Dietrich College of Humanities & Social Sciences

**36-149 Statistics Freshman Seminar**

Fall and Spring: 9 units

Networks: Where do they come from? What do they tell us? Thirty years ago, the word "network" was mostly used in reference to computers or television broadcasting channels. Now we have networks of friends, enemies, phones, stars, tweets, international governments, terrorists, etc. Where do these networks come from? How are they built? What do they represent? As we learn more about how everything is connected, we also face challenges in trying to understand the data that a network can generate. In this course, you'll learn about networks from a New England monastery facing a political crisis to social groups of friends (is obesity contagious? what about divorce?) to 15th century marriages among prominent Italian families to international political disputes and skirmishes (is the enemy of my enemy my friend?) to the spread of HIV among intravenous drug users. Along the way, we'll explore how to describe, visualize, analyze, and even break down the networks that surround us.

**36-201 Statistical Reasoning and Practice**

All Semesters: 9 units

This course will introduce students to the basic concepts, logic, and issues involved in statistical reasoning, as well as basic statistical methods used to analyze data and evaluate studies. The major topics to be covered include methods for exploratory data analysis, an introduction to research methods, elementary probability, and methods for statistical inference. The objectives of this course are to help students develop a critical approach to the evaluation of study designs, data and results, and to develop skills in the application of basic statistical methods in empirical research. An important feature of the course will be the use of the computer to facilitate the understanding of important statistical ideas and for the implementation of data analysis. In addition to three lectures a week, students will attend a computer lab once a week. Examples will be drawn from areas of applications of particular interest to H&SS students. Not open to students who have received credit for 36-207/70-207, 36-220, 36-225, 36-625, or 36-247

**36-202 Statistical Methods**

Spring: 9 units

This course builds on the principles and methods of statistical reasoning developed in 36-201 (or its equivalents). The course covers simple and multiple regression, analysis of variance methods and logistic regression. Other topics may include non-parametric methods and probability models, as time permits. The objectives of this course is to develop the skills of applying the basic principles and methods that underlie statistical practice and empirical research. In addition to three lectures a week, students attend a computer lab once week for "hands-on" practice of the material covered in lecture. Not open to students who have received credit for: 36-208/70-208, 36-309.

Prerequisites: 36-201 or 36-207 or 36-220 or 36-247 or 70-207

**36-207 Probability and Statistics for Business Applications**

Fall: 9 units

This is the first half of a year long sequence in basic statistical methods that are used in business and management. Topics include exploratory and descriptive techniques, probability theory, statistical inference in simple settings, basic categorical analysis, and statistical methods for quality control. Not open to students who have received credit for 36-201, 36-220, 36-625, or 36-247. Cross-listed as 70-207.

Prerequisites: 21-112 or 21-120 or 21-121.

**36-208 Regression Analysis**

Spring: 9 units

This is the second half of a year long sequence in basic statistical methods that are used in business and management. Topics include time series, regression and forecasting. In addition to two lectures a week, students will attend a computer lab once a week. Not open to students who have received credit for 36-202, 36-626. Cross-listed as 70-208.

Prerequisites: (21-120 or 21-121 or 21-112) and (36-207 or 70-207 or 36-201 or 36-220 or 36-247).

**36-217 Probability Theory and Random Processes**

All Semesters: 9 units

This course provides an introduction to probability theory. It is designed for students in electrical and computer engineering. Topics include elementary probability theory, conditional probability and independence, random variables, distribution functions, joint and conditional distributions, limit theorems, and an introduction to random processes. Some elementary ideas in spectral analysis and information theory will be given. A grade of C or better is required in order to use this course as a pre-requisite for 36-226 and 36-410. Not open to students who have received credit for 36-225, or 36-625.

Prerequisites: 21-112 or 21-122 or 21-123 or 21-256 or 21-259

**36-220 Engineering Statistics and Quality Control**

All Semesters: 9 units

This is a course in introductory statistics for engineers with emphasis on modern product improvement techniques. Besides exploratory data analysis, basic probability, distribution theory and statistical inference, special topics include experimental design, regression, control charts and acceptance sampling. Not open to students who have received credit for 36-201, 36-207/70-207, 36-226, 36-626, or 36-247, except when AP credit is awarded for 36-201.

Prerequisites: 21-112 or 21-120 or 21-121.

**36-225 Introduction to Probability Theory**

Fall: 9 units

This course is the first half of a year long course which provides an introduction to probability and mathematical statistics for students in economics, mathematics and statistics. The use of probability theory is illustrated with examples drawn from engineering, the sciences, and management. Topics include elementary probability theory, conditional probability and independence, random variables, distribution functions, joint and conditional distributions, law of large numbers, and the central limit theorem. A grade of C or better is required in order to advance to 36-226 and 36-410. Not open to students who have received credit for 36-217 or 36-625.

Prerequisites: 21-256 or 21-259

**36-226 Introduction to Statistical Inference**

Spring: 9 units

This course is the second half of a year long course in probability and mathematical statistics. Topics include maximum likelihood estimation, confidence intervals, and hypothesis testing. If time permits there will also be a discussion of linear regression and the analysis of variance. A grade of C or better is required in order to advance to 36-401, 36-402 or any 36-46x course. Not open to students who have received credit for 36-626.

Prerequisites: At least a C grade in 15-359 or 21-325 or 36-217 or 36-225

**36-247 Statistics for Lab Sciences**

Spring: 9 units

This course is a single-semester comprehensive introduction to statistical analysis of data for students in biology and chemistry. Topics include exploratory data analysis, elements of computer programming for statistics, basic concepts of probability, statistical inference, and curve fitting. In addition to two lectures, students attend a computer lab each week. Not open to students who have received credit for 36-201, 36-207/70-207, 36-220, or 36-226.

Prerequisites: 21-112 or 21-120 or 21-121.

**36-303 Sampling, Survey and Society**

Spring: 9 units

This course will revolve around the role of sampling and sample surveys in the context of U.S. society and its institutions. We will examine the evolution of survey taking in the United States in the context of its economic, social and political uses. This will eventually lead to discussions about the accuracy and relevance of survey responses, especially in light of various kinds of nonsampling error. Students will be required to design, implement and analyze a survey sample.

Prerequisites: 36-202 or 36-208 or 36-226 or 36-309 or 36-625 or 70-208 or 73-261 or 88-250.

**36-309 Experimental Design for Behavioral and Social Sciences**

Fall: 9 units

Statistical aspects of the design and analysis of planned experiments are studied in this course. A clear statement of the experimental factors will be emphasized. The design aspect will concentrate on choice of models, sample size and order of experimentation. The analysis phase will cover data collection and computation, especially analysis of variance and will stress the interpretation of results. In addition to a weekly lecture, students will attend a computer lab once a week.

Prerequisites: 36-201 or 36-207 or 36-217 or 36-220 or 36-247

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**36-315 Statistical Graphics and Visualization**

Spring: 9 units

Graphical displays of quantitative information take on many forms as they help us understand both data and models. This course will serve to introduce the student to the most common forms of graphical displays and their uses and misuses. Students will learn both how to create these displays and how to understand them. As time permits the course will consider some more advanced graphical methods such as computer-generated animations. Each student will be required to engage in a project using graphical methods to understand data collected from a real scientific or engineering experiment. In addition to two weekly lectures there will be lab sessions where the students learn to use software to aid in the production of appropriate graphical displays.

Prerequisites: 36-202 or 36-208 or 36-226 or 36-303 or 36-309 or 36-625 or 70-208 or 88-250.

**36-350 Statistical Computing**

Fall: 9 units

Statistical Computing: An introduction to computing targeted at statistics majors with minimal programming knowledge. The main topics are core ideas of programming (functions, objects, data structures, flow control, input and output, debugging, logical design and abstraction), illustrated through key statistical topics (exploratory data analysis, basic optimization, linear models, graphics, and simulation). The class will be taught in the R language. No previous programming experience required. Pre-requisites: (36-202 or 36-208), plus ("computing at Carnegie Mellon" or consent of instructor).

Prerequisites: 36-202 or 36-208 or 70-208

**36-401 Modern Regression**

Fall: 9 units

This course is an introduction to the real world of statistics and data analysis. We will explore real data sets, examine various models for the data, assess the validity of their assumptions, and determine which conclusions we can make (if any). Data analysis is a bit of an art; there may be several valid approaches. We will strongly emphasize the importance of critical thinking about the data and the question of interest. Our overall goal is to use a basic set of modeling tools to explore and analyze data and to present the results in a scientific report. A minimum grade of C in any one of the pre-requisites is required. A grade of C is required to move on to 36-402 or any 36-46x course.

Prerequisites: At least a C grade in (36-226 or 36-625 or 73-407 or 36-310) and (21-240 or 21-241).

**36-402 Advanced Data Analysis**

Spring: 9 units

This course introduces modern methods of data analysis, building on the theory and application of linear models from 36-401. Topics include nonlinear regression, nonparametric smoothing, density estimation, generalized linear and generalized additive models, simulation and predictive model-checking, cross-validation, bootstrap uncertainty estimation, multivariate methods including factor analysis and mixture models, and graphical models and causal inference. Students will analyze real-world data from a range of fields, coding small programs and writing reports. Prerequisites: 36-401

Prerequisite: At least a C grade in 36-401

**36-410 Introduction to Probability Modeling**

Spring: 9 units

An introductory-level course in stochastic processes. Topics typically include Poisson processes, Markov chains, birth and death processes, random walks, recurrent events, and renewal theory. Examples are drawn from reliability theory, queuing theory, inventory theory, and various applications in the social and physical sciences.

Prerequisites: 21-325 or 36-217 or 36-225 or 36-625

**36-461 Special Topics: Epidemiology**

Intermittent: 9 units

Epidemiology is concerned with understanding factors that cause, prevent, and reduce diseases by studying associations between disease outcomes and their suspected determinants in human populations. Epidemiologic research requires an understanding of statistical methods and design. Epidemiologic data is typically discrete, i.e., data that arise whenever counts are made instead of measurements. In this course, methods for the analysis of categorical data are discussed with the purpose of learning how to apply them to data. The central statistical themes are building models, assessing fit and interpreting results. There is a special emphasis on generating and evaluating evidence from observational studies. Case studies and examples will be primarily from the public health sciences.

Prerequisite: 36-401

**36-462 Topics in Statistics:**

Intermittent: 9 units

Data mining is the science of discovering patterns and learning structure in large data sets. Covered topics include information retrieval, clustering, dimension reduction, regression, classification, and decision trees. Prerequisites: 36-401 (C or better).

Prerequisite: 36-401

**36-463 Multilevel and Hierarchical Models**

Intermittent: 9 units

Multilevel and hierarchical models are among the most broadly applied "sophisticated" statistical models, especially in the social and biological sciences. They apply to situations in which the data "cluster" naturally into groups of units that are more related to each other than they are the rest of the data. In the first part of the course we will learn about Bayesian statistical methods. In the second part we will relate multilevel and hierarchical models to other areas of statistics, and in the third part of the course we will build and apply these models using a variety of data sets and examples.

Prerequisite: 36-401

**36-464 Topics in Statistics: Applied Multivariate Methods**

Intermittent: 9 units

This course is an introduction to applied multivariate methods. Topics include a discussion of the multivariate normal distribution, the multivariate linear model, repeated measures designs and analysis, principle component and factor analysis. Emphasis is on the application and interpretation of these methods in practice. Students will use at least one statistical package.

Prerequisite: 36-401

**36-465 Topics in Statistics: Data Mining**

Intermittent: 9 units

The course will focus on how to construct hypotheses from a large data set and confirm them statistically. Exploratory methods include discriminant analysis, principal component analysis, projection pursuit, clustering, and nonparametric density estimation. Confirmatory methods include confidence intervals, posterior distributions, and Bayes factors. In addition, students will learn how to think in terms of probabilistic models and use data mining software effectively. Some computer programming required. Pre-requisites: 36401 (grade of at least C) or permission from instructor.

Prerequisite: 36-401

**36-490 Undergraduate Research**

Spring: 9 units

This course is designed to give undergraduate students experience using statistics in real research problems. Small groups of students will be matched with clients and do supervised research for a semester. Students will gain skills in approaching a research problem, critical thinking, statistical analysis, scientific writing, and conveying and defending their results to an audience. Eligible students will receive information about the application processes for this course early in the fall.

Prerequisite: 36-401

Corequisite: 36-402

**36-625 Probability and Mathematical Statistics**

Fall: 12 units

This course is a rigorous introduction to the mathematical theory of probability, and it provides the necessary background for the study of mathematical statistics and probability modeling. A good working knowledge of calculus is required. Topics include combinatorial analysis, conditional probability, generating functions, sampling distributions, law of large numbers, and the central limit theorem. Students studying Computer Science, or considering graduate work in Statistics or Operations Research, should carefully consider taking this course instead of 36-225 after consultation with their advisor. Not open to students who have received credit for 36-217 or 36-225. Prerequisite: 21-122 and 21-241 and (21-256 or 21-259).

Prerequisites: 21-118 or 21-122 or 21-123 or 21-256

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