Probability. Probability distributions. Fundamentals of statistical inference. Estimation. Hypothesis testing. Correlation and regression. Multiple regression. One- way Classification. Analysis of variance. Introduction to categorical data analysis. Nonparametric methods. Prerequisites: Graduate Standing. This is a deficiency course cannot be taking for credit by STAT major

Axioms and foundations of probability. Conditional probability and Bayes’ theorem. Independence. Random variables and distribution functions and moments. Characteristic functions. Laplace transforms and moment generating functions. Function of random variables. Random vectors and their distributions. Convergence of sequences of random variables. Laws of large numbers and the central limit theorem. Random samples, sample moments and their distributions. Order statistics and their distributions.

Methods of estimation. Properties of estimators: consistency, sufficiency, completeness and uniqueness. Unbiased estimation. The method of moments. Maximum likelihood estimation. Techniques for constructing unbiased estimators and minimum variance unbiased estimators. Bayes estimators. Asymptotic property of estimators. Introduction to confidence intervals. Confidence intervals for parameters of normal distribution. Methods of finding confidence intervals. Fundamental notions of hypotheses testing. The Neyman-Pearson lemma. Most powerful test. Likelihood ratio test. Uniformly most powerful tests. Tests of hypotheses for parameters of normal distribution. Chi-square tests, t-tests, and F-tests.

Pre-Requisites: STAT501 Or STAT501

Selected topics from Probability theory, Statistical Inference, and Information Theory for Data Science with an emphasis on the implementation using statistical software, toolboxes, and libraries like R, NumPy, SciPy, Pandas, and Statsmodels. Topics include Probability; Conditional Probability; Bayes’ Theorem; Random variables; Discrete and Continuous Distributions; Central Limit Theorem; Point Estimation MLE and MAP; Confidence Interval Estimation; Hypothesis Testing; Non-parametric Statistics; Synthetic Data; Entropy, Mutual Information; Information Gain

Simple linear regression and multiple regressions with matrix approach. Development of linear models. Inference about model parameters. Residuals Analysis. Analysis of variance approach. Selection of the best regression equation. Using statistical packages to analyze real data sets.

Simple linear regression. Estimating and testing of intercept and slope. Multiple linear regressions. Estimation parameters and testing of regression coefficients. Prediction and correlation analysis. Analysis of variance technique. Completely randomized and randomized block designs. Latin Square designs. Incomplete block design. Factorial design, 2k factorial designs and blocking and confounding in 2k factorial designs. Using statistical packages to analyze real data sets. Prerequisites: Graduate Standing. Cannot be taken for credit with ISE 530. Cannot be taken by STAT major students.

Demographic fundamentals, Measurement of mortality, Life table, Multiple decrement life table, Analysis of Marriage, Measurement of fertility, Parity progression, Determinants of fertility, Population growth, Models of population structure, Survival analysis, Cox proportional hazards (single and multiple events), Competing events, Parametric demographic models.

Statistical tools for learning from the data by doing statistical analysis on the data with an emphasis on the implementation using various software, toolboxes, and libraries like R, Scikit-Learn, and Statsmodels. Topics include Simple and Multiple Linear Regression, Polynomial Regression, Splines, Generalized Additive Models; Hierarchical and Mixed Effects Models; Bayesian Modeling; Logistic Regression, Generalized Linear Models, Discriminant Analysis; Model Selection.

Basic classes of stochastic processes. Poisson processes. Renewal processes. Regenerative processes. Markov chains. Stochastic population models and branching processes. Queuing processes. Applications of Stochastic process models.

Pre-Requisites: STAT501 Or STAT501

Axioms of Probability, Random variables, Stochastic processes, Brownian motion, Stochastic integral, A simple version of the Itô lemma. Introduction of Stochastic differential equations (SDEs). Applications of Stochastic calculus in Finance: Black-Scholes equation and Black-Scholes Option Pricing formula.

Time Series Basics; Autocorrelation; Modeling and forecasting with MA, AR, ARMA, ARIMA models; Seasonal and non-seasonal models; Model validation; Parameter selection; Smoothing and decomposition methods; Advanced forecasting methods, Multivariate models, State Space Models, Arch and Garch Models; projects using various software, toolboxes, and libraries like R, Scikit-Learn, and Statsmodels.

The binomial test. The quantile test. Tolerance limits. The sign test. The Wlicoxon signed ranked test. The Mann-Whitney tests. Contingency tables. The median test. Measures of dependence. The chi squared goodness-of-fit test. Cochran's test. Tests for equal variances. Measures of rank correlation. Linear regression methods. One and two ways analysis of variance. Using statistical packages to analyze real data sets.

Completely randomized design. Randomized block design. Latin square designs. Models: Fixed, random, and mixed models. Incomplete block design. Factorial experiments 2k designs. Confounding in 2k designs. Nested and Split-plot designs. Fractional and orthogonal designs. Fractional replicate and orthogonal designs. Using statistical packages to analyze real data sets.

Aspects of multivariate analysis. Matrix algebra and random vectors. The multivariate normal distribution. The Wishart distribution. Distribution of a correlation matrix. Inference about a mean vector. Comparing several multivariate means. Multivariate linear regression models. Principal components. Factor analysis. Canonical correlation analysis. Discrimination and classification. Using statistical packages to analyze real data sets.

General approach to time series. Stationary models and autocorrelation. Linear processes and ARMA Models. Forecasting stationary time series. ARMA (p, q) models. Preliminary estimation and Yule-Walker approach. Method of moments and maximum likelihood estimations. ARIMA models for non-stationary time series. Forecasting non-stationary time series. Forecasting ARIMA models. Seasonal ARIMA models. Using statistical packages to analyze real data sets.

Examples of simple time series. Stationary time series and autocorrelation. Autoregressive moving average processes. Modeling and forecasting with ARMA processes. Maximum likelihood and least squares estimator. Nonstationary time series.

Simple random sample. Sampling proportion. Sample size estimation. Stratified random sampling. Ratio, regression, and difference estimators. Systematic sampling. Single stage cluster sampling. Multi-stage cluster sampling. Unequal probability sampling.

Two-way and three-way contingency tables. Log linear model and logistic regression model. Building and applying logit and loglinear models. Multicategory logit models. Models for matched pairs. Using statistical packages to analyze real data sets.

Advanced topics are selected from the broad area of Statistics. The contents of the course are given in detail one semester in advance of that in which it is to be offered. The approval of the Graduate Council will be necessary for offering this course.

Advanced topics are selected from the broad area of Statistics. The contents of the course are given in detail one semester in advance of that in which it is to be offered. The approval of the Graduate Council will be necessary for offering this course. Prerequisite: Graduate Standing.

Graduate students are required to attend the seminars by faculty members, visiting scholars, and fellow graduate students. Additionally, each student must present at least one seminar on a timely research topic. Among other things, this course is designed to give the students an overview of research in Statistics, and a familiarity with research methodology, journals and professional societies in his discipline. Graded on a Pass or Fail basis. Prerequisite: Graduate Standing.

The project course is arranged between a student and faculty member to train students in research methodology and to undertaking a real data set to analyze this set and make recommendations to the client. Students may study specific problems in the era of Applied Statistics. In this course students are asked to prepare a report and possibly publish a paper in reflecting advanced knowledge in the Statistics field. The work will be evaluated based on a report, a seminar and oral examination.

This course is intended to allow the student to conduct research in advanced problems in his MS research area. The faculty offering the course should submit a research plan to be approved by the Graduate Program Committee at the department of Mathematics and Statistics. The student is expected to deliver a public seminar and a report on his research outcomes at the end of the course. Prerequisite: Consent of Instructor.

The student has to undertake and complete a research topic under the supervision of a faculty member in order to probe in depth a specific problem in statistics

Pre-Requisites: STAT599