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Department of Statistics

Chris Genovese, Department Head
Paige Houser, Academic Advisor
Email: acadcoord@stat.cmu.edu
Department Office: Baker Hall 132

Uncertainty is inescapable: randomness, measurement error, deception, and incomplete or missing information complicate all our lives. Statistics is the science and art of making predictions and decisions in the face of uncertainty. Statistical issues are central to big questions in public policy, law, medicine, industry, computing, technology, finance, and science. Indeed, the tools of Statistics apply to problems in almost every area of human activity where data are collected.

Statisticians must master diverse skills in computing, mathematics, decision making, forecasting, interpretation of complicated data, and design of meaningful comparisons. Moreover, statisticians must learn to collaborate effectively with people in other fields and, in the process, to understand the substance of these other fields. For all these reasons, Statistics students are highly sought-after in the marketplace.

Recent Statistics majors at Carnegie Mellon have taken jobs at leading companies in many fields, including the National Economic Research Association, Boeing, Morgan Stanley, Deloitte, Rosetta Marketing Group, Nielsen, Proctor and Gamble, Accenture, and Goldman Sachs.  Other students have taken research positions at the National Security Agency, the U.S. Census Bureau, and the Science and Technology Policy Institute or worked for Teach for America.  Many of our students have also gone on to graduate study at some of the top programs in the country including Carnegie Mellon, the Wharton School at the University of Pennsylvania, Johns Hopkins, University of Michigan, Stanford University, Emory University, Yale University, Columbia University, and Georgia Tech.
 

The Department and Faculty

The Department of Statistics at Carnegie Mellon University is world-renowned for its contributions to statistical theory and practice. Research in the department runs the gamut from pure mathematics to the hottest frontiers of science. Current research projects are helping make fundamental advances in neuroscience, cosmology, seismology, finance, and genetics.

The faculty members are recognized around the world for their expertise and have garnered many prestigious awards and honors. (For example, three members of the faculty have been awarded the COPSS medal, the highest honor given by professional statistical societies.) At the same time, the faculty is firmly dedicated to undergraduate education. The entire faculty, junior and senior, teach courses at all levels. The faculty are accessible and are committed to involving undergraduates in research.

The Department augments all these strengths with a friendly, energetic working environment and exceptional computing resources. Talented graduate students join the department from around the world, and add a unique dimension to the department's intellectual life. Faculty, graduate students, and undergraduates interact regularly.
 

How to Take Part

There are many ways to get involved in Statistics at Carnegie Mellon:

  • The Bachelor of Science in Statistics in the Dietrich College of Humanities and Social Sciences (DC) is a broad-based, flexible program that helps you master both the theory and practice of Statistics. The program can be tailored to prepare you for later graduate study in Statistics or to complement your interests in almost any field, including Psychology, Physics, Biology, History, Business, Information Systems, and Computer Science.
  • The Minor (or Additional Major) in Statistics is a useful complement to a (primary) major in another Department or College. Almost every field of inquiry must grapple with statistical problems, and the tools of statistical theory and data analysis you will develop in the Statistics minor will give you a critical edge.
  • The Bachelor of Science in Economics and Statistics provides an interdisciplinary course of study aimed at students with a strong interest in the empirical analysis of economic data. Jointly administered by the Department of Statistics and the Undergraduate Economics Program, the major's curriculum provides students with a solid foundation in the theories and methods of both fields. (See Dietrich College Interdepartmental Majors as well as later in this section)
  • The Bachelor of Science in Statistics and Machine Learning is a program housed in the Department of Statistics in which students take courses focused on Machine Learning.
  • The Statistical and Mathematical Sciences Program (within the Science and Humanities Scholars Program) is an alternative path for the study of Statistics that is jointly administered by the Department of Mathematical Sciences and the Department of Statistics.
  • The Statistics Concentration and the OR and Statistics Concentration in the Mathematical Sciences Major (see Department of Mathematical Sciences) are jointly administered by the Department of Mathematical Sciences and the Department of Statistics.
  • There are several ongoing exciting research projects in the Department of Statistics, and the department enthusiastically seeks to involve undergraduates in this work. Both majors and non-majors are welcome.
  • Non-majors are eligible to take most of our courses, and indeed, they are required to do so by many programs on campus. Such courses offer one way to learn more about the Department of Statistics and the field in general.

Curriculum

Statistics consists of two intertwined threads of inquiry: Statistical Theory and Data Analysis. The former uses probability theory to build and analyze mathematical models of data in order to devise methods for making effective predictions and decisions in the face of uncertainty. The latter involves techniques for extracting insights from complicated data, designs for accurate measurement and comparison, and methods for checking the validity of theoretical assumptions. Statistical Theory informs Data Analysis and vice versa. The Statistics Department curriculum follows both of these threads and helps the student develop the complementary skills required.

Below, we describe the requirements for the Major in Statistics and the different categories within our basic curriculum, followed by the requirements for the Minor in Statistics and the requirements for the Major in Economics and Statistics.

Note: We recommend that you use the information provided below as a general guideline, and then schedule a meeting with a Statistics Undergraduate Advisor (email: acadcoord@stat.cmu.edu) to discuss the requirements in more detail, and build a program that is tailored to your strengths and interests.

B.S. in Statistics

Academic Advisor: Paige Houser
Faculty Advisor: Howard Seltman
Office: Baker Hall 132A
Email: acadcoord@stat.cmu.edu

Students in the Bachelor of Science program develop and master a wide array of skills in computing, mathematics, statistical theory, and the interpretation and display of complex data. In addition, Statistics majors gain experience in applying statistical tools to real problems in other fields and learn the nuances of interdisciplinary collaboration. The requirements for the Major in Statistics are detailed below and are organized by categories #1-#7.

1. Mathematical Foundations (Prerequisites)
29–39 units

Mathematics is the language in which statistical models are described and analyzed, so some experience with basic calculus and linear algebra is an important component for anyone pursuing a program of study in Statistics.

Calculus*:
Complete one of the following three sequences of mathematics courses at Carnegie Mellon, each of which provides sufficient preparation in calculus:

Sequence 1

21-111Calculus I10
21-112Calculus II10

and one of the following:

21-256Multivariate Analysis9
21-259Calculus in Three Dimensions9

Sequence 2

21-120Differential and Integral Calculus10

and one of the following:

21-256Multivariate Analysis9
21-259Calculus in Three Dimensions9

Note: Other sequences are possible, and require approval from the undergraduate advisor. 

Note: Passing the MSC 21-120 assessment test is an acceptable alternative to completing 21-120.

Linear Algebra**:
Complete one of the following three courses:

21-240Matrix Algebra with Applications10
21-241Matrices and Linear Transformations10
21-242Matrix Theory10

* It is recommended that students complete the calculus requirement during their freshman year.

**The linear algebra requirement needs to be completed before taking 36-401 Modern Regression

21-241 and 21-242 are intended only for students with a very strong mathematical background.

2. Data Analysis:
36–45 units

Data analysis is the art and science of extracting insight from data. The art lies in knowing which displays or techniques will reveal the most interesting features of a complicated data set. The science lies in understanding the various techniques and the assumptions on which they rely. Both aspects require practice to master.

The Beginning Data Analysis courses give a hands-on introduction to the art and science of data analysis. The courses cover similar topics but differ slightly in the examples they emphasize. 36-201 draws examples from many fields and satisfies the H&SS College Core Requirement in Statistical Reasoning. It is therefore the recommended course for students in the College. (Note: A score of 5 on the Advanced Placement (AP) Exam in Statistics may be used to waive this requirement). Other courses emphasize examples in business (36-207), engineering and architecture (36-220), and the laboratory sciences (36-247).

The Intermediate Data Analysis courses build on the principles and methods covered in the introductory course, and more fully explore specific types of data analysis methods in more depth.

The Advanced Data Analysis courses draw on students' previous experience with data analysis and understanding of statistical theory to develop advanced, more sophisticated methods. These core courses involve extensive analysis of real data with emphasis on developing the oral and writing skills needed for communicating results.

Sequence 1 (For students beginning their freshman or sophomore year)

Beginning*
Choose one of the following courses:

36-201Statistical Reasoning and Practice9
36/70-207Probability and Statistics for Business Applications9
36-220Engineering Statistics and Quality Control9
36-247Statistics for Lab Sciences9
*Or extra statistical elective

Note: Students who enter the program with 36-225 or 36-226 should discuss options with an advisor.  Any 36-300 or 36-400 level course that does not satisfy any other requirement for a Statistics Major and Minor may be counted as a Statistical Elective.

Intermediate
Choose one of the following courses

36-202Statistical Methods9
36/70-208Regression Analysis9
36-309Experimental Design for Behavioral and Social Sciences9
*Or extra statistical elective

Advanced
Choose one of the following courses:

36-303Sampling, Survey and Society9
36-315Statistical Graphics and Visualization9

Students can also take a second 36-46x (see section #5).

and take the following two courses:

36-401Modern Regression9
36-402Advanced Methods for Data Analysis9

Sequence 2 (For students beginning later in their college career)

Advanced
Choose two of the following courses:

36-303Sampling, Survey and Society9
36-315Statistical Graphics and Visualization9
36-461Special Topics: Statistical Methods in Epidemiology9
36-462Special Topics: Data Mining9
36-463Special Topics: Multilevel and Hierarchical Models9
36-464Special Topics: Applied Multivariate Methods9

and take the following two courses:

36-401Modern Regression9
36-402Advanced Methods for Data Analysis9
3. Probability Theory and Statistical Theory:
18 units

The theory of probability gives a mathematical description of the randomness inherent in our observations. It is the language in which statistical models are stated, so an understanding of probability is essential for the study of statistical theory. Statistical theory provides a mathematical framework for making inferences about unknown quantities from data. The theory reduces statistical problems to their essential ingredients to help devise and evaluate inferential procedures. It provides a powerful and wide-ranging set of tools for dealing with uncertainty.


To satisfy the theory requirement take the following two courses:

36-225Introduction to Probability Theory **9
and one of the following two courses:
36-226Introduction to Statistical Inference9
36-326Mathematical Statistics (Honors)9


**It is possible to substitute 36-217 or 21-325 for 36-225. (36-225 is the standard introduction to probability, 36-217 is tailored for engineers and computer scientists, and 21-325 is a rigorous Probability Theory course offered by the Department of Mathematics.)

Comments:

(i) In order to be a Major or a Minor in good standing, a grade of at least a C is required in 36-225, 36-226 and 36-401. In particular, a grade of C or higher is required in order to be able to continue in the major.

(ii) In special cases, and in consultation with the Statistics Advisor, the theory requirement can be satisfied by taking the single graduate level class 36-625 Probability and Mathematical Statistics I, which is much more mathematically rigorous. This option should be considered by strong Statistics Majors who are also majoring in Computer Science, Operations Research, or Mathematics and/or who are considering graduate study in Statistics. This option does require special permission from the advisor. Students who end up satisfying the theory requirement by taking the (single) course 36-625 are required  take  an additional statistics elective  (see category #6, Statistical Electives, below).

4. Statistical Computing:
9 units
36-350Statistical Computing *9

*A higher level Computer Science course approved by your Statistics advisor may be used as a substitute.

5. Special Topics
9 units

The Statistics Department offers advanced courses that focus on specific statistical applications or advanced statistical methods. These courses are numbered 36-46x (36-461, 36-462, etc.). Two of these courses will be offered every year, one per semester. Past topics included Statistical Learning, Data Mining, Statistics and the Law, Bayesian Statistics, Nonparametric Statistics, Statistical Genetics, Multilevel and Hierarchical Models, and Statistical Methods in Epidemiology. The objective of the course is to expose students to important topics in statistics and/or interesting applications which are not part of the standard undergraduate curriculum.

To satisfy the Special Topics requirement choose one of the 36-46x courses (which are 9 units).

Note: All 36-46x courses require 36-401 as a prerequisite or instructor permission.

6. Statistical Elective:
9–10 units

Students are required to take one* elective which can be within or outside the Statistics Department. Courses within statistics can be any 300 or 400 level course (that is not used to satisfy any other requirement for the statistics major). 

The following is a partial list of courses outside statistics that qualify as electives as they provide intellectual infrastructure that will advance the student's understanding of statistics and its applications. Other courses may qualify as well; consult with the Statistics Undergraduate Advisor.

15-110Principles of Computing10
15-121Introduction to Data Structures10
15-122Principles of Imperative Computation10
21-127Concepts of Mathematics10
21-260Differential Equations9
21-292Operations Research I9
21-301Combinatorics9
21-355Principles of Real Analysis I9
80-220Philosophy of Science9
80-221Philosophy of Social Science9
80-310Formal Logic9
85-310Research Methods in Cognitive Psychology9
85-320Research Methods in Developmental Psychology9
85-340Research Methods in Social Psychology9
88-223Decision Analysis and Decision Support Systems9
88-302Behavioral Decision Making9

Note: Additional prerequisites are required for some of these courses. Students should carefully check the course descriptions to determine if additional prerequisites are necessary.

* Students who enter the program through 36-225 or 36-226 and skip the beginning data analysis course, or students who end up satisfying the theory requirement using the (single) course 36-625, are required to take two electives only one of which can be outside the Statistics Department. (In general, any waived requirement is replaced by a statistical elective.)

7. Tracks*:
Self-Defined Concentration Area (with advisor's approval)
36 units

The power of Statistics, and much of the fun, is that it can be applied to answer such a wide variety of questions in so many different fields. A critical part of statistical practice is understanding the questions being asked so that appropriate methods of analysis can be used. Hence, a critical part of statistical training is to gain experience applying the abstract tools to real problems. The Concentration Area is a set of four related courses outside of Statistics that prepares the student to deal with statistical aspects of problems that arise in another field. These courses are usually drawn from a single discipline of interest to the student and are chosen in consultation with the Statistics Undergraduate Advisor. For example, students intending to pursue careers in public policy could take further courses in History or Economics, students intending to pursue careers in the health or biomedical sciences could take further courses in Biology or Chemistry, and students intending to pursue graduate work in Statistics could take further courses in advanced Mathematics.

Mathematical Statistics Track
46–52 units
21-127Concepts of Mathematics10
21-355Principles of Real Analysis I9
36-410Introduction to Probability Modeling9

And two of the following:

36-700Probability and Mathematical Statistics I12
36-705Intermediate Statistics12
21-228Discrete Mathematics9
21-257Models and Methods for Optimization
or
9
Operations Research I
21-301Combinatorics9
21-356Principles of Real Analysis II9
Statistics and Neuroscience Track
45–54 units
85-211Cognitive Psychology9
85-219Biological Foundations of Behavior9

And three electives (at least one from Methodology and Analysis and at least one from Neuroscientific Background):

Methodology and Analysis

36-625Probability and Mathematical Statistics I12
36-626Probability and Mathematical Statistics II12
10-601Introduction to Machine Learning12
18-290Signals and Systems12
85-314Cognitive Neuroscience Research Methods9
42/86-631Neural Data Analysis9

Neuroscientific Background

03-362Cellular Neuroscience9
03-363Systems Neuroscience9
15-386Neural Computation9
85-355Introduction to Cognitive Neuroscience9
85-414Cognitive Neuropsychology9
85-419Introduction to Parallel Distributed Processing9

* Note: The concentration/track requirement is only for students whose primary major is statistics and have no other additional major or minor. The requirement does not apply for students who pursue an additional major in statistics.

Total Number of Units for the Major:146-175*
Total Number of Units for the Degree:360

* Note: This number can vary depending on the calculus sequence a student takes. In addition this number includes the 36 units of the “Concentration Area” category which may not be required (see category 6 above for details).

Recommendations

Students in the College of Humanities and Social Sciences who wish to major or minor in Statistics are advised to complete both the calculus requirement (one Mathematical Foundations calculus sequence) and the Beginning Data Analysis course 36-201 Statistical Reasoning and Practice by the end of their Freshman year.

The linear algebra requirement is a prerequisite for the course 36-401. It is therefore essential to complete this requirement during your junior year at the latest! 

Recommendations for Prospective PhD Students

Students interested in pursuing a PhD in Statistics or Biostatistics (or related programs) after completing their undergraduate degree are strongly recommended to pursue the Mathematical Statistics Track.

Additional Major in Statistics

Students who elect Statistics as a second or third major must fulfill all Statistics degree requirements except for the Concentration Area requirement.  Majors in many other programs would naturally complement a Statistics Major, including Tepper's undergraduate business program, Social and Decision Sciences, Policy and Management, and Psychology.

With respect to double-counting courses, it is departmental policy that students must have at least five statistics courses that do not count for their primary major. If students do not have at least five, they typically take additional advanced electives.

Students are advised to begin planning their curriculum (with appropriate advisors) as soon as possible. This is particularly true if the other major has a complex set of requirements and prerequisites or when many of the other major's requirements overlap with the requirements for a Major in Statistics.

Research

One goal of the Statistics program is to give students experience with statistical research. There is a wide variety of ongoing research projects in the department, and students have several opportunities to get involved in a project that interests them.

Before graduation, students are encouraged to participate in a research project under faculty supervision. Students can do this through projects in specific courses (such as 36-303), through an independent study, or through a summer research position.

Qualified students are also encouraged to participate in an advanced research project through 36-490 Undergraduate Research or independent study under the supervision of a Statistics faculty advisor.  Students who maintain a quality point average of 3.25 overall may also apply to participate in the H&SS Senior Honors Program.

Sample Programs

The following sample programs illustrate three (of many) ways to satisfy the requirements of the Statistics Major. However, keep in mind that the program is flexible enough to support many other possible schedules and to emphasize a wide variety of interests.

The first schedule uses calculus sequence 1, and 21-127 Concepts of Mathematics as a Statistical Elective outside of Statistics.

The second schedule is an example of the case when a student enters the program through 36-225 and 36-226 (and therefore skips the beginning data analysis course). The schedule uses calculus sequence 2, and includes two electives (36-315 and 36-410), both within the Statistics Department. This schedule has more emphasis on statistical theory and probability.

The third schedule is an example of the Mathematical Statistics track.

In these schedules, C.A. refers to Concentration Area courses.

Schedule 1
FreshmanSophomore
FallSpringFallSpring
36-201 Statistical Reasoning and Practice36-202 Statistical Methods21-127 Concepts of Mathematics36-315 Statistical Graphics and Visualization
21-111 Calculus I21-112 Calculus II21-256 Multivariate AnalysisC.A.

JuniorSenior
FallSpringFallSpring
36-225 Introduction to Probability Theory36-226 Introduction to Statistical Inference36-401 Modern Regression36-402 Advanced Methods for Data Analysis
21-240 Matrix Algebra with ApplicationsC.A.C.A.36-46x Special Topics
36-350 Statistical ComputingC.A.
Schedule 2
FreshmanSophomore
FallSpringFallSpring
21-120 Differential and Integral Calculus21-256 Multivariate Analysis36-225 Introduction to Probability Theory36-226 Introduction to Statistical Inference
21-240 Matrix Algebra with Applications

JuniorSenior
FallSpringFallSpring
36-350 Statistical Computing36-315 Statistical Graphics and Visualization36-46x Special Topics36-410 Introduction to Probability Modeling
36-401 Modern Regression36-402 Advanced Methods for Data AnalysisC.A.C.A.
C.A.C.A.
Schedule 3
FreshmanSophomore
FallSpringFallSpring
21-120 Differential and Integral Calculus21-256 Multivariate Analysis36-225 Introduction to Probability Theory36-226 Introduction to Statistical Inference
21-127 Concepts of Mathematics21-260 Differential Equations21-241 Matrices and Linear Transformations

JuniorSenior
FallSpringFallSpring
36-350 Statistical Computing36-315 Statistical Graphics and Visualization36-46x Special Topics36-410 Introduction to Probability Modeling
36-401 Modern Regression36-402 Advanced Methods for Data Analysis21-355 Principles of Real Analysis I
21-228 Discrete Mathematics21-341 Linear Algebra

B.S. in Economics and Statistics

Academic Advisor: Paige Houser
For questions about Economics courses contact: Carol Goldburg or Kathleen Conway
For questions about Statistics courses contact: Rebecca Nugent or Paige Houser

Office: Baker Hall 132A
Email: acadcoord@stat.cmu.edu

The Major in Economics and Statistics provides an interdisciplinary course of study aimed at students with a strong interest in the empirical analysis of economic data. With joint curriculum from the Department of Statistics and the Undergraduate Economics Program, the major provides students with a solid foundation in the theories and methods of both fields. Students in this major are trained to advance the understanding of economic issues through the analysis, synthesis and reporting of data using the advanced empirical research methods of statistics and econometrics. Graduates are well positioned for admission to competitive graduate programs, including those in statistics, economics and management, as well as for employment in positions requiring strong analytic and conceptual skills - especially those in economics, finance, education, and public policy.

The requirements for the B.S. in Economics and Statistics are the following:

I. Prerequisites

38-39 units

1. Mathematical Foundations
38-39 units

Calculus

21-120Differential and Integral Calculus10

and one of the following three:

21-122Integration and Approximation10
21-127Concepts of Mathematics10
21-257Models and Methods for Optimization9

and one of the following:

21-256Multivariate Analysis9
21-259Calculus in Three Dimensions9

Note: Passing the MSC 21-120 assessment test is an acceptable alternative to completing 21-120.

Note: Taking both 21-111 and 21-112 is equivalent to 21-120. The Mathematical Foundations total is then 48-49 units. The Economics and Statistics major would then total 201-202 units.

Linear Algebra

One of the following three courses:

21-240Matrix Algebra with Applications10
21-241Matrices and Linear Transformations10
21-242Matrix Theory10

Note: 21-241 and 21-242 are intended only for students with a very strong mathematical background.

II. Foundations

18-27 units

2. Economics Foundations
9 units
73-100Principles of Economics9
3. Statistical Foundations
9-18 units

Sequence 1 (For students beginning their freshman or sophomore year)

36-201Statistical Reasoning and Practice9

and one of the following:

36-202Statistical Methods9
36-208Regression Analysis9
36-309Experimental Design for Behavioral and Social Sciences9
Or extra statistical elective**

*Acceptable equivalents for 36-201 are 36-207 (70-207), 36-220 and 36-247.

**Students who enter the program with 36-225/36-226 should discuss options with their advisors.

Sequence 2 (For students beginning later in their college career)

Advanced
Choose one of the following courses:

36-303Sampling, Survey and Society9
36-315Statistical Graphics and Visualization9
36-461Special Topics: Statistical Methods in Epidemiology9
36-462Special Topics: Data Mining9
36-463Special Topics: Multilevel and Hierarchical Models9
36-464Special Topics: Applied Multivariate Methods9

III. Disciplinary Core

126 units

1. Economics Core
36 units
73-230Intermediate Microeconomics9
73-240Intermediate Macroeconomics9
73-270Writing for Economists9
73-374Econometrics II9
2. Statistics Core
36 units
36-225Introduction to Probability Theory *#9

 and one of the following two courses:

36-226Introduction to Statistical Inference *9
36-326Mathematical Statistics (Honors) *9

and both of the following two courses:

36-401Modern Regression *9
36-402Advanced Methods for Data Analysis9

 *In order to be a major in good standing, a grade of C or better is required in 36-225 (or equivalents), 36-226 or 36-326 and 36-401.  Otherwise you will not be allowed to continue in the major.

#It is possible to substitute 36-217 or 21-325 for 36-225. (36-225 is the standard introduction to probability, 36-217 is tailored for engineers and computer scientists, and 21-325 is a rigorous Probability Theory course offered by the Department of Mathematics.)

3. Computing
9 units
36-350Statistical Computing *9

*A higher level Computer Science course approved by your Academic Advisor may be used as a substitute.

4. Advanced Electives
45 units

Students must take three advanced Economics elective courses (numbered 73-300 through 73-495, excluding 73-374, 73-407 and 73-450) and two advanced Statistics elective courses (numbered 36-303, 36-315, or 36-410 through 36-495).

Total number of units for the major182-192 units
Total number of units for the degree360 units

Sample Program

The following sample program illustrates one way to satisfy the requirements of the Economics and Statistics Major.  Keep in mind that the program is flexible and can support other possible schedules (see footnotes below the schedule).

FreshmanSophomore
FallSpringFallSpring
21-120 Differential and Integral Calculus36-202 Statistical Methods21-122 Integration and Approximation **21-240 Matrix Algebra with Applications
36-201 Statistical Reasoning and Practice21-256 Multivariate Analysis36-225 Introduction to Probability Theory36-226 Introduction to Statistical Inference
73-100 Principles of Economics73-155 Legonomics: Building Blocks of Economic Analysis73-230 Intermediate Microeconomics73-240 Intermediate Macroeconomics
-----*---------------
--------------------

JuniorSenior
FallSpringFallSpring
36-350 Statistical Computing36-402 Advanced Methods for Data AnalysisStatistics ElectiveEconomics Elective
36-401 Modern Regression73-270 Writing for EconomistsEconomics ElectiveStatistics Elective
73-374 Econometrics IIEconomics Elective----------
--------------------
--------------------

*In each semester, ----- represents other courses (not related to the major) which are needed in order to complete the 360 units that the degree requires.

** Students can also take 21-127 or 21-257. Students should consult with their advisor.

73-155 is not required but it is recommended by the Economics department.

Prospective PhD students might add 21-127 fall of sophomore year, replace 21-240 with 21-241, add 21-260 in spring of junior year and 21-355 in fall of senior year.

Students who elect Economics and Statistics as a second major must fulfill all Economic and Statistics degree requirements. Majors in many other programs would naturally complement a Statistics Major, including Business Administration, Social and Decision Sciences, Policy and Management, Social & Political History, and Psychology.

With respect to double-counting courses, it is departmental policy that students must have at least six courses (three Economics and three Statistics) that do not count for their primary major. If students do not have at least six, they typically take additional advanced electives.

Students are advised to begin planning their curriculum (with appropriate advisors) as soon as possible. This is particularly true if the other major has a complex set of requirements and prerequisites.


B.S. in Statistics and Machine Learning

Academic Advisor: Paige Houser
Faculty Advisor: Ryan Tibshirani
Office: Baker Hall 132A
Email: acadcoord@stat.cmu.edu

Students in the Bachelor of Science program develop and master a wide array of skills in computing, mathematics, statistical theory, and the interpretation and display of complex data. In addition, Statistics and Machine Learning majors gain experience in applying statistical tools to real problems in other fields and learn the nuances of interdisciplinary collaboration. This program is geared towards students interested in statistical computation, data science, or “Big Data” problems.  The requirements for the Major in Statistics and Machine Learning are detailed below and are organized by categories.

1. Mathematical Foundations (Prerequisites)                                             49 - 59 units

Mathematics is the language in which statistical models are described and analyzed, so some experience with basic calculus and linear algebra is an important component for anyone pursuing a program of study in Statistics and Machine Learning.

Calculus*:
Complete one of the following three sequences of mathematics courses at Carnegie Mellon, each of which provides sufficient preparation in calculus:

Sequence 1

21-111Calculus I10
21-112Calculus II10

and one of the following:

21-256Multivariate Analysis9
21-259Calculus in Three Dimensions9

Sequence 2

21-120Differential and Integral Calculus10

and one of the following:

21-256Multivariate Analysis9
21-259Calculus in Three Dimensions9

Note: Other sequences are possible, and require approval from the undergraduate advisor. 

Note: Passing the MSC 21-120 assessment test is an acceptable alternative to completing 21-120.

Integration and Approximation

21-122Integration and Approximation10

Linear Algebra**:
Complete one of the following three courses:

21-240Matrix Algebra with Applications10
21-241Matrices and Linear Transformations10
21-242Matrix Theory10

* It is recommended that students complete the calculus requirement during their freshman year.

**The linear algebra requirement needs to be completed before taking 36-401 Modern Regression. 

21-241 and 21-242 are intended only for students with a very strong mathematical background.

Mathematical Theory:

21-127Concepts of Mathematics10

2. Data Analysis                                                                                            45 - 54 units

Data analysis is the art and science of extracting insight from data. The art lies in knowing which displays or techniques will reveal the most interesting features of a complicated data set. The science lies in understanding the various techniques and the assumptions on which they rely. Both aspects require practice to master.

The Beginning Data Analysis courses give a hands-on introduction to the art and science of data analysis. The courses cover similar topics but differ slightly in the examples they emphasize. 36-201 draws examples from many fields and satisfies the Dietrich College Core Requirement in Statistical Reasoning. It is therefore the recommended course for students in the College. (Note: A score of 4 or 5 on the Advanced Placement (AP) Exam in Statistics may be used to waive this requirement). Other courses emphasize examples in business (36-207), engineering and architecture (36-220), and the laboratory sciences (36-247).

The Intermediate Data Analysis courses build on the principles and methods covered in the introductory course, and more fully explore specific types of data analysis methods in more depth.

The Advanced Data Analysis courses draw on students' previous experience with data analysis and understanding of statistical theory to develop advanced, more sophisticated methods. These core courses involve extensive analysis of real data with emphasis on developing the oral and writing skills needed for communicating results.

Sequence 1

Beginning*
Choose one of the following courses:

36-201Statistical Reasoning and Practice9
36/70-207Probability and Statistics for Business Applications9
36-220Engineering Statistics and Quality Control9
36-247Statistics for Lab Sciences9
*Or extra statistical elective

Note: Students who enter the program with 36-225 or 36-226 should discuss options with an advisor.  Any 36-300 or 36-400 level course that does not satisfy any other requirement for a Statistics Major and Minor may be counted as a Statistical Elective.

Intermediate
Choose one of the following courses:

36-202Statistical Methods9
36/70-208Regression Analysis9
36-309Experimental Design for Behavioral and Social Sciences9
*Or extra statistical elective

Advanced
Choose two of the following courses:

36-303Sampling, Survey and Society9
36-315Statistical Graphics and Visualization9
36-461Special Topics: Statistical Methods in Epidemiology9
36-462Special Topics: Data Mining9
36-463Special Topics: Multilevel and Hierarchical Models9
36-464Special Topics: Applied Multivariate Methods9

and take the following two courses:

36-401Modern Regression9
36-402Advanced Methods for Data Analysis9

Sequence 2

Advanced
Choose three of the following courses:

36-303Sampling, Survey and Society9
36-315Statistical Graphics and Visualization9
36-461Special Topics: Statistical Methods in Epidemiology9
36-462Special Topics: Data Mining9
36-463Special Topics: Multilevel and Hierarchical Models9
36-464Special Topics: Applied Multivariate Methods9

and take the following two courses:

36-401Modern Regression9
36-402Advanced Methods for Data Analysis9

3. Probability Theory and Statistical Theory                                                       18 units

The theory of probability gives a mathematical description of the randomness inherent in our observations. It is the language in which statistical models are stated, so an understanding of probability is essential for the study of statistical theory. Statistical theory provides a mathematical framework for making inferences about unknown quantities from data. The theory reduces statistical problems to their essential ingredients to help devise and evaluate inferential procedures. It provides a powerful and wide-ranging set of tools for dealing with uncertainty.


To satisfy the theory requirement take the following two courses**:

36-225Introduction to Probability Theory9
36-226Introduction to Statistical Inference9


**It is possible to substitute 36-217 or 21-325 for 36-225. (36-225 is the standard introduction to probability, 36-217 is tailored for engineers and computer scientists, and 21-325 is a rigorous Probability Theory course offered by the Department of Mathematics.) 36-326 Mathematical Statistics (Honors) can be substituted for 36-226 Introduction to Statistical Inference and is considered an honors course.

Comments:

(i) In order to be a Major or a Minor in good standing, a grade of at least a C is required in 36-225, 36-226 and 36-401. In particular, a grade of C or higher is required in order to be able to continue in the major.

(ii) In special cases, and in consultation with the Statistics Advisor, the entire theory requirement can be satisfied by taking the graduate level class 36-625 Probability and Mathematical Statistics I, which is much more mathematically rigorous. This option should be considered by strong Statistics Majors who are also majoring in Computer Science, Operations Research, or Mathematics and/or who are considering graduate study in Statistics. This option requires special permission from the advisor. Students who end up satisfying the theory requirement by taking the (single) course 36-625 are required  take  an additional statistics elective  (see category #6, Statistical Electives, below).

4. Computing:                                                                                                64 - 67 units

Statistical modeling in practice nearly always requires computation in one way or another. Computational algorithms are sometimes treated as “black-boxes”, whose innards the statistician need not pay attention to. But this attitude is becoming less and less prevalent, and today there is much to be gained from a strong working knowledge of computational tools. Understanding the strengths and weaknesses of various methods allows the data analyst to select the right tool for the job; understanding how they can be adapted to work in new settings greatly extends the realm of problems that he/she can solve. While all Majors in Statistics are given solid grounding in computation, extensive computational training is really what sets the Major in Statistics and Machine Learning apart.

36-350Statistical Computing9
15-112Fundamentals of Programming and Computer Science12
15-122Principles of Imperative Computation10
10-601Introduction to Machine Learning12
15-351Algorithms and Advanced Data Structures12

*A higher level Computer Science course approved by your Statistics advisor may be used as a substitute.

and take one of the following courses:

10-605Machine Learning with Large Datasets12
15-381Artificial Intelligence: Representation and Problem Solving9
15-386Neural Computation9
16-720Computer Vision12
16-311Introduction to Robotics12
11-411Natural Language Processing12
11-761Language and Statistics12
*PhD level ML course as approved by Statistics advisor
** Independent research with an ML faculty member

Total number of units for the major                                                         166-188 units

Total number of units for the degree                                                              360 units

Recommendations

Students in the Dietrich College of Humanities and Social Sciences who wish to major or minor in Statistics are advised to complete both the calculus requirement (one Mathematical Foundations calculus sequence) and the Beginning Data Analysis course 36-201 Statistical Reasoning and Practice by the end of their Freshman year.

The linear algebra requirement is a prerequisite for the course 36-401. It is therefore essential to complete this requirement during your junior year at the latest! 

Recommendations for Prospective PhD Students

Students interested in pursuing a PhD in Statistics or Machine Learning (or related programs) after completing their undergraduate degree are strongly recommended to take additional Mathematics courses. They should see a faculty advisor as soon as possible. Students should consider 36-326 Mathematical Statistics (Honors) as an alternative to 36-226. Although 21-240 Matrix Algebra with Applications is recommended for Statistics majors, students interested in PhD programs should consider taking 21-241 Matrices and Linear Transformations or 21-242 Matrix Theory instead. Additional courses to consider are 21-228 Discrete Mathematics, 21-260 Differential Equations, 21-341 Linear Algebra, 21-355 Principles of Real Analysis I, and 21-356 Principles of Real Analysis II.

Additional experience in programming and computational modeling is also recommended. Students should consider taking more than course from the list of Machine Learning electives provided under the Computing section.

Additional Major in Statistics and Machine Learning

Students who elect Statistics and Machine Learning as a second or third major must fulfill all degree requirements. 

With respect to double-counting courses, it is departmental policy that students must have at least six courses (three Machine Learning and three Statistics) that do not count for their primary major. If students do not have at least six, they typically take additional advanced electives.

Students are advised to begin planning their curriculum (with appropriate advisors) as soon as possible. This is particularly true if the other major has a complex set of requirements and prerequisites or when many of the other major's requirements overlap with the requirements for a Major in Statistics and Machine Learning.

Sample Programs

The following sample program illustrates one way to satisfy the requirements of the Statistics and Machine Learning program.  Keep in mind that the program is flexible and can support other possible schedules (see footnotes below the schedule). Sample program 1 is for students who have not satisfied the basic calculus requirements. Sample program 2 is for students who have satisfied the basic calculus requirements and choose option 2 for their data analysis courses (see section #2)

FreshmanSophomore
FallSpringFallSpring
21-120 Differential and Integral Calculus21-122 Integration and Approximation36-217 Probability Theory and Random Processes21-241 Matrices and Linear Transformations
36-201 Statistical Reasoning and Practice36-202 Statistical Methods21-256 Multivariate Analysis36-226 Introduction to Statistical Inference
15-112 Fundamentals of Programming and Computer Science21-127 Concepts of Mathematics36-350 Statistical Computing15-122 Principles of Imperative Computation
-----*---------------
--------------------

JuniorSenior
FallSpringFallSpring
15-351 Algorithms and Advanced Data Structures36-402 Advanced Methods for Data Analysis10-601 Introduction to Machine Learning10-605 Machine Learning with Large Datasets
36-401 Modern RegressionStat ElectiveStat ElectiveML Elective
--------------------
--------------------
--------------------

*In each semester, ----- represents other courses (not related to the major) which are needed in order to complete the 360 units that the degree requires.

FreshmanSophomore
FallSpringFallSpring
21-256 Multivariate Analysis15-122 Principles of Imperative Computation36-217 Probability Theory and Random Processes21-241 Matrices and Linear Transformations
15-112 Fundamentals of Programming and Computer Science21-127 Concepts of Mathematics15-351 Algorithms and Advanced Data Structures36-226 Introduction to Statistical Inference
-----*----------Stat Elective
--------------------
--------------------

JuniorSenior
FallSpringFallSpring
36-350 Statistical Computing36-402 Advanced Methods for Data Analysis10-601 Introduction to Machine Learning10-605 Machine Learning with Large Datasets
36-401 Modern RegressionStat ElectiveStat ElectiveML Elective
--------------------
--------------------
--------------------

*In each semester, ----- represents other courses (not related to the major) which are needed in order to complete the 360 units that the degree requires.
 

The Minor in Statistics

Academic Advisor: Paige Houser
Faculty Advisor: Howard Seltman
Office: Baker Hall 132A
Email: acadcoord@stat.cmu.edu

The Minor in Statistics develops skills that complement major study in other disciplines. The program helps the student master the basics of statistical theory and advanced techniques in data analysis. This is a good choice for deepening understanding of statistical ideas and for strengthening research skills.

In order to get a minor in Statistics a student must satisfy all the requirements in categories 1, 2 and 3 of the major requirement (see above) with the exception that in the advanced data analysis part only 36-401 and 36-402 are required. In other words, the requirements for the minor are (read the section about the Major in Statistics for details):

1. Mathematical Foundations (Prerequisites)
28–38 units

Identical to Major requirements (read relevant section above carefully).

2. Data Analysis
36 units

    Beginning Data Analysis:  9 units (one course) - see Major requirements above.       

    Intermediate Data Analysis: 9 units (one course) - see Major requirements above.

    Advanced Data Analysis: 18 units - 36-401 and 36-402

3. Probability Theory and Statistical Theory
18 units

    Identical to Major requirements (read relevant section above carefully).

Total number of units required for the minor82 Units

With respect to double-counting courses, it is departmental policy that students must have at least three statistics courses that do not count for their primary major. If students do not have at least three, they typically take additional advanced electives.

Sample Programs for the Minor

The following two sample programs illustrates two (of many) ways to satisfy the requirements of the Statistics Minor. Keep in mind that the program is flexible and can support many other possible schedules.

The first schedule uses calculus sequence 1, and 36-309 to satisfy the intermediate data analysis requirement. The second schedule is an example of the case when a student enters the Minor through 36-225 and 36-226 (and therefore skips the beginning data analysis course). The schedule uses calculus sequence 2, and 36-315 as an elective (to replace the beginning data analysis course).

Schedule 1

FreshmanSophomore
FallSpringFallSpring
21-111 Calculus I21-112 Calculus II21-256 Multivariate Analysis21-240 Matrix Algebra with Applications
36-201 Statistical Reasoning and Practice36-309 Experimental Design for Behavioral and Social Sciences

JuniorSenior
FallSpringFallSpring
36-225 Introduction to Probability Theory36-226 Introduction to Statistical Inference36-401 Modern Regression36-402 Advanced Methods for Data Analysis

Schedule 2

FreshmanSophomore
FallSpringFallSpring
21-120 Differential and Integral Calculus21-256 Multivariate Analysis36-225 Introduction to Probability Theory36-226 Introduction to Statistical Inference

JuniorSenior
FallSpringFallSpring
21-240 Matrix Algebra with Applications36-315 Statistical Graphics and Visualization36-401 Modern Regression36-402 Advanced Methods for Data Analysis

Substitutions and Waivers

Many departments require Statistics courses as part of their Major or Minor programs. Students seeking transfer credit for those requirements from substitute courses (at Carnegie Mellon or elsewhere) should seek permission from their advisor in the department setting the requirement. The final authority in such decisions rests there. The Statistics Department does not provide approval or permission for substitution or waiver of another department's requirements.

However, the Statistics Director of Undergraduate Studies will provide advice and information to the student's advisor about the viability of a proposed substitution. Students should make available as much information as possible concerning proposed substitutions. Students seeking waivers may be asked to demonstrate mastery of the material.

Statistics Majors and Minors seeking substitutions or waivers should speak to the Statistics Director of Undergraduate Studies.

Faculty

XIZHEN CAI, Assistant Teaching Professor – Ph.D., The Pennsylvania State University; Carnegie Mellon, 2014–.DAVID CHOI, Assistant Professor of Statistics and Information Systems – Ph.D., Stanford University; Carnegie Mellon, 2004–.ALEXANDRA CHOULDECHOVA, Assistant Professor of Statistics and Public Policy – Ph.D. , Standford University; Carnegie Mellon, 2014–.STEPHEN E. FIENBERG, University Professor and Maurice Falk Professor of Statistics and Social Sciences – Ph.D., Harvard University; Carnegie Mellon, 1980–.MAX G'SELL, Assistant Professor – Ph.D., Stanford University ; Carnegie Mellon, 2014–.CHRISTOPHER GENOVESE, Department Head and Professor of Statistics – Ph.D., University of California, Berkeley; Carnegie Mellon, 1994–.JOEL B. GREENHOUSE, Professor of Statistics – Ph.D., University of Michigan; Carnegie Mellon, 1982–.AMELIA HAVILAND, Anna Loomis McCandless Professorship of Statistics and Public Policy – Ph.D., Carnegie Mellon University; Carnegie Mellon, 2003–.JIASHUN JIN, Professor of Statistics – Ph.D., Stanford University; Carnegie Mellon, 2007–.BRIAN JUNKER, Associate Dean and Professor of Statistics – Ph.D., University of Illinois; Carnegie Mellon, 1990–.ROBERT E. KASS, Professor of Statistics – Ph.D., University of Chicago; Carnegie Mellon, 1981–.ANN LEE, Associate Professor – Ph.D., Brown University; Carnegie Mellon, 2005–.JOHN P. LEHOCZKY, Thomas Lord Professor of Statistics – Ph.D., Stanford University; Carnegie Mellon, 1969–.JING LEI, Assistant Professor – Ph.D., University of California, Berkeley; Carnegie Mellon, 2011–.DANIEL NAGIN, Teresa and H. John Heinz III Professor of Public Policy – Ph.D., Carnegie Mellon University; Carnegie Mellon, 1976–.REBECCA NUGENT, Teaching Professor – Ph.D., University of Washington; Carnegie Mellon, 2006–.ALESSANDRO RINALDO, Associate Professor – Ph.D., Carnegie Mellon; Carnegie Mellon, 2005–.KATHRYN ROEDER, Professor of Statistics – Ph.D., Pennsylvania State University; Carnegie Mellon, 1994–.CHAD M. SCHAFER, Associate Professor – Ph.D., University of California, Berkeley; Carnegie Mellon, 2004–.MARK J. SCHERVISH, Professor of Statistics – Ph.D., University of Illinois; Carnegie Mellon, 1979–.TEDDY SEIDENFELD, Herbert A. Simon Professor of Philosophy and Statistics – Ph.D., Columbia University; Carnegie Mellon, 1985–.COSMA SHALIZI, Associate Professor – Ph.D., University of Wisconsin, Madison; Carnegie Mellon, 2005–.RYAN TIBSHIRANI, Assistant Professor – Ph.D., Stanford University; Carnegie Mellon, 2011–.VALERIE VENTURA, Associate Professor – Ph.D., University of Oxford; Carnegie Mellon, 1997–.LARRY WASSERMAN, Professor of Statistics – Ph.D., University of Toronto; Carnegie Mellon, 1988–.

Emeriti Faculty

GEORGE T. DUNCAN, Professor of Statistics and Public Policy – Ph.D., University of Minnesota; Carnegie Mellon, 1974–.WILLIAM F. EDDY, John C. Warner Professor of Statistics – Ph.D, Yale University; Carnegie Mellon, 1976–.JOSEPH B. KADANE, Leonard J. Savage Professor of Statistics and Social Sciences – Ph.D., Stanford University; Carnegie Mellon, 1969–.

Adjunct Faculty

ANTHONY BROCKWELL, – Ph.D., Melbourne University; Carnegie Mellon, 1999–.BERNIE DEVLIN, – Ph.D., Pennsylvania State University; Carnegie Mellon, 1994–.

Special Faculty

PETER FREEMAN, Research Associate – Ph.D., University of Chicago; Carnegie Mellon, 2004–.HOWARD SELTMAN, Senior Research Statistician – Ph.D., Carnegie Mellon; M.D., Medical College of Pennsylvania; Carnegie Mellon, 1999–.ISABELLA VERDINELLI, Professor in Residence – Ph.D., Carnegie Mellon University; Carnegie Mellon, 1991–.GORDON WEINBERG, Lecturer – M.A. Mathematics, University of Pittsburgh; Carnegie Mellon, 2004–.

Visiting Faculty

JARED MURRAY, Assistant Professor – Ph.D., Duke University; Carnegie Mellon, 2013–.JORDAN RODU, Assistant Professor – Ph.D., University of Pennsylvania ; Carnegie Mellon, 2014–.SAM VENTURA, Assistant Professor – Ph.D., Carnegie Mellon University; Carnegie Mellon, 2015–.

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Faculty

XIZHEN CAI, Assistant Teaching Professor – Ph.D., The Pennsylvania State University; Carnegie Mellon, 2014–.DAVID CHOI, Assistant Professor of Statistics and Information Systems – Ph.D., Stanford University; Carnegie Mellon, 2004–.ALEXANDRA CHOULDECHOVA, Assistant Professor of Statistics and Public Policy – Ph.D. , Standford University; Carnegie Mellon, 2014–.STEPHEN E. FIENBERG, University Professor and Maurice Falk Professor of Statistics and Social Sciences – Ph.D., Harvard University; Carnegie Mellon, 1980–.MAX G'SELL, Assistant Professor – Ph.D., Stanford University ; Carnegie Mellon, 2014–.CHRISTOPHER GENOVESE, Department Head and Professor of Statistics – Ph.D., University of California, Berkeley; Carnegie Mellon, 1994–.JOEL B. GREENHOUSE, Professor of Statistics – Ph.D., University of Michigan; Carnegie Mellon, 1982–.AMELIA HAVILAND, Anna Loomis McCandless Professorship of Statistics and Public Policy – Ph.D., Carnegie Mellon University; Carnegie Mellon, 2003–.JIASHUN JIN, Professor of Statistics – Ph.D., Stanford University; Carnegie Mellon, 2007–.BRIAN JUNKER, Associate Dean and Professor of Statistics – Ph.D., University of Illinois; Carnegie Mellon, 1990–.ROBERT E. KASS, Professor of Statistics – Ph.D., University of Chicago; Carnegie Mellon, 1981–.ANN LEE, Associate Professor – Ph.D., Brown University; Carnegie Mellon, 2005–.JOHN P. LEHOCZKY, Thomas Lord Professor of Statistics – Ph.D., Stanford University; Carnegie Mellon, 1969–.JING LEI, Assistant Professor – Ph.D., University of California, Berkeley; Carnegie Mellon, 2011–.DANIEL NAGIN, Teresa and H. John Heinz III Professor of Public Policy – Ph.D., Carnegie Mellon University; Carnegie Mellon, 1976–.REBECCA NUGENT, Teaching Professor – Ph.D., University of Washington; Carnegie Mellon, 2006–.ALESSANDRO RINALDO, Associate Professor – Ph.D., Carnegie Mellon; Carnegie Mellon, 2005–.KATHRYN ROEDER, Professor of Statistics – Ph.D., Pennsylvania State University; Carnegie Mellon, 1994–.CHAD M. SCHAFER, Associate Professor – Ph.D., University of California, Berkeley; Carnegie Mellon, 2004–.MARK J. SCHERVISH, Professor of Statistics – Ph.D., University of Illinois; Carnegie Mellon, 1979–.TEDDY SEIDENFELD, Herbert A. Simon Professor of Philosophy and Statistics – Ph.D., Columbia University; Carnegie Mellon, 1985–.COSMA SHALIZI, Associate Professor – Ph.D., University of Wisconsin, Madison; Carnegie Mellon, 2005–.RYAN TIBSHIRANI, Assistant Professor – Ph.D., Stanford University; Carnegie Mellon, 2011–.VALERIE VENTURA, Associate Professor – Ph.D., University of Oxford; Carnegie Mellon, 1997–.LARRY WASSERMAN, Professor of Statistics – Ph.D., University of Toronto; Carnegie Mellon, 1988–.

Emeriti Faculty

GEORGE T. DUNCAN, Professor of Statistics and Public Policy – Ph.D., University of Minnesota; Carnegie Mellon, 1974–.WILLIAM F. EDDY, John C. Warner Professor of Statistics – Ph.D, Yale University; Carnegie Mellon, 1976–.JOSEPH B. KADANE, Leonard J. Savage Professor of Statistics and Social Sciences – Ph.D., Stanford University; Carnegie Mellon, 1969–.

Adjunct Faculty

ANTHONY BROCKWELL, – Ph.D., Melbourne University; Carnegie Mellon, 1999–.BERNIE DEVLIN, – Ph.D., Pennsylvania State University; Carnegie Mellon, 1994–.

Special Faculty

PETER FREEMAN, Research Associate – Ph.D., University of Chicago; Carnegie Mellon, 2004–.HOWARD SELTMAN, Senior Research Statistician – Ph.D., Carnegie Mellon; M.D., Medical College of Pennsylvania; Carnegie Mellon, 1999–.ISABELLA VERDINELLI, Professor in Residence – Ph.D., Carnegie Mellon University; Carnegie Mellon, 1991–.GORDON WEINBERG, Lecturer – M.A. Mathematics, University of Pittsburgh; Carnegie Mellon, 2004–.

Visiting Faculty

JARED MURRAY, Assistant Professor – Ph.D., Duke University; Carnegie Mellon, 2013–.JORDAN RODU, Assistant Professor – Ph.D., University of Pennsylvania ; Carnegie Mellon, 2014–.SAM VENTURA, Assistant Professor – Ph.D., Carnegie Mellon University; Carnegie Mellon, 2015–.