Course Meeting Times

Lectures: 2 sessions / week, 1.5 hours / session

Welcome to ESD.86, Models, Data, Inference for Socio-Technical Systems! This subject is part of the ESD PhD core, following the ESD doctoral seminar ESD.83 and requiring a solid undergraduate subject in applied probability as a prerequisite. At MIT the best prerequisite would be 6.041/6.431. With your help, this subject will be a great learning experience exposing you to interesting ideas, challenging you to think deeply, and providing skills useful in professional practice.

This is the first offering of this course, and is a work in progress. The instructors welcome suggestions for improvement. Please submit your suggestions via the OCW feedback form.

Course Objectives

ESD.86 is a required subject for all ESD doctoral students. Its aim is to develop proficiency in developing and testing two types of models of systems operating under uncertainty:

  1. Axiomatic models, in which reasonable assumptions based on observations and/or independent logic are stated a priori, and the resulting probabilistic model is developed axiomatically. There are no statistics in this approach. This is applied probabilistic modeling. The process resembles processes carried out by physicists, engineers and operations researchers.
  2. Statistical models, requiring acquisition of data and testing hypotheses of alternative models, estimating parameters values, making other inferences, etc.

We hope to show the strong linkages between applied probability and statistics in this subject. We believe that both types of modeling will be important in the research of most ESD doctoral students.


ESD.83 and 6.041

Class Sessions

There are two 90-minute class sessions each week. We expect you to be present at these sessions and to participate thoughtfully. At the end of each week, our TA will offer an optional, guided office hour in which he will answer questions about that week’s material and work through illustrative problems. Depending on how many students show up, this session may resemble a recitation, a tutorial or a one-on-one office hour’s session.


Two books are recommended but not required for this class.

Wu, C. F. Jeff, and Michael Hamada. Experiments: Planning, Analysis, and Parameter Design Optimization. New York, NY: J. Wiley & Sons, 2000. ISBN: 9780471255116.

Larson, Richard C., and Amedeo R. Odoni. Urban Operations Research. 2nd ed. Belmont, MA: Dynamic Ideas, 2007. ISBN: 9780975914632. (A version of this text is also available online.)

Additional readings from other sources will be assigned during the term.

Weekly Contest

Each week there will be a contest relating to the worst use, misuse or abuse of statistics and probabilistic reasoning in the media - press, TV, blogs, radio, magazines, etc. Examples could be related to interpretations of statistical studies, or proposed new systems in which statistics plays a large role (here, likely unintended consequences of the ‘reform’ would be acceptable as part of the submission), etc.

Each Monday we will ask students to submit their nomination for the week. On Wednesday, after the teaching staff has had time to review the candidates, the ‘winner’ will be announced. This effort will be viewed as part of class participation. Plus winners will get the benefit of the doubt if their final grade is border-line. We intend for this to be both fun and educational.

Term Project

There will be term projects. We have reserved the last two class periods for presentation of the projects. Details of the projects will be presented by end of February.


Computation is essential to modern analysis of systems operating under uncertainty. However, it is not a primary objective of this subject to develop your proficiency with any particular software tool. We have developed assignments, especially later in the subject, that require substantial computation, but we leave it to each student to select the software to use. Many of the computations that need to be carried out are statistical or probabilistic in nature. For example, one may need to generate samples drawn from a normally distributed population or may need to compute the standard deviation of a large data set or plot a histogram. A good choice for doing such tasks is MATLAB® and the associated Statistics Toolbox. Similar capabilities are embedded in Mathcad®, Maple®, and Mathematica®, as well as other software. One might be able to do all the assignments in a spreadsheet like Microsoft® Excel or QuattroPro®, but such tools may also limit the depth of the analysis that can be achieved. The assignments can also be done using programming language like C or FORTRAN, but this would probably be an inefficient use of time due to the needed coding. For those on campus, note that MATLAB® is available for use through the campus network. A further consideration in selecting computer tools for use in this subject is the level of support the teaching staff can provide. Prof. Frey can generally provide help with MATLAB®, MathCad®, MiniTab®, and Microsoft® Excel.

Note on Submission of Work

The manner in which you present your work can be just as important (and in some cases more so) than the overall approach manifested within the response. Be sure to clearly explain your work, the methods used, and the underlying assumptions. Such practices make it possible for us to fairly assess your work and happen also to be good practices for documenting work in industry.

Late Policy

It is expected that responses to assignments will be submitted on the due date and time noted on the assignment. The usual policy for late assignments is that a letter grade is lost per day late. In the case of unusual circumstances or unavoidable conflicts, please contact Prof. Larson or Prof. Frey to discuss the details and explore alternatives.

Time Commitment

The units on an MIT subject correspond to the time that an adequately prepared student is expected to spend in a normal week. This is divided into three numbers associated with the subject (X-Y-Z) with X being class time, Y being laboratory time, and Z being work outside of class. The numbers associated with ESD.86 are (3-0-9) making this a 12-unit subject.


Your grade in ESD.86 will be determined based on your performance on homework, quizzes, a term project, and class participation as described in the table below:

Homework (6 assignments) 40%
Quizzes (2) 30%
Class participation 5%
Term project 25%


This is a doctoral subject, and we expect everyone who works hard in the subject to receive either an A or a B.



Introduction and overview

3-door problem

Prof. Richard C. Larson and Prof. Daniel D. Frey  

Analyzing a probability problem

Probability mass functions

Prof. Richard C. Larson  

Broken stick problem

Working in sample space

Prof. Richard C. Larson  
4 Pedestrian crossing problem Prof. Richard C. Larson Homework 1 due
5 Random incidence: A major source of selection bias Prof. Richard C. Larson  
6 Random incidence and more Prof. Richard C. Larson  
7 Spatial models Prof. Richard C. Larson Homework 2 due
8 Markov processes and their application to queueing, part 1 Prof. Richard C. Larson  
9 Markov processes and their application to queueing, part 2 Prof. Richard C. Larson Homework 3 due
10 Queueing and transitions: Sampling from distributions, Gauss Prof. Richard C. Larson  
11 Derived distributions to statistics Aman Chawla (guest lecturer) Homework 4 due

The Queue Inference Engine and the psychology of queueing

Beyond the physics of queueing

Prof. Richard C. Larson  
  Quiz 1    
13 The Weibull distribution and parameter estimation Prof. Daniel D. Frey  
14 Hypothesis testing Prof. Daniel D. Frey  
15 Descriptive statistics and statistical graphics Prof. Daniel D. Frey  
16 Regression Prof. Daniel D. Frey Homework 5 due
17 Analysis of variance, with discussion of Bayesian and frequentist statistics Prof. Daniel D. Frey  
18 Multiple regression Prof. Daniel D. Frey  

Design of experiments, part 1

Design of experiments, part 2

Prof. Daniel D. Frey Homework 6 due
20 Design of computer experiments Prof. Daniel D. Frey  
21 Closure - Threats to validity of inference Prof. Daniel D. Frey  
  Quiz 2    
22 Final presentations 1    
23 Final presentations 2    


Academic Honesty

The fundamental principle of academic integrity is that one must fairly represent the source of the intellectual content of the work one submits for credit. Students are trusted to adhere to this principle and its meaning in the context of this subject as subsequently explained. Official Institute policy regarding academic honesty can be found in the current Bulletin under “Academic Procedures and Institute Regulations”.

What is the policy on examinations? The examinations in this subject are to represent individual work. You may not receive any help from other students or any other individuals.

What about homework assignments? Can we work together? We encourage students to work together in this subject to understand the home assignments and to learn in general. There is much to be gained in sharing the learning process. However, the final submission should represent your own expression of the final response to the assignment and not a copy of someone else’s expression thereof, whether directly from a person or as recorded on paper (e.g. a book) or electronically (e.g. on a Web site). Furthermore, you must fairly represent the authorship of the intellectual content of the work you submit for credit by acknowledging the contribution of sources (e.g., books, Web sites) you consult in the process of completing assignments. In addition, at the end of each assignment on which you collaborated with other students, you must cite the students and the interaction. The purpose of this is to acknowledge their contribution to your work. Some examples follow:

  1. You discuss concepts, approaches and methods which could be applied to a homework assignment before starting your write-up. This process is encouraged. You are not required to make a written acknowledgment of this type of interaction.
  2. After working an assignment independently, you compare responses with another student which confirms your results and response. You should acknowledge that the other student’s write-up was used to check your own. No credit will be lost if the response is correct, the acknowledgment is made, and no direct copying of the other response is involved.
  3. After working an assignment independently, you compare responses with another student which alerts you to an error in your own work which you then correct. You should state at the end of your submission that you corrected your error on the basis of checking responses with the other student. No credit will be lost if the response is correct, the acknowledgment is made, and no direct copying of the other response is involved.
  4. You and another student work through an assignment together exchanging ideas as the effort progresses. You both should state at the end of your individual submissions that you worked jointly. No credit will be lost if the responses are correct, the acknowledgment is made, and the assignment write-up is independent.
  5. You copy all or part of an assignment write-up from a reference such as a textbook or past solution (this is in contrast to referring to such a reference and developing the solution yourself). You must cite the reference. Partial credit will be given, since there is some educational value in reading and understanding the solution.
  6. You copy verbatim all or part of a write-up from another student. You must cite the person by name. Very little partial credit will be given.
  7. Verbatim copying of any material which you submit for credit without reference to the source is considered to be academically dishonest.

Course Info

Learning Resource Types

assignment_turned_in Problem Sets with Solutions
grading Exams
notes Lecture Notes
assignment_turned_in Written Assignments with Examples