry
Program.)
STAT 501 Statistical Theory I (4-0)4
Discrete probabilitiy spaces, combinatorial
analysis, probabilities in a continuum, random variables,
expectations, conditional probability and characteristic
functions, distribution functions, sampling, multivariate
normal distribution. Prerequisite: Advanced Calculus,
Probability Theory.
STAT 502 Statistical Theory II (4-0)4
Interval and point estimation, hypothesis
testing. Sufficiency, invariance, unbiasedness, decision
theory. Bayesian procedures, most powerful tests, likelihood
ratio tests. Prerequisite: STAT 501.
STAT 503 Linear Statistical Models (4-0)4
Generalized and conditional inverses,
derivatives of quadratic and linear forms, expectation of a
matrix. Distributions of quadratic forms. Theory of general
linear hypotheses, theory of least squares, full rank and less
than full rank models, design models, components of variance
models, estimation, hypothesis testing and correlation
analysis. Applications to ANOVA and regression. CCH. (1-0) 1.
Prerequisite: Linear Algebra and equivalent of STAT 351-352.
STAT 504 Nonparametric Statistical Inference and Methods
(3-0)3
Use of order statistics and other
distribution-free statistics for estimation and hypothesis
testing, exact non-parametric tests and measures of rank
correlation. Relative efficiency, asymptotic relative
efficiency and normal-score procedures. Test of goodness of
fit. CCH:(1-0) 1. Prerequisite: STAT 501.
STAT 505 Sampling Theory and Methods (3-0)3
General randomization theory of simple and
multistage sampling, sampling with and without replacement and
with equal and unequal probabilities, ratio and regression
estimates, analytical studies and multiframe problems in
relation to stratification, systematic sampling, clustering
and double sampling. CCH: (1-0) 1. Prerequisite: equivalent of
STAT 351-352.
STAT 507 Multivariate Statistics I (3-0)3
Groups and Jacobian of transformations.
Multivariate distributions and notion of invariance in
statistical inference. Estimation of the mean vector and the
covariance matrix. Distributions and use of sample correlation
and sample covariance matrix and generalized variance.
Generalized T2 statistics, Wishart distribution. CCH: (1-0)1.
Prerequisite: Advanced Calculus, Linear Algebra and equivalent
of STAT 351- 352.
STAT 508 Multivariate Statistics II (3-0)3
Classification of observations. Tests
concerning covariance matrices and mean vectors, general
linear hypothesis. Discriminant analysis. Covariance models,
principal components, factor analysis, canonical correlations.
Distributions of certain characteristic roots that depend or
do not depend on parameters. CCH: (1-0)1. Prerequisite: STAT
507.
STAT 509 Applied Stochastic Processes (3-0)3
Markov chains, discrete and continuous Markov
processes and associated limit theorems. Poisson and birth and
death processes. Renewal processes, martingales, Brownian
motion, branching processes. Weakly and strongly stationary
processes, spectral analysis. Gaussian systems. CCH:(1-0)1.
Prerequisite: Advanced Calculus, Probabilitiy Theory and
equivalent of STAT 351-352.
STAT 510 Sequential Analysis (3-0)3
Sequential experiments, the sequential
probability ratio test for simple and composite tests.
Sequential estimation of points on regression, and quantal
response functions. Selection procedures and ranking. CCH:
(1-0)1. Prerequisite: STAT 501.
STAT 511 Time Series Analysis I (3-0)3
Random fields. Properties of autocovariance
and autocorrelation functions of time series. Complex scalar
equations. Trend, seasonality and smoothing. Fourier analysis.
Spectral theory. CCH: (1-0)1. Prerequisite: Advanced Calculus,
equivalent of Stat. 351-352, Differential Equations.
STAT 512 Time Series Analysis II (3-0)3
Large sample theory. Order in probability and
convergence in distribution. Approximation of expectations.
Estimation of mean and autocorrelations. The periodogram.
Estimated spectrum. Filtering, integrated moving average
autoregressive schemes. Transfer functions. Classical and
Box-Jenkins modelling. CCH: (1-0)1. Prerequisite: STAT 511.
STAT 513 Reliability Theory and Methods I (3-0)3
Order statistics. Limit theorems useful in
reliability theory. Extreme value theory. Statistical failure
models. Hazard-rate concept. Poisson, Gamma, Weibull, Gumbel,
Lognormal models. Distribution of time to failure.
Birnbaum-Saunders distribution. Point and interval estimation
procedures for failure models.CCH:(1-0)1. Prerequisite:
Advanced Calculus, equivalent of STAT 351-352.
STAT 514 Reliability Theory and Methods II (3-0)3
Testing reliability hypothesis.
Distribution-free methods. Bayes methods. Accelerated life
testing, parametric and non-parametric methods; system
reliability for maintained and nonmaintained systems,
confidence bounds for system reliability. CCH:(1-0)1.
Prerequisite: STAT 513
STAT 515 Computational Statistics and Data Analysis I
(3-0)3
Computer algorithms for programming
statistical analysis. Efficient uses of existing statistical
computer programs. Generation of random numbers and
statistical computer programming of simulation studies.
Selected topics in statistical analysis of complete and
censored data. Graphical methods and data plotting and
preparation for statistical analysis. Kinds of nonnormality
and robustness. Residual analysis and curve fitting. Hunting
and assessment of outliers in statistical inference. Meaning
and analysis of Type I and Type II censored data. CCH: (1-0)1.
Prerequisite: CENG 200 and equivalent of STAT 251-252.
STAT 516 Computational Statistics and Data Analysis II
(3-0)3
Analysis of data censored by time or by size
of the sample. Concepts of Type I and Type II censoring.
Modelling of censored data by exponential, Weibull, Gumbell,
Log-normal etc., distributions, and the censored data model
parameters. CCH: (1-0)1. Prerequisite: STAT 515.
STAT 518 Statistical Analysis of Designed Experiments
(3-0)3
Randomization theory of experimental design.
Principles of blocking. General analysis of experimental
design models. Construction and analysis of balanced and
partially balanced complete and incomplete block designs.
Factorial design: confounding, aliasing, fractional
replication. Designs for special situations. CCH: (1-0)1.
Prerequisite: STAT 501 and STAT 503.
STAT 519 Bio-Statistics (3-0)3
Bio assay for quantitative and quantal
responses. Absolute and comparative potences, dose, time, dose
x time response curves. Application of probit analysis to
insecticide and radiation dose response studies.CCH: (1-0)1.
Prerequisite:equivalent of STAT 251-252.
STAT 520 Decision Theory (3-0)3
Subjective probability and utility. Bayes
risk and Bayes decisions, loss functions. Estimation, testing
hypothesis and linear statistical models. Sequential testing.
Optimal stopping rules. Sequential choice of experiments. CCH:
(1-0)1 Prerequisite: STAT 501.
STAT 521 Special Topics I (3-0)3
Independent study in the area of interest.
STAT 522 Special Topics II (3-0)3
Independent study in the area of interest.
STAT 523 Advanced Mathematical Methods of Statistics I
(3-0)3
Measures and measurable sets. Measurable
functions of real and complex variables. Continuity and
semicontinuity. Convergence and uniform convergence. The
Riemann-Stieltjes integral. Lebesque integral. Lp spaces.
Abstract Banach and Hilbert spaces, limit theorems for sums,
polynomial approximation theorems. Prerequisite: Consent of
instructor.
STAT 524 Advanced Mathematical Methods of Statistics II
(3-0)3
Analytic functions in n-dimensional complex
and real spaces. Analytic continuous functions, continuous and
singular measures. Radon-Nikodym theorem. Product measures.
Differentiation theory. Transformation of functions. Expansion
of functions. Expansion of functions in series. Fourier
expansions. Some special functions. Uniformization.
Prerequisite: STAT 523.
STAT 525 Regression Theory and Methods (3-0)3
General regression models, residual analysis,
selection of regression models, response surface methods,
nonlinear regression models, experimental design and analysis
of covariance models. Least squares, Gauss-Markov theorem.
Confidence, prediction and tolerance intervals. Simultaneous
inference, multiple comparison procedures. CCH: (1-0)1.
STAT 526 Advanced Data Analysis (3-0)3
Useful display of data. Boxplots and batch
comparisons. Transforming data. Resistant lines. Examining
residuals. Mathematical aspects of transformation. Refined
estimators. Exploratory data analysis techniques. CCH: (1-0)1.
Prerequisite: STAT 515.
STAT 542 Seminar in Statistics (Non-credit)
Seminar course for M.S. students in Statistics.
STAT 599 M.S. Thesis in Statistics (Non-credit)
STAT 601 Advanced Probability Theory I (3-0)3
Notions of measure theory. General concepts
and tools of probability theory. Independence; convergence;
laws of large number. Random walks. Prerequisite: Consent of
instructor.
STAT 602 Advanced Probability Theory II (3-0)3
Concept of conditioning. From independence to
dependence. Ergodic theorems. Martingales and decomposibility.
Brownian motion and limit distributions. Prerequisite: Consent
of instructor.
STAT 603 Advanced Theory of Statistics I (3-0)3
Advanced topics in linear and non-linear
statistical estimation. Prerequisite: Consent of instructor.
STAT 604 Advanced Theory of Statistics II (3-0)3
Advanced topics in statistical hypothesis
testing. Prerequisite: Consent of instructor.
STAT 605 Theory of Linear and Nonlinear Statistical Models
(3-0)3
General linear and nonlinear models. Topics
related to the statistical inference in model building.
Prerequisite: Consent of instructor.
STAT 606 Theory of Experimental Designs (3-0)3
Balanced and partially balanced incomplete
block designs. Mixture designs. Factorial designs. Response
surfaces. Optimal allocation of observations. Prerequisite:
Consent of instructor.
STAT 607 Nonparametric Theory of Statistics (3-0)3
Rank testing and estimation procedures.
Locally most powerful rank tests. Criteria for unbiasedness.
Exact and asymptotic distribution theory. Asymptotic
efficiency. Rank correlation. Sequential procedures.
Prerequisite: Consent of instructor.
STAT 608 Probability Models and Stochastic Processes (3-0)3
Discrete and continuous time Markov chains
and Brownian motion. Gaussian processes, queues, epidemic
models, branching processes, renewal processes. Prerequisite:
Consent of instructor.
STAT 609 Statistical Decision Theory (3-0)3
Decision theoretic approach to statistical
problems. Complete class theorems. Bayes and minimax
procedures. Multiple, sequential, invariant statistical
decision problems. Prerequisite: Consent of instructor.
STAT 610 Sequential Analysis (3-0)3
Sequential probability ratio test.
Approximations for stopping boundaries. Power curve and
expected stopping time. Wald's lemmas. Bayes character of
SPRT. Composite hypothesis. Ranking and selection CCH: (1-0)1.
Prerequisite. Consent of instructor.
STAT 611 Multivariate Analysis (3-0)3
Advanced topics in multivariate statistical
analysis. CCH: (1-0)1 Prerequisite: Consent of instructor.
STAT 612 Advanced Topics in Time Series Analysis (3-0)3
Univariate and multivariate time series
analysis. Estimation and hypothesis testing in the time and
frequency domains. CCH: (1-0)1. Prerequisite: Consent of
instructor.
STAT 613 Advanced Topics in Life Testing and Reliability
(3-0)3
Advanced topics in life models, reliability
and hazard functions. Decision making in life testing. Design
of experiments in life testing. CCH:(1-0)1. Prerequisite:
Consent of instructor.
STAT 614 Interpretation of Data I (3-0)3
Application of statistical theory and
procedures to various types of data. Use of computers and
numerical methods are emphasized. CCH: (1-0)1. Prerequisite:
Consent of instructor
STAT 615 Interpretation of Data II (3-0)3
Continuation of Stat. 614 CCH: (1-0)1.
Prerequisite: Consent of instructor.
STAT 616 Applications of Statistics in Industry (3-0)3
A strong background in control charts
including adoptations, acceptance sampling for attributes and
variables data. Acceptance plans. Statistics of combinations.
CCH: (1-0)1. Prerequisite: Consent of instructor.
STAT 617 Large Sample Theory of Statistics (3-0)3
Large sample properties of tests and
estimates. Problems of consistency and various forms of
asymptotic efficiencies. Irregular estimation problems.
Inference from stochastic processes. CCH: (1-0)1.
Prerequisite: Consent of instructor.
STAT 618 Mathematical Models and Response Surface
Methodology (3-0)3
Two level factorial and fractional factorial
designs, blocking, polynomial models, first order and second
order designs, several responses, determination and optimum
conditions, design criteria involving variance and bias. CCH:
(1-0)1. Prerequisite: Consent of instructor.
STAT 619 Advanced Topics in Regression and Analysis of
Variance (3-0)3
Development of linear classification models,
components of variance for balanced designs, polynomial
models, harmonic regression, crossed models for combined
qualitative and quantitative factors. Analysis of variance for
fixed, random and mixed effects models. Randomization.
Violation of assumptions. CCH: (1-0)1. Prerequisite: Consent
of instructor.
STAT 620 Bayesian Inference (3-0)3
Sampling theory, subjective probability,
likelihood principles. Bayes theorem, Bayesian analysis of
normal theory, inference problems, assessment of model
assumptions, robustness of inference, analysis of variance,
some aspects of multivariate problems. Bayesian aspects of
statistical modelling. CCH: (1-0) 1. Prerequisite: Consent of
instructor.
STAT 621 Robust Statistics (3-0)3
Transforming data. More refined estimators.
Comparing location estimators. M and L estimators. Robust
scale estimators and confidence intervals. Relevance to
hypothesis testing. CCH: (1-0)1. Prerequisite: Consent of
instructor.
STAT 622 Discrete Multivariate Analysis (3-0)3
Structural models for counted data, maximum
likelihood estimates for complete tables, formal goodness of
fit; summary statistics and model selection, maximum
likelihood estimates for incomplete tables, estimating the
size of a closed population, models for measuring change,
analysis of square tables; symmetry and marginal homogeneity,
measures of association and agreement, Pseudo-Bayes estimates
of cell probabilities, asymptotic methods. CCH: (1-0)1.
Prerequisite: Consent of instructor.
STAT 623 Spatial Statistics (3-0)3
Purely spatial processes. Spatial
autocorrelation. Distribution theory for spatial statistics.
Analysis for point patterns. Parametric spatial models.
Estimation and testing procedures. CCH: (1-0)1. Prerequisite:
Consent of instructor.
STAT 630 Advanced Topics in Statistical Inference (3-0)3
Several advanced topics of statistical
inference suited to the needs of researcher. Prerequisite:
Consent of instructor.
STAT 632 Inference for Stochastic Processes (3-0)3
Special models. Large sample theory for
discrete and continuous parameter stochastic pocesses. Optimal
testing. Bayesian, nonparametric and sequential inference for
stochastic processes. Martingales. Stochastic differential
equations. Prerequisite: Consent of instructor.
STAT 634 Theory of Stationary Random Functions (3-0)3
Second moment models of random variables and
vectors. Correlation theory of random processes in the time
and frequency domains. Theory of random fields in the time and
frequency domains. Crossings and extremes of random functions.
Applications. Prerequisite: Consent of instructor.
STAT 642 Seminar in Statistics (Non-credit)
Seminar course for Ph.D. students in
Statistics
STAT 699 Ph.D. Thesis in Statistics (Non-credit)
STAT 800-899 Special Studies (4-2)Non-credit
STAT 900-999 Special Topics (4-0)Non-credit
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