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- Faculty Publications (571)
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- All HBS Web (620)
- Faculty Publications (571)
- 2002
- Case
Qualitative Response Models: Ordinal and Multinomial Models
By: William B. Simpson
Keywords: Mathematical Methods
Simpson, William B. "Qualitative Response Models: Ordinal and Multinomial Models." 2002. Electronic.
- 1979
- Dissertation
Inference in Partially Identified Models
By: Dutch Leonard
Keywords: Mathematical Methods
- May–June 2025
- Article
Branch-and-Price for Prescriptive Contagion Analytics
By: Alexandre Jacquillat, Michael Lingzhi Li, Martin Ramé and Kai Wang
Contagion models are ubiquitous in epidemiology, social sciences, engineering, and management. This paper formulates a prescriptive contagion analytics model where a decision maker allocates shared resources across multiple segments of a population, each governed by... View Details
Jacquillat, Alexandre, Michael Lingzhi Li, Martin Ramé, and Kai Wang. "Branch-and-Price for Prescriptive Contagion Analytics." Operations Research 73, no. 3 (May–June 2025): 1558–1580.
- Article
How Much Should We Trust Staggered Difference-In-Differences Estimates?
By: Andrew C. Baker, David F. Larcker and Charles C.Y. Wang
We explain when and how staggered difference-in-differences regression estimators, commonly applied to assess the impact of policy changes, are biased. These biases are likely to be relevant for a large portion of research settings in finance, accounting, and law that... View Details
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?" Journal of Financial Economics 144, no. 2 (May 2022): 370–395. (Editor's Choice, May 2022; Jensen Prize, First Place, June 2023.)
- Article
Oracle Efficient Private Non-Convex Optimization
By: Seth Neel, Aaron Leon Roth, Giuseppe Vietri and Zhiwei Steven Wu
One of the most effective algorithms for differentially private learning and optimization is objective perturbation. This technique augments a given optimization problem (e.g. deriving from an ERM problem) with a random linear term, and then exactly solves it.... View Details
Neel, Seth, Aaron Leon Roth, Giuseppe Vietri, and Zhiwei Steven Wu. "Oracle Efficient Private Non-Convex Optimization." Proceedings of the International Conference on Machine Learning (ICML) 37th (2020).
- Article
Aztec Castles and the dP3 Quiver
By: Megan Leoni, Gregg Musiker, Seth Neel and Paxton Turner
Bipartite, periodic, planar graphs known as brane tilings can be associated to a large class of quivers. This paper will explore new algebraic properties of the well-studied del Pezzo 3 (dP3) quiver and geometric properties of its corresponding brane tiling. In... View Details
Leoni, Megan, Gregg Musiker, Seth Neel, and Paxton Turner. "Aztec Castles and the dP3 Quiver." Journal of Physics A: Mathematical and Theoretical 47, no. 47 (November 28, 2014).
- 1990
- Chapter
Refinement of Nash Equilibrium: The Main Ideas
By: E. Kohlberg
Keywords: Mathematical Methods
Kohlberg, E. "Refinement of Nash Equilibrium: The Main Ideas." In Game Theory and Applications, edited by T. Ichiishi, A. Neyman, and Y. Tauman. San Diego: Academic Press, 1990.
- Article
Refined Configuration Results for Extremal Type II Lattices of Ranks 40 and 80
By: Noam D. Elkies and Scott Duke Kominers
We show that, if L is an extremal Type II lattice of rank 40 or 80, then L is generated by its vectors of norm min(L)+2. This sharpens earlier results of Ozeki, and the second author and Abel, which showed that such lattices L are generated by their vectors of norms... View Details
Keywords: Mathematical Methods
Elkies, Noam D., and Scott Duke Kominers. "Refined Configuration Results for Extremal Type II Lattices of Ranks 40 and 80." Proceedings of the American Mathematical Society 138, no. 1 (January 2010): 105–108.
- February 2006
- Teaching Note
Cost-Volume-Profit Models (TN)
By: David F. Hawkins, V.G. Narayanan, Michele Jurgens and Jacob Cohen
Keywords: Mathematical Methods
- August 2005 (Revised April 2008)
- Teaching Note
Store24 (A): Statistics Review with Data Desk (TN)
By: Frances X. Frei
Presents an overview of the statistical analysis covered in the case discussion. View Details
- 2006
- Chapter
Advanced Regression Models
By: Raghuram Iyengar and Sunil Gupta
Keywords: Mathematical Methods
- 1978
- Chapter
Matrix-Weighted Averages: Computation and Presentation
By: Dutch Leonard
Keywords: Mathematical Methods
Leonard, Dutch. "Matrix-Weighted Averages: Computation and Presentation." In Proceedings of the Eleventh Symposium on the Interface of Computers and Statistics, edited by Ronald A. Gallant and Thomas Michael Gerig. Raleigh, NC: North Carolina State University, Institute of Statistics, 1978.
- July 1982 (Revised March 1984)
- Background Note
Worked Examples in Dynamic Programming
By: David E. Bell
Keywords: Mathematical Methods
Bell, David E. "Worked Examples in Dynamic Programming." Harvard Business School Background Note 183-028, July 1982. (Revised March 1984.)
- 2022
- Working Paper
A Linear Panel Model with Heterogeneous Coefficients and Variation in Exposure
By: Jesse M. Shapiro and Liyang Sun
Linear panel models featuring unit and time fixed effects appear in many areas of empirical economics. An active literature studies the interpretation of the ordinary least squares estimator of the model, commonly called the two-way fixed effects (TWFE) estimator, in... View Details
Shapiro, Jesse M., and Liyang Sun. "A Linear Panel Model with Heterogeneous Coefficients and Variation in Exposure." NBER Working Paper Series, No. 29976, April 2022.
- 2021
- Working Paper
Population Interference in Panel Experiments
By: Iavor I Bojinov, Kevin Wu Han and Guillaume Basse
The phenomenon of population interference, where a treatment assigned to one experimental unit affects another experimental unit's outcome, has received considerable attention in standard randomized experiments. The complications produced by population interference in... View Details
Bojinov, Iavor I., Kevin Wu Han, and Guillaume Basse. "Population Interference in Panel Experiments." Harvard Business School Working Paper, No. 21-100, March 2021.
- 2021
- Article
Prisoners, Rooms, and Lightswitches
By: Daniel M. Kane and Scott Duke Kominers
We examine a new variant of the classic prisoners and lightswitches puzzle: A warden leads his n prisoners in and out of r rooms, one at a time, in some order, with each prisoner eventually visiting every room an arbitrarily large number of times. The... View Details
Keywords: Mathematical Methods
Kane, Daniel M., and Scott Duke Kominers. "Prisoners, Rooms, and Lightswitches." Electronic Journal of Combinatorics 28, no. 1 (2021).
- 2019
- Article
Configurations of Extremal Type II Codes via Harmonic Weight Enumerators
By: Noam D. Elkies and Scott Duke Kominers
We prove configuration results for extremal Type II codes, analogous to the configuration results of Ozeki and of the second author for extremal Type II lattices. Specifically, we show that for n ∈{8,24,32,48,56,72,96} every extremal Type II code of length n is... View Details
Keywords: Mathematical Methods
Elkies, Noam D., and Scott Duke Kominers. "Configurations of Extremal Type II Codes via Harmonic Weight Enumerators." Journal de Théorie des Nombres de Bordeaux 31, no. 3 (2019): 679–688.
- Article
A New Proof of Serre's Homological Characterization of Regular Local Rings
By: Ravi Jagadeesan and Aaron Landesman
We give a new proof of Serre’s result that a Noetherian local ring is regular if and only if it has finite global dimension. Our proof avoids the explicit construction of a Koszul complex. View Details
Keywords: Mathematical Methods
Jagadeesan, Ravi, and Aaron Landesman. "A New Proof of Serre's Homological Characterization of Regular Local Rings." Art. 18. Research in Number Theory 2 (December 2016).
- October 2015
- Article
A New Gal(ℚ^⎯/ℚ)-invariant of Dessins d'enfants
By: Ravi Jagadeesan
We study the action of Gal(ℚ^⎯/ℚ) on the category of Belyĭ functions (finite étale covers of ℙ^1_(ℚ^⎯) \ {0,1,∞}. We describe a new combinatorial Gal(ℚ^⎯/ℚ)‐invariant for Belyĭ functions whose monodromy cycle types above 0 and ∞ are the same. We use a version of our... View Details
Keywords: Mathematical Methods
Jagadeesan, Ravi. "A New Gal(ℚ^⎯/ℚ)-invariant of Dessins d'enfants." Proceedings of the London Mathematical Society 111, no. 4 (October 2015): 911–935.