Introduction to Statistical Science (formerly MATH 0116) A practical introduction to statistical methods and the examination of data sets. Computer software will play a central role in analyzing a variety of real data sets from the natural and social sciences. Topics include descriptive statistics, elementary distributions for data, hypothesis tests, confidence intervals, correlation, regression, contingency tables, and analysis of variance. The course has no formal mathematics prerequisite, and is especially suited to students in the physical, social, environmental, and life sciences who seek an applied orientation to data analysis. (Not open to students who have taken BIOL 0211 or ECON 0111 (formerly ECON 0210) or PSYC 0201)

Introduction to Data Science (formerly MATH 0118) In this course students will gain exposure to the entire data science pipeline: forming a statistical question, collecting and cleaning data sets, performing exploratory data analyses, identifying appropriate statistical techniques, and communicating the results, all the while leaning heavily on open source computational tools, in particular the R statistical software language. We will focus on analyzing real, messy, and large data sets, requiring the use of advanced data manipulation/wrangling and data visualization packages. Students will be required to bring alaptop (owned or college-loaned) to class as many lectures will involve in-class computational activities. (formerly MATH 0216) 3 hrs lect./disc.

Introduction to Statistical and Data Sciences An introduction to statistical methods and the examination of data sets for students with a background in calculus. Topics include descriptive statistics, elementary distributions for data, hypothesis tests, confidence intervals, and regression. Students develop skills in data cleaning, wrangling, visualization, and model fitting using the Statistical Software R.  Emphasis will be placed on reproducibility. (MATH 0121 or equivalent, or by placement.) (Not open to students who have taken MATH 0116, MATH 0118, ECON 0111 (formerly ECON 0210), PSYC 0201, STAT 0116, STAT 0118, BIOL 1230, ECON 1230, ENVS 1230, FMMC 1230, HARC 1230, JAPN 1230, LNGT 1230, NSCI 1230, MATH 1230, SOCI 1230, LNGT 1230, PSCI 1230, WRPR 1230, or GEOG 1230.)

Regression Theory and Applications (formerly MATH 0211) Regression is a popular statistical technique for making predictions and for modeling relationships between variables.  In this course we will discuss the theory and practical applications of linear, log-linear, and logistic regression models.  Topics include least squares estimation, coding for categorical predictors, analysis of variance, and model diagnostics.  We will apply these concepts to real datasets using R, a statistical programming language. (Concurrent or prior MATH 0200, and STAT 0116 or STAT 0201 or PSYC 0201 or ECON 0111) (Not open to students who have taken ECON 0211.) 3 hrs lect./disc.

Statistical Learning (formerly MATH 0218) This course is an introduction to modern statistical, machine learning, and computational methods to analyze large and complex data sets that arise in a variety of fields, from biology to economics to astrophysics. The theoretical underpinnings of the most important modeling and predictive methods will be covered, including regression, classification, clustering, resampling, and tree-based methods. Student work will involve implementation of these concepts using open-source computational tools.

Time Series Analysis An introduction to statistical methods for time series analysis for students with a background in statistics. Topics include time series regression, auto-regressive models, moving average models, and ARIMA models, with an emphasis on estimation and forecasting with real data applications. Students will develop skills visualizing and summarizing serially correlated data structures and fitting time series models in various statistical software packages, including R and Julia.

History of Statistics In this course we explore how statistical ideas developed historically, beginning with the emergence of data collection in the late 17th century and concluding with modern reflections on big data and AI. Through discussion of primary source material, we examine how key individuals and historical problems culminate in the creation of statistical methods. In the course we recreate historical experiments, analyses, and visualizations using modern tools, gaining insight into how concepts such as uncertainty, error, evidence, and inference evolved over time. We will examine ethical questions that can arise from data collection and analysis and reflect on how historical perspectives inform the use of statistics today.

Probability An introduction to the concepts of probability and their applications, covering both discrete and continuous random variables. Probability spaces, elementary combinatorial analysis, densities and distributions, conditional probabilities, independence, expectation, variance, weak law of large numbers, central limit theorem, and numerous applications.

Statistical Inference       An introduction to the mathematical methods and applications of statistical inference using both classical methods and modern resampling techniques. Topics will include: permutation tests, parametric and nonparametric problems, estimation, efficiency and the Neyman-Pearsons lemma. Classical tests within the normal theory such as F-test, t-test, and chi-square test will also be considered. Methods of linear least squares are used for the study of analysis of variance and regression. There will be some emphasis on applications to other disciplines. This course is taught using R.

Randomness and Strategy in Video Games Colloquially, randomness is the lack of predictability and pattern. In statistics, randomness describes events whose outcomes are unknown but whose behavior is characterized by probability distributions. In this course, we will explore a variety of implementations of both input and output randomness in modern video games and assess how they inform strategy and affect the user experience. Do random events yield a variety of strategies, a dominant one, or no strategy at all? How does randomness relate to user experience? We will explore the answers to these questions and more in an exploration of the intersection of statistics and video game design.

Stochastic Processes Stochastic processes are mathematical models for random phenomena evolving in time or space. This course will introduce important examples of such models, including random walk, branching processes, the Poisson process and Brownian motion. The theory of Markov chains in discrete and continuous time will be developed as a unifying theme. Depending on time available and interests of the class, applications will be selected from the following areas: queuing systems, mathematical finance (Black-Scholes options pricing), probabilistic algorithms, and Monte Carlo simulation.

Bayesian Statistics (formerly MATH 0412) In this course, we will learn about the Bayesian paradigm of statistics, in which one’s inferences about parameters or hypotheses are updated as evidence accumulates. The goals of the course include understanding basic concepts of Bayesian inference; deriving posterior distributions; assessing the adequacy of Bayesian models; and effectively communicating results. Topics covered include one-parameter models, conjugacy, and Gibbs samplers. Real-world data and applications will feature heavily in this course. (concurrent or prior STAT 0311) 2.5 hr. lect.

Spatial Statistics In this course students will be introduced to statistical methodology for data that are collected over space. Following a brief introduction to Bayesian inference and probabilistic programming languages (Stan, NIMBLE, and JAGS), we will investigate how spatial dependence challenges classical modeling assumptions. We will learn about spatial correlation and covariance functions, Poisson point processes, methods for areal data, and methods for geostatistical data including Gaussian process regression and ordinary Kriging. Students will also develop skills in visualizing and summarizing spatially correlated data structures, learn to fit spatial models in R, and develop the theory of spatial statistics. (STAT 0310, STAT 0311 concurrently).

Advanced Probability Seminar An introduction to the mathematical foundations of Probability for students who have completed work in Probability and Real Analysis.  The central ideas correspond to the Lebesgue theory of measure and integration.  Probability provides additional perspective and motivates intriguing applications of the theory, which students will explore in their final projects.  Working independently and in small groups, students will gain experience reading advanced sources and communicating their insights through expository writing and oral presentations.  This course fulfills the capstone senior work requirement for the mathematics major.

Statistical Consulting In this course we will work with community partners to solve real-world problems using modern statistical and data science techniques. Students will work in small groups to translate research questions into actionable analysis and visualizations. Students will select a project of interest from a subset of community partners, maintain contact and collaboration with the community partner, and present their findings in a final symposium.

Advanced Hierarchical Modeling (formerly MATH 0712) Hierarchical or multilevel models provide a principled way to model data that are naturally grouped in order to take advantage of the relationship between observations in the same group, but also allow for borrowing of information across groups. In this senior seminar, we will introduce a variety of multilevel models, with a balance between the theoretical and conceptual foundations, as well as implementation and interpretation of the results. This seminar will focus on multilevel linear and logistic models. Every student will write a senior capstone paper.

Data Science Across Disciplines In this course, we will gain exposure to the entire data science pipeline—obtaining and cleaning large and messy data sets, exploring these data and creating engaging visualizations, and communicating insights from the data in a meaningful manner. During morning sessions, we will learn the tools and techniques required to explore new and exciting data sets. During afternoon sessions, students will work in small groups with one of several faculty members on domain-specific research projects in Anthropology, Biology, Classics, Political Science, and Statistics. This course will use the R programming language. No prior experience with programming is necessary. (Not open to students who have taken STAT 0118, STAT 0201, ANTH 1230, BIOL 1230, CLAS 1230, ECON 1230, ECSC 1230, ENVS 1230, FMMC 1230, GEOG 1230, HARC 1230, HIST 1230, JAPN 1230, LNGT 1230, MATH 1230, NSCI 1230, PSCI 1230, SOCI 1230, STAT 1230, or WRPR 1230.)  ANTH/LNGT 1230: In this section we will explore indigenous political voice in unexpected places. The data we will analyze will consist of bilingual Apache-English and Maidu-English stories, songs and speeches originally recorded by anthropological linguists in the early twentieth century as examples of traditional culture. Students will use R to search this corpora for how indigenous contributors were also making claims on the future in their address to the researcher and to wider anticipated audiences.  BIOL/ECSC 1230: In this section we will work with data collected by elephant seals equipped with oceanographic instruments in the Southern Ocean. Depending on your interests, you can approach the project from different angles: students focusing on biology will explore where the seals travel and what drives their movements, while those interested in earth science will investigate the temperature and salinity profiles gathered during their dives. Working in teams, you’ll combine these perspectives to build a fuller picture of both seal ecology and the oceanographic processes that shape their environment. Along the way, you’ll practice manipulating and visualizing different types of data including maps of seal tracks, temperature and salinity profiles, and cross-sections of ocean properties. We will also bring in satellite  and autonomous float data to place seal activity and the data they collect in a broader context. By the end, you’ll have a sense of how these different data sources fit together and what unique insights we gain from using seals as oceanographers.  CLAS 1230: In this section students will gain hands-on experience with a variety of natural language processing and text mining techniques by exploring the writings of the ancient historian Plutarch, who lived during the first and second centuries AD.  We will focus on the biographies of "great men" in Plutarch’s Lives, which chronicles the history, morals, and virtues of major figures who played parallel roles in ancient Greek and Roman society. The public domain English translation from Project Gutenberg will serve as our main corpus; however, students with a background or interest in Ancient Greek can work with the text in the original language. Using the R programming language, students will transform unstructured text into quantitative data for statistical analysis and morphosyntactic parsing. We will also apply machine learning models to our data to reveal underlying patterns in large amounts of text. No prior experience with R is necessary.  PSCI 1230: Who votes in elections? Who attends protests? Why? In this section we will use the tools of data science to explore these and other questions about political participation in the Americas. We will examine engagement in different forms of participation and the demographic, economic, social, and other factors that shape participation. The class will introduce students to the basics of survey research and the study of political participation.  Students will complete a final group project showcasing the concepts and tools learned in class.   STAT 1230: In this section students will dive into the world of data science by focusing on invasive species monitoring data. Early detection is crucial to controlling many invasive species; however, there is a knowledge gap regarding the sampling effort needed to detect the invader early. In this course, we will work with decades of invasive species monitoring data collected across the United States to better understand how environmental variables play a role in the sampling effort required to detect invasive species. Students will gain experience in the entire data science pipeline, but the primary focus will be on data scraping, data visualization, and communication of data-based results to scientists and policymakers.

Alex Lyford

Becky Tang

Bill Peterson

Casey Schine

Christian Stratton

Emily Malcolm-White

Evan Camrud

Meaghan Winder

Michael Czekanski

Steve Abbott

Read 177 reviews for Statistics courses at Middlebury College. Find the best Statistics professors and courses.  Discover your new major today!

I thought the projects/tests were very similar to what we did in class. At times, it was hard to pay attention since it was an 8am, but overall enjoyed my experience, although the topics were relatively difficult.

Professor Lyford is passionate about the course and always willing to help students out. The class has three oral exams based on projects. The class itself is very fun as it is incredibly interactive.

Alex is the man. He's super passionate and a great teacher. Course revolves around 3 homework assignments and some oral exams where you have a 15-20 minute chat with Alex about the homework and other statistics concepts you learn. A lot of the lectures are really fun, others are mainly just coding in R studio. Everything is group work and overall workload is very light. 