Linguistics 251: Probabilistic Methods in Linguistics (Fall 2010)

Instructor info

Instructor Roger Levy (
Office Applied Physics & Math (AP&M) 4220
Office hours Tuesdays 2-3pm, Thursdays 10-11am
Class Time TuTh 12:30-2pm
Class Location AP&M 4301
Class webpage

Course Description

This course is about probabilistic approaches to language knowledge, acquisition, and use. Today, studying language from a probabilistic perspective requires mastery of the fundamentals of probability and statistics, as well as familiarity with more recent developments in probabilistic modeling. In this course we'll move quickly through basic probability theory, then cover fundamental ideas in statistics—parameter estimation and hypothesis testing. We'll then cover a fundamental class of probabilistic models—the linear model—which as a side effect will familiarize you with the most widely used tools in statistics: linear regression, analysis of variance (ANOVA), and generalized linear models (including logistic regression). We'll cover these topics using both frequentist methods (what you need to use in order to write publishable data analyses) and Bayesian methods (which are becoming increasingly popular in all sorts of settings, especially in cognitive modeling of language). We'll then move on to the more advanced topic of hierarchical (a.k.a. multilevel or mixed-effects) modeling, and perhaps even a bit of probabilistic grammars if we have a chance.

The course will involve a hands-on approach to data, and we'll be using the open-source R programming language (and a bit of JAGS, which interfaces nicely with R, for Bayesian modeling). You'll learn the basics of data visualization and statistical analysis in R, and the class will involve periodic programming practica to ensure that your R programming questions are adequately addressed. Transcripts of programming practica will also be put up online. I encourage you to download R here as soon as you can, get it running on your own computer, and go through the R tutorial found in Chapter 1 of Harald Baayen's new book, or this hands-on introduction to R. You can also download JAGS here.

Reading material

The primary text for this course will be a book that I'm currently in the process of writing, Probabilistic Models in the Study of Language. The current draft is always available here. The goal is to go from the beginning through to the material in Chapter 8.


Week Day Topic Reading Materials Homework Assignments
Week 0 23 Sep Introduction and motivating material; Fundamentals of probability theory: probability spaces, conditional probability Chapter 2.1-2.5 Introduction/Motivation Slides HW 1
Week 1 28 Sep Bayes' rule; discrete random variables; the Bernoulli and multinomial distributions; cumulative density functions
30 Sep Continuous random variables; the uniform distribution; expectation and variance; Chapter 2.6-2.8
Week 2 5 Oct The normal distribution Chapter 2.9 Homework 2; Peterson & Barney's vowel dataset
7 Oct Estimating probability densities; first R practicum Chapter 2.10
Week 3 12 Oct First R practicum R transcript
14 Oct Joint probability distributions; marginalization; linearity of the expectation; covariance Chapter 3.1-3.4 R transcript
Week 4 19 Oct Correlation; the binomial distribution; multivariate normal distributions Chapter 3.5 R transcript Homework 3; brown-counts-lengths-nsyll file for HW 3
21 Oct Introductory parameter estimation; consistency, bias, and variance of estimators Chapter 4.1-4.2
Week 5 26 Oct The method of maximum likelihood Chapter 4.3
28 Oct Bayesian parameter estimation and density estimation Chapter 4.4-4.5 Homework 4
Week 6 2 Nov Bayesian confidence intervals and hypothesis testing Chapter 5.1-5.2
4 Nov Frequentist confidence intervals and hypothesis testing Chapter 5.3-5.4 Homework 5; spillover_word_rts data file for Homework 5
Week 7 9 Nov Intro to generalized linear models: linear models Chapter 6.1-6.2
11 Nov Veteran's day, no class
Week 8 16 Nov Linear models II Chapter 6.3-6.5 R transcript
18 Nov Linear models III R transcript
Week 9 23 Nov Analysis of Variance I Chapter 6.6
25 Nov Thanksgiving vacation, no class
Week 10 30 Nov Analysis of Variance II Homework 6; Problem 1 dataset; Problem 2 dataset
2 Dec Logit models Chapter 6
Finals 10 Dec Final projects due!


If you are taking the course for credit, there are four things expected of you:

1. Regular attendance in class.

2. Doing the assigned readings and coming ready to discuss them in class.

3. Doing several homework assignments to be assigned throughout the quarter. Email submission of the homework assignments is encouraged, but please send it to instead of to me directly. If you send it to me directly I may lose track of it.

You can find some guidelines on writing good homework assignments here. The source file to this PDF is here.

4. A final project which will involve the analysis and/or modeling of some dataset, either your own or a "standard" dataset that I will provide. Guidelines for the final project can be found here.

Mailing List

There is a mailing list for this class, Please subscribe to the mailing list by filling out the form at! We'll use it to communicate with each other.

R linguistics programming help

For this class I'll be maintaining an FAQ for our use of R. Read the FAQ here.

I also run the R-lang mailing list. I suggest that you subscribe to it; it's a low-traffic list and is a good clearinghouse for technical and conceptual issues that arise in the statistical analysis of language data.

In addition, the searchable R mailing lists are likely to be useful.

Background materials

In addition to my own textbook, there are lots of new and useful books for statistics, both in linguistics and more generally. We may be making direct use of some of them. Also, it's always good to read about the same idea or method as described by multiple authors. Here are some sources:

Harald Baayen's textbook Analyzing Linguistic Data. A Practical Introduction to Statistics. University Press. It's available online here. — get this free while it's still online! Or get it on Amazon.

Keith Johnson's book on quantitative methods in linguistics ($40 on Amazon; no longer available as a free download)

Shravan Vasishth's book draft: The foundations of statistics: A simulation-based approach (free download)

John Rice's Mathematical Statistics and Data Analysis — a good general book for introductory statistics (mostly classical).

David MacKay's Information Theory, Inference, and Learning Algorithms (free download of a first-rate published book!!!)

Chapter 2 of Manning & Schuetze