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(840)
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Show Results For
- All HBS Web
(840)
- News (77)
- Research (639)
- Events (12)
- Multimedia (4)
- Faculty Publications (635)
- January 2016
- Article
Zooming In: A Practical Manual for Identifying Geographic Clusters
By: Juan Alcacer and Minyuan Zhao
This paper takes a close look at the reasons, procedures, and results of cluster identification methods. Despite being a popular research topic in strategy, economics, and sociology, geographic clusters are often studied with little consideration given to the... View Details
Keywords: Mathematical Methods
Alcacer, Juan, and Minyuan Zhao. "Zooming In: A Practical Manual for Identifying Geographic Clusters." Strategic Management Journal 37, no. 1 (January 2016): 10–21.
- 2013
- Chapter
Weighted Generating Functions for Type II Lattices and Codes
By: Noam D. Elkies and Scott Duke Kominers
We give a new structural development of harmonic polynomials on Hamming space, and harmonic weight enumerators of binary linear codes, that parallels one approach to harmonic polynomials on Euclidean space and weighted theta functions of Euclidean lattices. Namely, we... View Details
Keywords: Mathematical Methods
Elkies, Noam D., and Scott Duke Kominers. "Weighted Generating Functions for Type II Lattices and Codes." In Quadratic and Higher Degree Forms. Vol. 31, edited by Alladi Krishnaswami, Manjul Bhargava, David Savitt, and Pham Huu Tiep, 63–108. Developments in Mathematics. Springer, 2013.
- Article
Asymptotic Improvements of Lower Bounds for the Least Common Multiples of Arithmetic Progressions
By: Daniel M. Kane and Scott Duke Kominers
For relatively prime positive integers and r, we consider the least common multiple L_n:=\mathop{\textrm{lcm}}(u_0,u_1,\dots, u_n) of the finite arithmetic progression \{u_k:=u_0+kr\}_{k=0}^n. We derive new lower bounds on L_n that improve upon those obtained... View Details
Keywords: Mathematical Methods
Kane, Daniel M., and Scott Duke Kominers. "Asymptotic Improvements of Lower Bounds for the Least Common Multiples of Arithmetic Progressions." Canadian Mathematical Bulletin 57, no. 3 (September 2014): 551–561.
- 1987
- Chapter
Continuous-Time Stochastic Models
By: Robert C. Merton
Keywords: Mathematical Methods
Merton, Robert C. "Continuous-Time Stochastic Models." In The New Palgrave: A Dictionary of Economic Theory and Doctrine, edited by John Eatwell, Murray Milgate, and Peter Newman. London: Macmillan Press, 1987. (Revised in The New Palgrave Dictionary of Money and Finance, London: MacMillan Press, Ltd., 1992.)
- February 1996
- Exercise
Problems in Variance Analysis
By: William J. Bruns Jr.
Keywords: Mathematical Methods
Bruns, William J., Jr. "Problems in Variance Analysis." Harvard Business School Exercise 196-120, February 1996.
- May 1983
- Article
Optimality Conditions and Strong Duality in Abstract and Continuous Time Linear Programming
By: André Perold and R. Meidan
Keywords: Mathematical Methods
Perold, André, and R. Meidan. "Optimality Conditions and Strong Duality in Abstract and Continuous Time Linear Programming." Journal of Optimization Theory and Applications 40, no. 1 (May 1983): 61–76.
- February 2005 (Revised November 2006)
- Background Note
Using Data Desk for Statistical Analysis
By: Frances X. Frei and Dennis Campbell
Describes how to use the Data Desk software package to perform statistical analysis. View Details
Keywords: Mathematical Methods
Frei, Frances X., and Dennis Campbell. "Using Data Desk for Statistical Analysis." Harvard Business School Background Note 605-060, February 2005. (Revised November 2006.)
- March 2004
- Tutorial
Variance Analysis Tutorial
By: David F. Hawkins and Jacob Cohen
An interactive tutorial on variance analysis, flexible budgets, and overhead allocation. View Details
Keywords: Mathematical Methods
- 1977
- Article
On the Joint Distribution of Left- and Right-sided Outliner Statistics
By: André Perold and D. M. Hawkins
Keywords: Mathematical Methods
Perold, André, and D. M. Hawkins. "On the Joint Distribution of Left- and Right-sided Outliner Statistics." Utilitas mathematica 12 (1977): 129–143.
- Profile
Tessa Vacher-Desvernais
analytics, but truly appreciate aesthetics. I’m very conscious of my inner tension between analytical and creative thinking.” Following her mathematical and sciences baccalaureate, she pursued liberal arts at an all-girl military boarding... View Details
- February 2021
- Article
A Dynamic Theory of Multiple Borrowing
By: Daniel Green and Ernest Liu
Multiple borrowing—a borrower obtains overlapping loans from multiple lenders—is a common phenomenon in many credit markets. We build a highly tractable, dynamic model of multiple borrowing and show that, because overlapping creditors may impose default externalities... View Details
Keywords: Commitment; Multiple Borrowing; Common Agency; Misallocation; Microfinance; Investment; Mathematical Methods
Green, Daniel, and Ernest Liu. "A Dynamic Theory of Multiple Borrowing." Journal of Financial Economics 139, no. 2 (February 2021): 389–404.
- 28 Mar 2023
- Blog Post
Meet Professor Elisabeth Paulson: A Conversation on Life, Research, and Teaching
mom was a statistics professor, so a career in academia was always something that I considered. During undergrad, I started doing research and was involved in high school tutoring programs. I loved diving deep into complex problems, and helping others apply View Details
- 1992
- Chapter
Thinking Coalitionally: Party Arithmetic, Process Opportunism, and Strategic Sequencing
By: James K. Sebenius and David Lax
- 2024
- Working Paper
Anytime-Valid Inference in Linear Models and Regression-Adjusted Causal Inference
By: Michael Lindon, Dae Woong Ham, Martin Tingley and Iavor I. Bojinov
Linear regression adjustment is commonly used to analyze randomized controlled experiments due to its efficiency and robustness against model misspecification. Current testing and interval estimation procedures leverage the asymptotic distribution of such estimators to... View Details
Lindon, Michael, Dae Woong Ham, Martin Tingley, and Iavor I. Bojinov. "Anytime-Valid Inference in Linear Models and Regression-Adjusted Causal Inference." Harvard Business School Working Paper, No. 24-060, March 2024.
- 2023
- Article
Verifiable Feature Attributions: A Bridge between Post Hoc Explainability and Inherent Interpretability
By: Usha Bhalla, Suraj Srinivas and Himabindu Lakkaraju
With the increased deployment of machine learning models in various real-world applications, researchers and practitioners alike have emphasized the need for explanations of model behaviour. To this end, two broad strategies have been outlined in prior literature to... View Details
Bhalla, Usha, Suraj Srinivas, and Himabindu Lakkaraju. "Verifiable Feature Attributions: A Bridge between Post Hoc Explainability and Inherent Interpretability." Advances in Neural Information Processing Systems (NeurIPS) (2023).
- May 2020
- Article
Scalable Holistic Linear Regression
By: Dimitris Bertsimas and Michael Lingzhi Li
We propose a new scalable algorithm for holistic linear regression building on Bertsimas & King (2016). Specifically, we develop new theory to model significance and multicollinearity as lazy constraints rather than checking the conditions iteratively. The resulting... View Details
Bertsimas, Dimitris, and Michael Lingzhi Li. "Scalable Holistic Linear Regression." Operations Research Letters 48, no. 3 (May 2020): 203–208.
- March 2022
- Article
Sensitivity Analysis of Agent-based Models: A New Protocol
By: Emanuele Borgonovo, Marco Pangallo, Jan Rivkin, Leonardo Rizzo and Nicolaj Siggelkow
Agent-based models (ABMs) are increasingly used in the management sciences. Though useful, ABMs are often critiqued: it is hard to discern why they produce the results they do and whether other assumptions would yield similar results. To help researchers address such... View Details
Keywords: Agent-based Modeling; Sensitivity Analysis; Design Of Experiments; Total Order Sensitivity Indices; Organizations; Behavior; Decision Making; Mathematical Methods
Borgonovo, Emanuele, Marco Pangallo, Jan Rivkin, Leonardo Rizzo, and Nicolaj Siggelkow. "Sensitivity Analysis of Agent-based Models: A New Protocol." Computational and Mathematical Organization Theory 28, no. 1 (March 2022): 52–94.
- November 1990 (Revised August 1996)
- Background Note
Sampling and Statistical Inference
An introduction to sampling and statistical inference that covers the main concepts (confidence intervals, tests of statistical significance, choice of sample size) that are needed in making inferences about a population mean or percent. Includes discussion of problems... View Details
Schleifer, Arthur, Jr. "Sampling and Statistical Inference." Harvard Business School Background Note 191-092, November 1990. (Revised August 1996.)
- January 2008 (Revised April 2008)
- Teaching Note
Pilgrim Bank (C): Statistics Review with Data Desk
By: Frances X. Frei
Teaching Note for [602103]. View Details