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- All HBS Web (610)
- Faculty Publications (559)
- Article
The Similarity Heuristic
By: Daniel Read and Yael Grushka-Cockayne
Decision makers often make snap judgments using fast‐and‐frugal decision rules called cognitive heuristics. Research into cognitive heuristics has been divided into two camps. One camp has emphasized the limitations and biases produced by the heuristics; another has...
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Read, Daniel, and Yael Grushka-Cockayne. "The Similarity Heuristic." Journal of Behavioral Decision Making 24, no. 1 (January 2011): 23–46.
- October 1, 2021
- Article
An Evaluation of Cross-efficiency Methods: With an Application to Warehouse Performance.
By: B.M. Balk, M.R. De Koster, Christian Kaps and J.L. Zofio
Cross-efficiency measurement is an extension of Data Envelopment Analysis that allows for tie-breaking ranking of the Decision Making Units (DMUs) using all the peer evaluations. In this article we examine the theory of cross-efficiency measurement by comparing a...
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Keywords:
Efficiency Analysis;
Performance Benchmarking;
Warehousing;
Analytics and Data Science;
Performance Evaluation;
Measurement and Metrics;
Mathematical Methods
Balk, B.M., M.R. De Koster, Christian Kaps, and J.L. Zofio. "An Evaluation of Cross-efficiency Methods: With an Application to Warehouse Performance." Art. 126261. Applied Mathematics and Computation 406 (October 1, 2021).
- 2013
- Book
Keeping Up with the Quants: Your Guide to Understanding and Using Analytics
By: Thomas H. Davenport and Jinho Kim
Managers today need to be able to analyze and make sense of data. They need to be conversant with analytical technology and methods and to make decisions on quantitative analysis. This book offers a variety of practical tools and examples to improve a manager's...
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Robert C. Merton
Robert C. Merton is the School of Management Distinguished Professor of Finance at the MIT Sloan School of Management.
Merton is University Professor Emeritus at Harvard University and was the George Fisher Baker Professor of...
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- July–August 2011
- Article
Robust Optimization Made Easy with ROME
By: Joel Goh and Melvyn Sim
We introduce ROME, an algebraic modeling toolbox for a class of robust optimization problems. ROME serves as an intermediate layer between the modeler and optimization solver engines, allowing modelers to express robust optimization problems in a mathematically...
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Keywords:
Robust Optimization;
Algebraic Modeling Toolbox;
MATLAB;
Stochastic Programming;
Decision Rules;
Inventory Control;
PERT;
Project Management;
Portfolio Optimization;
Information Technology;
Mathematical Methods;
Operations
Goh, Joel, and Melvyn Sim. "Robust Optimization Made Easy with ROME." Operations Research 59, no. 4 (July–August 2011): 973–985.
- 2008
- Chapter
Allocating Marketing Resources
By: Sunil Gupta and Thomas J. Steenburgh
Companies spend billions of dollars on marketing every year because it is essential to organic growth. Given these large investments, marketing managers have the responsibility to optimally allocate resources and to demonstrate that their investments generate... View Details
Keywords:
Investment Return;
Resource Allocation;
Marketing;
Demand and Consumers;
Mathematical Methods
Gupta, Sunil, and Thomas J. Steenburgh. "Allocating Marketing Resources." In Marketing Mix Decisions: New Perspectives and Practices, edited by Roger A. Kerin and Rob O'Regan. Chicago, IL: American Marketing Association, 2008.
- September 2021
- Article
Oh's 8-Universality Criterion Is Unique
Using the methods developed for the proof that the 2-universality criterion is unique, we partially characterize criteria for the n-universality of positive-definite integer-matrix quadratic forms. We then obtain the uniqueness of Oh’s 8-universality criterion as an...
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Keywords:
N-universal Lattice;
8-universal Lattice;
Universality Criteria;
Quadratic Forms;
Additively Indecomposable;
Mathematical Methods
Kominers, Scott Duke. "Oh's 8-Universality Criterion Is Unique." Kyungpook Mathematical Journal 61, no. 3 (September 2021): 455–459.
- November 2021
- Article
Gaussian Process Subset Scanning for Anomalous Pattern Detection in Non-iid Data
By: William Herlands, Edward McFowland III, Andrew Gordon Wilson and Daniel B. Neill
Identifying anomalous patterns in real-world data is essential for understanding where, when, and how systems deviate from their expected dynamics. Yet methods that separately consider the anomalousness of each individual data point have low detection power for subtle,...
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Herlands, William, Edward McFowland III, Andrew Gordon Wilson, and Daniel B. Neill. "Gaussian Process Subset Scanning for Anomalous Pattern Detection in Non-iid Data." Proceedings of Machine Learning Research (PMLR) 84 (2018): 425–434. (Also presented at the 21st International Conference on Artificial Intelligence and Statistics (AISTATS), 2018.)
- 20 Oct 2011
- Research & Ideas
Getting the Marketing Mix Right
firms; and by using direct-to-consumer advertising (DTCA). First, they employed the complex mathematical formulas of traditional models to study different marketing strategies used by the drug companies. They found that the IPS property...
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Keywords:
by Dina Gerdeman
- March 2001 (Revised April 2002)
- Case
Rent-Way, Inc. (A)
By: David F. Hawkins
The company uses the units of activity method to account for its rental inventory. A prominent hedge fund advisor recommends the company's stock be sold short.
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Keywords:
Mathematical Methods;
Stock Shares;
Fair Value Accounting;
Quality;
Investment Funds;
Service Industry
Hawkins, David F. "Rent-Way, Inc. (A)." Harvard Business School Case 101-089, March 2001. (Revised April 2002.)
- August 2003 (Revised May 2009)
- Background Note
Basic Venture Capital Formula, The
By: William A. Sahlman and Matthew Willis
Briefly summarizes the process that venture capitalists use to analyze high-risk, long-term investments. Contains information on methods that can be used to calculate valuation, share price, percent ownership, implied valuation, dilution, and option pools.
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Sahlman, William A., and Matthew Willis. "Basic Venture Capital Formula, The." Harvard Business School Background Note 804-042, August 2003. (Revised May 2009.)
- 2020
- Working Paper
Design Rules, Volume 2: How Technology Shapes Organizations: Chapter 5 Ecosystems and Complementarities
The purpose of this chapter is to introduce two new building blocks to the theory of how technology shapes organizations. The first is a new layer of organization structure: a business “ecosystem.” The second is the economic concept of “complementarity.” Ecosystems are...
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Baldwin, Carliss Y. "Design Rules, Volume 2: How Technology Shapes Organizations: Chapter 5 Ecosystems and Complementarities." Harvard Business School Working Paper, No. 21-033, August 2020.
- January 2024
- Article
Subset Scanning for Multi-Trait Analysis Using GWAS Summary Statistics
By: Rui Cao, Evan Olawsky, Edward McFowland III, Erin Marcotte, Logan Spector and Tianzhong Yang
Multi-trait analysis has been shown to have greater statistical power than single-trait analysis. Most of the existing multi-trait analysis methods only work with a limited number of traits and usually prioritize high statistical power over identifying relevant traits,...
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Cao, Rui, Evan Olawsky, Edward McFowland III, Erin Marcotte, Logan Spector, and Tianzhong Yang. "Subset Scanning for Multi-Trait Analysis Using GWAS Summary Statistics." Bioinformatics 40, no. 1 (January 2024).
- March 2010
- Article
Correcting for Cross-Sectional and Time-Series Dependence in Accounting Research
By: Ian D. Gow, Daniel Taylor and Gaizka Ormazabal
We review and evaluate the methods commonly used in the accounting literature to correct for cross-sectional and time-series dependence. While much of the accounting literature studies settings in which variables are cross-sectionally and serially correlated, we find...
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Keywords:
History;
Cost of Capital;
Activity Based Costing and Management;
Performance Evaluation;
Cost Accounting;
Time Management;
Research;
Mathematical Methods;
Equity;
Borrowing and Debt;
Accounting Audits;
Accounting Industry
Gow, Ian D., Daniel Taylor, and Gaizka Ormazabal. "Correcting for Cross-Sectional and Time-Series Dependence in Accounting Research." Accounting Review 85, no. 2 (March 2010): 483–512.
- 2009
- Article
On Universal Binary Hermitian Forms
Earnest and Khosravani, Iwabuchi, and Kim and Park recently gave a complete classification of the universal binary Hermitian forms. We give a unified proof of the universalities of these Hermitian forms, relying upon Ramanujan's list of universal quadratic forms...
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Keywords:
Mathematical Methods
Kominers, Scott Duke. "On Universal Binary Hermitian Forms." A02. INTEGERS: Electronic Journal of Combinatorial Number Theory 9 (2009): 9–15.
- June 2013 (Revised November 2022)
- Exercise
Competition Simulator Exercise
In the Competition Simulator Exercise, students explore through trial and error some important economic foundations of competitive strategy and managerial economics. In particular, the nine simulator exercises let students explore horizontal differentiation with and...
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Keywords:
Competition;
Economics;
Game Theory;
Competitive Strategy;
Learning;
Mathematical Methods;
Analysis
Van den Steen, Eric J. "Competition Simulator Exercise." Harvard Business School Exercise 713-804, June 2013. (Revised November 2022.)
- November 2007
- Background Note
Bayesian Estimation & Black-Litterman
By: Joshua D. Coval and Erik Stafford
Describes a practical method for asset allocation that is more robust to estimation errors than the traditional implementation of mean-variance optimization with sample means and covariances. The Bayesian inspired Black-Litterman model is described after introducing...
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Coval, Joshua D., and Erik Stafford. "Bayesian Estimation & Black-Litterman." Harvard Business School Background Note 208-085, November 2007.
- December 2008
- Article
Behavioral Frontiers in Choice Modeling
We review the discussion at a workshop whose goal was to achieve a better integration among behavioral, economic, and statistical approaches to choice modeling. The workshop explored how current approaches to the specification, estimation, and application of choice...
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Keywords:
Mathematical Methods;
Integration;
Goals and Objectives;
Decision Choices and Conditions;
Problems and Challenges;
Business Processes;
Customers;
Behavior;
Economics
Adamowicz, Wiktor, David Bunch, Trudy Ann Cameron, Benedict G.C. Dellaert, Michael Hanneman, Michael Keane, Jordan Louviere, Robert Meyer, Thomas J. Steenburgh, and Joffre Swait. "Behavioral Frontiers in Choice Modeling." Marketing Letters 19, nos. 3/4 (December 2008): 215–219.
- 2021
- Working Paper
How Much Should We Trust Staggered Difference-In-Differences Estimates?
By: Andrew C. Baker, David F. Larcker and Charles C.Y. Wang
Difference-in-differences analysis with staggered treatment timing is frequently used to assess the impact of policy changes on corporate outcomes in academic research. However, recent advances in econometric theory show that such designs are likely to be biased in the...
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Keywords:
Difference In Differences;
Staggered Difference-in-differences Designs;
Generalized Difference-in-differences;
Dynamic Treatment Effects;
Mathematical Methods
Baker, Andrew C., David F. Larcker, and Charles C.Y. Wang. "How Much Should We Trust Staggered Difference-In-Differences Estimates?" European Corporate Governance Institute Finance Working Paper, No. 736/2021, February 2021. (Harvard Business School Working Paper, No. 21-112, April 2021.)
- 2022
- Working Paper
The Disagreement Problem in Explainable Machine Learning: A Practitioner's Perspective
By: Satyapriya Krishna, Tessa Han, Alex Gu, Javin Pombra, Shahin Jabbari, Steven Wu and Himabindu Lakkaraju
As various post hoc explanation methods are increasingly being leveraged to explain complex models in high-stakes settings, it becomes critical to develop a deeper understanding of if and when the explanations output by these methods disagree with each other, and how...
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Krishna, Satyapriya, Tessa Han, Alex Gu, Javin Pombra, Shahin Jabbari, Steven Wu, and Himabindu Lakkaraju. "The Disagreement Problem in Explainable Machine Learning: A Practitioner's Perspective." Working Paper, 2022.