An Introduction To Probability And Statistical Inference [VERIFIED]

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In this course, the student learns the basic rules of calculating the probabilities and the basics of combinatorics. He or she understands the concept of a random variable and knows the properties of expectation and variance. The student is familiar with the most often used discrete and continuous probability distributions and is able to perform probability calculations under these distributions. The student understands the concept of joint probability distribution and knows the properties of covariance and correlation. The student obtains an understanding how random sampling is used in statistical inference, and why the concept of sample statistic and the distribution of the statistic are important in inference. The student learns the basic principles of estimation and hypothesis testing theory and is able to calculate confidence interval estimates and to perform statistical hypotheses testing especially in situations of one and two groups. The student understands the limitations of the testing theory and is able to calculate different effect size measures.

Introduces the full data cycle. Topics include data collection and retrieval, data cleaning, exploratory analysis and visualization, introduction to statistical modeling, inference, and communicating findings. Applications include real data from a wide-range of fields with emphasis on understanding reproducible practices.

Introductory statistical techniques used to collect and analyze experimental and observational data from health sciences and biology. Includes exploration of data, probability and sampling distributions, basic statistical inference for means and proportions, linear regression, and analysis of variance.

Basic Bayesian concepts and methods with emphasis on data analysis. Prior and posterior probability distributions, modeling, and Markov Chain Monte Carlo techniques are presented in the context of data analysis within a statistical computing environment.

Theory and application of multivariate statistical methods. Topics include statistical inference for the multivariate normal model and its extensions to multiple samples and regression, use of statistical packages for data visualization and reduction, discriminant analysis, cluster analysis, and factor analysis.

Fundamental probability and distribution theory needed for statistical inference. Topics include axiomatic foundations of probability theory, discrete and continuous distributions, expectation and moment generating functions, multivariate distributions, transformations, sampling distributions, and limit theorems.

Fundamental theory and methods for statistical inference. Topics include data reduction (sufficient, ancillary, and complete statistics), estimation (method of moments, maximum likelihood estimators, Bayes estimators), evaluating methods (mean squared error, best unbiased estimators, asymptotic evaluations), hypothesis testing, and confidence intervals.

Introduction to the Bayesian approach to statistical inference. Topics include univariate and multivariate models, choice of prior distributions, hierarchical models, computation including Markov chain Monte Carlo, model checking, and model selection.

Theory and application of multivariate statistical methods. Topics include statistical inference for the multivariate normal model and its extensions to multiple samples and regression, use of statistical packages for data visualization and dimension reduction, discriminant analysis, cluster analysis, factor analysis.

This course provides an elementary introduction to probability and statistics with applications. Topics include: basic combinatorics, random variables, probability distributions, Bayesian inference, hypothesis testing, confidence intervals, and linear regression.

STAT 180 Introduction to Data Science (4) RSNSurvey course introducing the essential elements of data science: data collection, management, curation, and cleaning; summarizing and visualizing data; basic ideas of statistical inference, machine learning. Students will gain hands-on experience through computing labs. Offered: AWSp.View course details in MyPlan: STAT 180

STAT 221 Statistical Concepts and Methods for the Social Sciences (5) NSc, RSNDevelops statistical literacy. Examines objectives & pitfalls of statistical studies; study designs, data analysis, inference; graphical & numerical summaries of numerical &categorical data; correlation and regression; estimation, confidence intervals, & significance tests. Emphasizes social science examples and cases. May only receive credit for one of STAT 220, STAT 221/CS&SS 221/SOC 221, or STAT 290. Offered: jointly with CS&SS 221/SOC 221; AWSp.View course details in MyPlan: STAT 221

STAT 302 Statistical Computing (3)An introduction to the foundations of statistical computing and data analysis. Topics include programming fundamentals, data cleaning, data visualization, debugging, and version control. Topics are motivated by methods in statistics and machine learning. Taught using the R programming language. Prerequisite: either STAT 311, STAT 390, or Q SCI 381; recommended: previous coursework in R programming language.View course details in MyPlan: STAT 302

STAT 321 Data Science and Statistics for Social Sciences I (5) SSc, RSNIntroduction to applied data analysis for social scientists. Focuses on using programming to prepare, explore, analyze, and present data that arise in social science research. Data science topics include loading, cleaning, and exploring data, basic visualization, reproducible research practices. Statistical topics include measurement, probability, modeling, assessment of statistical evidence. Lectures intermixed with programming and lab sessions. Offered: jointly with CS&SS 321/SOC 321; W.View course details in MyPlan: STAT 321

STAT 391 Quantitative Introductory Statistics for Data Science (4)The basic concepts of statistics, machine learning and data science, as well as their computational aspects. Statistical models, likelihood, maximum likelihood and Bayesian estimation, regression, classification, clustering, principal component analysis, model validation, statistical testing. Practical implementation and visualization in data analysis. Assumes knowledge of basic probability, mathematical maturity, and ability to program. Prerequisite: either CSE 312, or STAT 394/MATH 394 and STAT 395/MATH 395. Offered: Sp.View course details in MyPlan: STAT 391

STAT 424 Generalized Linear Models (4)Theory and application of generalized linear models. Key elements include estimation and model fitting, diagnostics, statistical inference, and model selection. Prerequisite: STAT 342 and STAT 423. Offered: Sp.View course details in MyPlan: STAT 424

STAT 506 Applied Probability and Statistics (4)Discrete and continuous random variables, independence and conditional probability, central limit theorem, elementary statistical estimation and inference, linear regression. Emphasis on physical applications. Prerequisite: some advanced calculus and linear algebra.View course details in MyPlan: STAT 506

STAT 535 Statistical Learning: Modeling, Prediction, and Computing (3)Covers statistical learning over discrete multivariate domains, exemplified by graphical probability models. Emphasizes the algorithmic and computational aspects of these models. Includes additional topics in probability and statistics of discrete structures, general purpose discrete optimization algorithms like dynamic programming and minimum spanning tree, and applications to data analysis. Prerequisite: experience with programming in a high level language. Offered: A.View course details in MyPlan: STAT 535

STAT 544 Bayesian Statistical Methods (3)Statistical methods based on the idea of a probability distribution over the parameter space. Coherence and utility. Subjective probability. Likelihood principle. Conjugate families. Structure of Bayesian inference. Limit theory for posterior distributions. Sequential experiments. Exchangeability. Bayesian nonparametrics. Empirical Bayes methods. Prerequisite: STAT 513 or permission of instructor.View course details in MyPlan: STAT 544

STAT 564 Bayesian Statistics for the Social Sciences (4)Statistical methods based on the idea of probability as a measure of uncertainty. Topics covered include subjective notion of probability, Bayes' Theorem, prior and posterior distributions, and data analysis techniques for statistical models. Prerequisite: SOC 504, SOC 505, SOC 506 or equivalent. Offered: jointly with CS&SS 564.View course details in MyPlan: STAT 564

STAT 591 Special Topics in Statistics (1-5, max. 15)Distribution-free inference, game and decision theory, advanced theory of estimation (including sequential estimation), robustness, advanced probability theory, stochastic processes or empirical processes. Prerequisite: permission of instructor. Offered: A.View course details in MyPlan: STAT 591

STAT 592 Special Topics in Statistics (1-5, max. 15)Distribution-free inference, game and decision theory, advanced theory of estimation (including sequential estimation), robustness, advanced probability theory, stochastic processes or empirical processes. Prerequisite: permission of instructor. Offered: W.View course details in MyPlan: STAT 592 1e1e36bf2d