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Show Results For
- All HBS Web
(853)
- News (79)
- Research (640)
- Events (14)
- Multimedia (4)
- Faculty Publications (634)
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- 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).
- 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... 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?" European Corporate Governance Institute Finance Working Paper, No. 736/2021, February 2021. (Harvard Business School Working Paper, No. 21-112, April 2021.)
- 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.)
- 23 Jan 2018
- Working Paper Summaries
Transaction Costs and the Duration of Contracts
Keywords: by Alexander MacKay
- May–June 2018
- Article
Data Uncertainty in Markov Chains: Application to Cost-Effectiveness Analyses of Medical Innovations
By: Joel Goh, Mohsen Bayati, Stefanos A. Zenios, Sundeep Singh and David Moore
Cost-effectiveness studies of medical innovations often suffer from data inadequacy. When Markov chains are used as a modeling framework for such studies, this data inadequacy can manifest itself as imprecision in the elements of the transition matrix. In this paper,... View Details
Keywords: Markov Chains; Cost Effectiveness; Medical Innovations; Colorectal Cancer; Health Care and Treatment; Cost vs Benefits; Innovation and Invention; Mathematical Methods; Health Industry
Goh, Joel, Mohsen Bayati, Stefanos A. Zenios, Sundeep Singh, and David Moore. "Data Uncertainty in Markov Chains: Application to Cost-Effectiveness Analyses of Medical Innovations." Operations Research 66, no. 3 (May–June 2018): 697–715. (Winner, 2014 INFORMS Health Applications Society Pierskalla Award & Finalist, 2014 INFORMS George E. Nicholson student paper competition.)
- March 2011 (Revised November 2011)
- Teaching Note
Harmonic Hearing Co. (Brief Case)
By: Howard H. Stevenson and Craig Stephenson
Teaching Note for 4271. View Details
- January 2008 (Revised July 2009)
- Case
Forecasting the Great Depression
What is proper role of professional economic forecasting in financial decision making? The case presents excerpts from three leading economic forecasters on the eve of, and just after, the stock market crash of October 1929. The first set of excerpts is from Roger... View Details
Keywords: History; Mathematical Methods; Personal Development and Career; Forecasting and Prediction; Financial Crisis
Friedman, Walter A. "Forecasting the Great Depression." Harvard Business School Case 708-046, January 2008. (Revised July 2009.)
- April 2006
- Background Note
Informing Service Management with Customer Data
By: Frances X. Frei and Dennis Campbell
Taught as the third module in a Harvard Business School course on Managing Service Operations. Explores the role of data analysis in ongoing service management. Describes how to realize the maximum amount of value from analyses and use this information in... View Details
Keywords: Decision Making; Design; Analytics and Data Science; Service Operations; Mathematical Methods; Value
Frei, Frances X., and Dennis Campbell. "Informing Service Management with Customer Data." Harvard Business School Background Note 606-097, April 2006.
- 13 Mar 2017
- Research & Ideas
Hiding Products From Customers May Ultimately Boost Sales
sushi restaurant where customers order from a fixed menu.” Next steps The mathematical model in the paper assumes a situation in which a retailer would sell all styles of a product at the same price (e.g., all fall sandals would be priced... View Details
- February 2024
- Article
Fifty Shades of QE: Robust Evidence
By: Brian Fabo, Marina Jančoková, Elisabeth Kempf and Ľuboš Pástor
Fabo et al. (2021) show that papers written by central bank researchers find quantitative easing (QE) to be more effective than papers written by academics. Weale and Wieladek (2022) show that a subset of these results lose statistical significance when OLS regressions... View Details
Keywords: Quantitative Easing; Research; Mathematical Methods; Perception; Banks and Banking; Body of Literature
Fabo, Brian, Marina Jančoková, Elisabeth Kempf, and Ľuboš Pástor. "Fifty Shades of QE: Robust Evidence." Art. 107065. Journal of Banking & Finance 159 (February 2024).
- October 2013
- Article
How Much to Make and How Much to Buy? An Analysis of Optimal Plural Sourcing Strategies
By: Phanish Puranam, Ranjay Gulati and Sourav Bhattacharya
While many theories of the firm seek to explain when firms make rather than buy, in practice, firms often make and buy the same input—they engage in plural sourcing. We argue that explaining the mix of external procurement and internal sourcing for the same input... View Details
Keywords: Supply Chain; Forecasting and Prediction; Framework; Prejudice and Bias; Mathematical Methods
Puranam, Phanish, Ranjay Gulati, and Sourav Bhattacharya. "How Much to Make and How Much to Buy? An Analysis of Optimal Plural Sourcing Strategies." Strategic Management Journal 34, no. 10 (October 2013): 1145–1161.
- 2010
- Working Paper
Substitution Patterns of the Random Coefficients Logit
By: Thomas J. Steenburgh and Andrew Ainslie
Previous research suggests that the random coefficients logit is a highly flexible model that overcomes the problems of the homogeneous logit by allowing for differences in tastes across individuals. The purpose of this paper is to show that this is not true. We prove... View Details
Steenburgh, Thomas J., and Andrew Ainslie. "Substitution Patterns of the Random Coefficients Logit." Harvard Business School Working Paper, No. 10-053, January 2010.