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Course Criteria
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3.00 Credits
Data come from a variety of sources sometimes from planned experiments or designed surveys, but also arise by much less organized means. In this course we'll explore the kinds of models and predictions that we can make from both kinds of data as well as design aspects of collecting data. We'll focus on model building, especially multiple regression, and talk about its potential as well as its limits to answer questions about the world. We\'ll emphasize applications over theory and analyze real data sets throughout the course.
Prerequisite:
Statistics 201 or permission of the instructor
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3.00 Credits
What does statistics have to do with designing and carrying out experiments? The answer is, surprisingly perhaps, a great deal. In this course, we will study how to design an experiment with the fewest number of observations possible to achieve a certain power. We will also learn how to analyze and present the resulting data and draw conclusions. After reviewing basic statistical theory and two sample comparisons, we cover one and two-way ANOVA and (fractional) factorial designs extensively. The culmination of the course will be a project where each student designs, carries out, analyzes, and presents an experiment of interest to him or her. Throughout the course, we will use the free statistical software program R to carry out the statistical analysis.
Prerequisite:
A previous introductory course in statistics and no fear of simple computer programming and calculus
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3.00 Credits
The probability of an event can be defined in two ways: (1) the long-run frequency of the event, or (2) the belief that the event will occur. Classical statistical inference is built on the first definition given above, while Bayesian statistical inference is built on the second. This course will introduce the student to methods in Bayesian statistics. Topics covered include: prior distributions, posterior distributions, conjugacy, and Bayesian inference in single-parameter, multi-parameter, and hierarchical models. The computational issues associated with each of these topics will also be discussed.
Prerequisite:
Statistics 201 and Mathematics 211, or permission of instructor
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3.00 Credits
This course focuses on the building of empirical models through data in order to predict, explain, and interpret scientific phenomena. The main focus will be on multiple regression as a technique for doing this. We will study both the mathematics of regression analysis and its applications, including a discussion of the limits to such analyses. The applications will range from a broad range of disciplines, such as predicting the waiting time between eruptions of the Old Faithful geyser, forecasting housing prices or modeling the probability of O-ring failure at Space Shuttle launches.
Prerequisite:
Statistics 101 or 201, and Mathematics 105 and 211; or permission of instructor
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3.00 Credits
This course will introduce students to advanced mathematical concepts and techniques for a deeper understanding of statistical inference. Many topics from STAT 201 such as random variables, the central limit theorem or how to test and estimate unknown parameters will be revisited and put on a more rigorous footing. In addition, emphasis will be placed on simulation and resampling (e.g., permutation and bootstrap) approaches to statistical inference and implemented with the statistical software R.
Prerequisite:
Mathematics 105, Mathematics 211, and Statistics 201
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3.00 Credits
No course description available.
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3.00 Credits
Directed independent study in Statistics.
Prerequisite:
Permission of the department
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3.00 Credits
This course focuses on methods for analyzing categorical response data. In contrast to continuous data, categorical data consist of observations classified into two or more categories. Traditional tools of statistical data analysis are not designed to handle such data and pose inappropriate assumptions. We will develop methods specifically designed to address the discrete nature of the observations and consider applications to the social sciences (e.g., is there a gender difference in the belief in life after death) the biological/medical sciences (e.g., does the probability of a severe side effects increase with the dosage of a drug) and economics. All methods are extensions of traditional ANOVA and regression models to categorical data.
Prerequisite:
Statistics 201 and Statistics 346
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3.00 Credits
Each student carries out an individual research project under the direction of a faculty member that culminates in a thesis. See description under The Degree with Honors in Mathematics.
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3.00 Credits
Each student carries out an individual research project under the direction of a faculty member that culminates in a thesis. See description under The Degree with Honors in Mathematics.
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