Publications

August 2020
Technical Note

Comparing Two Groups: Sampling and t-Testing

By: Iavor I Bojinov, Chiara Farronato, Yael Grushka-Cockayne, Willy C. Shih and Michael W. Toffel

This note describes sampling and t-tests, two fundamental statistical concepts. View Details

Keywords: Statistics; Econometric Analyses; Experimental Methods; Data Analysis; Data Analytics; Analytics and Data Science; Analysis; Surveys; Mathematical Methods

Article

How Much Is a Reduction of Your Customers' Wait Worth? An Empirical Study of the Fast-Food Drive-Thru Industry Based on Structural Estimation Methods

In many service industries, companies compete with each other on the basis of the waiting time their customers experience, along with other strategic instruments such as the price they charge for their service. The objective of this paper is to conduct an empirical... View Details

Keywords: Customer Satisfaction; Price; Service Delivery; Mathematical Methods; Competition; Food and Beverage Industry; Service Industry

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Article

Detecting Adversarial Attacks via Subset Scanning of Autoencoder Activations and Reconstruction Error

By: Celia Cintas, Skyler Speakman, Victor Akinwande, William Ogallo, Komminist Weldemariam, Srihari Sridharan and Edward McFowland III

Reliably detecting attacks in a given set of inputs is of high practical relevance because of the vulnerability of neural networks to adversarial examples. These altered inputs create a security risk in applications with real-world consequences, such as self-driving... View Details

Keywords: Autoencoder Networks; Pattern Detection; Subset Scanning; Computer Vision; Statistical Methods And Machine Learning; Machine Learning; Deep Learning; Data Mining; Big Data; Large-scale Systems; Mathematical Methods; Analytics and Data Science

2020
Working Paper

Demystifying the Math of the Coronavirus

By: Elon Kohlberg and Abraham Neyman

We provide an elementary mathematical description of the spread of the coronavirus. We explain two fundamental relationships: How the rate of growth in new infections is determined by the “effective reproductive number” and how the effective reproductive number is... View Details

Keywords: Coronavirus; Health Pandemics; Mathematical Methods

Katherine Coffman is the Piramal Associate Professor of Business Administration in the Negotiations, Organizations & Markets unit. Before joining HBS, she was an assistant professor of economics at The Ohio State University and a visiting assistant professor of... View Details

December 2019
Technical Note

Technical Note on Bayesian Statistics and Frequentist Power Calculations

By: Amitabh Chandra and Ariel Dora Stern

This Technical Note provides an introduction to Bayes’ Rule and the statistical intuition that stems from it. In this note, we review the concepts that underlie Bayesian statistics, and we offer several simple mathematical examples to illustrate applications of Bayes’... View Details

Keywords: Bayesian Statistics; Mathematical Methods

November 2018
Case

Sportradar (A): From Data to Storytelling

By: Ramon Casadesus-Masanell, Karen Elterman and Oliver Gassmann

In 2013, the Swiss sports data company Sportradar debated whether to expand from its core business of data provision to bookmakers into sports media products. Sports data was becoming a commodity, and in the future, sports leagues might reduce their dependence on... View Details

Celia Stafford is a doctoral student in Health Policy (Management). She received a B.A. in Mathematics and Economics from Emory University in 2017 and an MPH focused in Biostatistics from the University of North Carolina at Chapel Hill in 2020. She is also... View Details

Research Summary

Valuation Theory and Practice

Timothy A. Luehrman's primary research interest is in the application of valuation methods to companies, businesses, and individual assets. Some of his work involves applications of tools originally developed for valuing derivative securities to the valuation of other... View Details

Elisabeth C. Paulson

Elisabeth Paulson is an Assistant Professor of Business Administration in the Technology and Operations Management Unit at Harvard Business School. She teaches the first year course on Technology and Operations Management in the required curriculum.
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Keywords: agriculture; federal government; state government; grocery; nonprofit industry

February 2021
Tutorial

What is AI?

By: Tsedal Neeley

This video explores the elements that constitute artificial intelligence (AI). From its mathematical basis to current advances in AI, this video introduces students to data, tools, and statistical models that make a computer 'intelligent.' Through an explanation of... View Details

Keywords: Artificial Intelligence; Digital; Technological Innovation; Leadership; AI and Machine Learning; Mathematical Methods

Article

Bilateral Contracts

By: Jerry R. Green and Seppo Honkapohja

A mathematical characterization of self-enforcing bilateral contracts is given. Contracts where both parties exercise some control over the quantity traded can sometimes be superior to contracts that rest control entirely with one side. Some qualitative characteristics... View Details

Keywords: Contracts; Mathematical Methods

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Research Summary

Overview

Professor Goh’s primary research interest is applying mathematical models to real-world problems in health care in order to inform, improve, and enhance medical decision making and health policy. His recent work in this domain focuses on developing new methods for... View Details

Keywords: Uncertainty; Optimization; Inventory Management; Health; Decision Making; Supply Chain

16 May 2015
Blog Post

Using an MBA to Reimagine the Music Industry

through the case method? Our HBS Takeaways series is an effort to help prospective students understand life at HBS through the experiences of students who are about to graduate. Kiran Gandhi studied mathematics at Georgetown before... View Details

August 2005 (Revised September 2006)
Case

Polyphonic HMI: Mixing Music and Math

By: Anita Elberse, Jehoshua Eliashberg and Julian Villanueva

In 2003, Mike McCready, CEO of Barcelona-based Polyphonic HMI, was preparing to launch an artificial intelligence tool that could create significant value for music businesses. The technology, referred to as Hit Song Science (HSS), analyzed the mathematical... View Details

Keywords: Forecasting and Prediction; Music Entertainment; Business History; Leadership; Marketing Strategy; Strategic Planning; Problems and Challenges; Mathematical Methods; Entertainment and Recreation Industry

13 Apr 2012
HBS Seminar

Drazen Prelec, Professor of Management Science and Economics at MIT Sloan School of Management

Article

Improved Bounds on the Sizes of S.P Numbers

By: Paul Myer Kominers and Scott Duke Kominers

A number which is S.P in base r is a positive integer which is equal to the sum of its base-r digits multiplied by the product of its base-r digits. These numbers have been studied extensively in The Mathematical Gazette. Recently, Shah Ali... View Details

Keywords: Mathematical Methods

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2022
Article

Which Explanation Should I Choose? A Function Approximation Perspective to Characterizing Post hoc Explanations

By: Tessa Han, Suraj Srinivas and Himabindu Lakkaraju

A critical problem in the field of post hoc explainability is the lack of a common foundational goal among methods. For example, some methods are motivated by function approximation, some by game theoretic notions, and some by obtaining clean visualizations. This... View Details

Keywords: Mathematical Methods; Decision Choices and Conditions; Analytics and Data Science