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- 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.
- 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. View Details
Sahlman, William A., and Matthew Willis. "Basic Venture Capital Formula, The." Harvard Business School Background Note 804-042, August 2003. (Revised May 2009.)
- 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,... View Details
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... View Details
Keywords: by Dina Gerdeman
- 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... View Details
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,... View Details
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... View Details
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.
- 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... View Details
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.)
- 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... View Details
Keywords: Mathematical Methods
Kominers, Scott Duke. "On Universal Binary Hermitian Forms." A02. INTEGERS: Electronic Journal of Combinatorial Number Theory 9 (2009): 9–15.
- 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... View Details
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... View Details
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.
- 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... View Details
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.
- January 1995
- Case
Understanding User Needs
By: Marco Iansiti and Ellen Stein
Presents an introduction to methods for understanding user needs in product development. Describes a number of techniques including the use of focus groups, interviews, questionnaires, the Kano method, Lead User analysis, the Product Value matrix, OFD, etc. Provides a... View Details
Keywords: Customer Satisfaction; Customer Value and Value Chain; Product Development; Mathematical Methods
Iansiti, Marco, and Ellen Stein. "Understanding User Needs." Harvard Business School Case 695-051, January 1995.
- 2021
- Conference Presentation
An Algorithmic Framework for Fairness Elicitation
By: Christopher Jung, Michael J. Kearns, Seth Neel, Aaron Leon Roth, Logan Stapleton and Zhiwei Steven Wu
We consider settings in which the right notion of fairness is not captured by simple mathematical definitions (such as equality of error rates across groups), but might be more complex and nuanced and thus require elicitation from individual or collective stakeholders.... View Details
Jung, Christopher, Michael J. Kearns, Seth Neel, Aaron Leon Roth, Logan Stapleton, and Zhiwei Steven Wu. "An Algorithmic Framework for Fairness Elicitation." Paper presented at the 2nd Symposium on Foundations of Responsible Computing (FORC), 2021.
- October 2020
- Article
Comparative Statics for Size-Dependent Discounts in Matching Markets
By: David Delacretaz, Scott Duke Kominers and Alexandru Nichifor
We prove a natural comparative static for many-to-many matching markets in which agents’ choice functions exhibit size-dependent discounts: reducing the extent to which some agent discounts additional partners leads to improved outcomes for the agents on the other side... View Details
Keywords: Size-dependent Discounts; Path-independence; Respect For Improvements; Market Design; Mathematical Methods
Delacretaz, David, Scott Duke Kominers, and Alexandru Nichifor. "Comparative Statics for Size-Dependent Discounts in Matching Markets." Journal of Mathematical Economics 90 (October 2020): 127–131.
- March 2022
- Article
Estimating the Effectiveness of Permanent Price Reductions for Competing Products Using Multivariate Bayesian Structural Time Series Models
By: Fiammetta Menchetti and Iavor Bojinov
Researchers regularly use synthetic control methods for estimating causal effects when a sub-set of units receive a single persistent treatment, and the rest are unaffected by the change. In many applications, however, units not assigned to treatment are nevertheless... View Details
Keywords: Causal Inference; Partial Interference; Synthetic Controls; Bayesian Structural Time Series; Mathematical Methods
Menchetti, Fiammetta, and Iavor Bojinov. "Estimating the Effectiveness of Permanent Price Reductions for Competing Products Using Multivariate Bayesian Structural Time Series Models." Annals of Applied Statistics 16, no. 1 (March 2022): 414–435.
- 2022
- Article
Fairness via Explanation Quality: Evaluating Disparities in the Quality of Post hoc Explanations
By: Jessica Dai, Sohini Upadhyay, Ulrich Aivodji, Stephen Bach and Himabindu Lakkaraju
As post hoc explanation methods are increasingly being leveraged to explain complex models in high-stakes settings, it becomes critical to ensure that the quality of the resulting explanations is consistently high across all subgroups of a population. For instance, it... View Details
Dai, Jessica, Sohini Upadhyay, Ulrich Aivodji, Stephen Bach, and Himabindu Lakkaraju. "Fairness via Explanation Quality: Evaluating Disparities in the Quality of Post hoc Explanations." Proceedings of the AAAI/ACM Conference on Artificial Intelligence, Ethics, and Society (2022): 203–214.
- 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–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.)
- November 2007
- Background Note
Asset Allocation I
By: Joshua D. Coval, Erik Stafford, Rodrigo Osmo, John Jernigan, Zack Page and Paulo Passoni
The goal of these simulations is to understand the mathematics of mean-variance optimization and the equilibrium pricing of risk if all investors use this rule with common information sets. Simulation A focuses on five to 10 years of monthly sector returns that are... View Details