A standard approach to statistical analysis primarily for students of business and economics; elementary probability, sampling distributions, normal theory estimation and hypothesis testing, regression and correlation, exploratory data analysis. Learning to do statistical analysis on a personal computer is an integral part of the course.

Standard and nonparametric approaches to statistical analysis; exploratory data analysis, elementary probability, sampling distributions, estimation and hypothesis testing, one- and two-sample procedures, regression and correlation. Learning to do statistical analysis on a personal computer is an integral part of the course.

Analysis of variance, multiple regression, chi-square tests, and non-parametric procedures.

Introduction to statistical programming via Python including data types, control flow, object-oriented programming, and graphical user interface-driven applications such as Jupyter notebooks. Emphasis on algorithmic thinking, efficient implementation of different data structures, control and data abstraction, file processing, and data analysis and visualization.

(Also offered as AH 3005.) Introduction to biostatistical techniques, concepts, and reasoning using in a broad range of biomedical and public health related scenarios. Specific topics include description of data, statistical hypothesis testing and its application to group comparisons, and tools for modeling different type of data, including categorical, and time-event, data. Emphasis on the distinction of these methods, their implementation using statistical software, and the interpretation of results applied to health sciences research questions and variables.

Basic probability distributions, point and interval estimation, tests of hypotheses, correlation and regression, analysis of variance, experimental design, non-parametric procedures.

Straight-line regression, multiple regression, regression diagnostics, transformations, dummy variables, one-way and two-way analysis of variance, analysis of covariance, stepwise regression.

Applied multiple linear regression analysis in data science, with an emphasis on modern statistical regression methods: simple linear regression and correlation analysis, multiple linear regression, analysis of variance, goodness of fit, comparing regression models through partial and sequential F tests, dummy variables, regression assumptions and diagnostics, model selection and penalized regression, prediction and model validation, principles of design of experiments, one-way and two-way analysis of variance.

Introduction to data science for effectively storing, processing, analyzing and making inferences from data. Topics include project management, data preparation, data visualization, statistical models, machine learning, distributed computing, and ethics.

Probability set functions, random variables, expectations, moment generating functions, discrete and continuous random variables, joint and conditional distributions, multinomial distribution, bivariate normal distribution, functions of random variables, central limit theorms, computer simulation of probability models.

The mathematical theory underlying statistical methods. Probability spaces, distributions in one and several dimensions, generating functions, and limit theorems.

Sampling distributions and parameter estimation. Neyman-Pearson theory of hypothesis testing, correlation, regression, analysis of variance.

The student will attend 6-8 seminars per semester, and choose one statistical topic to investigate in detail. The student will write a well-revised, comprehensive paper on this topic, including a literature review, description of technical details, and a summary and discussion.

Methods of designing experiments utilizing regression analysis and the analysis of variance.

Introduction to computing for statistical problems; obtaining features of distributions, fitting models and implementing inference (obtaining confidence intervals and running hypothesis tests); simulation-based approaches and basic numerical methods. One hour per week devoted to computing and programming skills.

(Also offered as MATH 3170.) Conditional distributions, discrete and continuous time Markov chains, limit theorems for Markov chains, random walks, Poisson processes, compound and marked Poisson processes, and Brownian motion. Selected applications from actuarial science, biology, engineering, or finance.

Supervised field work relevant to some area of Statistics or Data Science with a regional industry, government agency, or non-profit organization. Evaluated by the field supervisor and by the instructor (based on a detailed written report submitted by the student). Students taking this course will be assigned a final grade of S (satisfactory) or U (unsatisfactory).

Modern statistical learning methods arising frequently in data science and machine learning with real-world applications: linear and logistic regression, generalized additive models, decision trees, boosting, support vector machines, and neural networks (deep learning).

Supervised research in probability or statistics. A final written report and oral presentation are required.

Sampling and nonsampling error, bias, sampling design, simple random sampling, sampling with unequal probabilities, stratified sampling, optimum allocation, proportional allocation, ratio estimators, regression estimators, super population approaches, inferences in finite populations.

Rates and proportions, sensitivity, specificity, two-way tables, odds ratios, relative risk, ordered and non-ordered classifications, trends, case-control studies, elements of regression including logistic and Poisson, additivity and interaction, combination of studies and meta-analysis.

Introduction to prediction using time-series regression methods with non-seasonal and seasonal data. Smoothing methods for forecasting. Modeling and forecasting using univariate, autoregressive, moving average models.

Applied statistical methodology and computing for spatio-temporal data, including visualization, models, and inferences. Extreme value analysis in spatio-temporal contexts. Focus on models that account for spatio-temporal dependence and inferences that provide appropriate uncertainty measures, with applications to real-world problems using open-source software.

Basic ideas, the empirical distribution function and its applications, uses of order statistics, one- two- and c-sample problems, rank correlation, efficiency.

Capstone course in data science. Real-world statistical data science in practice: problem formulation; integration of statistics, computing, and domain knowledge; collaboration; communication; reproducibility; project management.

The course is a companion course to STAT 4915, which must be taken concurrently. Students will write a well-revised and comprehensive paper on their STAT 4915 course project, including literature review, description of technical details, reproducible statistical and data scientific analyses, and discussion of results.