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  • All HBS Web  (1,932)
    • People  (5)
    • News  (750)
    • Research  (972)
    • Events  (9)
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  • 2018
  • Working Paper

Averaging Probability Forecasts: Back to the Future

By: Robert L. Winkler, Yael Grushka-Cockayne, Kenneth C. Lichtendahl Jr. and Victor Richmond R. Jose
The use and aggregation of probability forecasts in practice is on the rise. In this position piece, we explore some recent, and not so recent, developments concerning the use of probability forecasts in decision-making. Despite these advances, challenges still exist.... View Details
Keywords: Probability Forecast; Forecast Combination; Forecast Evaluation; Decision Analysis; Forecasting and Prediction; Decision Making; Analysis
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Winkler, Robert L., Yael Grushka-Cockayne, Kenneth C. Lichtendahl Jr., and Victor Richmond R. Jose. "Averaging Probability Forecasts: Back to the Future." Harvard Business School Working Paper, No. 19-039, October 2018.
  • Article

Is it Better to Average Probabilities or Quantiles?

By: Kenneth C. Lichtendahl, Yael Grushka-Cockayne and Robert L. Winkler
We consider two ways to aggregate expert opinions using simple averages: averaging probabilities and averaging quantiles. We examine analytical properties of these forecasts and compare their ability to harness the wisdom of the crowd. In terms of location, the two... View Details
Keywords: Probability Forecasts; Quantile Forecasts; Expert Combination; Linear Opinion Pooling; Forecasting and Prediction
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Lichtendahl, Kenneth C., Yael Grushka-Cockayne, and Robert L. Winkler. "Is it Better to Average Probabilities or Quantiles?" Management Science 59, no. 7 (July 2013): 1594–1611.
  • February 2021
  • Technical Note

Probability Distributions

By: Michael Parzen and Paul Hamilton
This technical note introduces students to the concept of random variables, and from there the normal and binomial distributions. After a brief introduction to random variables, the note describes the standard properties of the normal distribution: a single peak, and a... View Details
Keywords: Analysis; Risk and Uncertainty; Theory; Analytics and Data Science
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Parzen, Michael, and Paul Hamilton. "Probability Distributions." Harvard Business School Technical Note 621-704, February 2021.
  • August 1974
  • Background Note

Describing Probability Distributions

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Jackson, Barbara B. "Describing Probability Distributions." Harvard Business School Background Note 175-036, August 1974.
  • August 2006
  • Article

Confidence Intervals for Probabilities of Default

By: Samuel G. Hanson and Til Schuermann
In this paper we conduct a systematic comparison of confidence intervals around estimated probabilities of default (PD) using several analytical approaches as well as parametric and nonparametric bootstrap methods. We do so for two different PD estimation... View Details
Keywords: Credit Risk; Bootstrap; Mathematical Methods; Credit; Risk Management
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Hanson, Samuel G., and Til Schuermann. "Confidence Intervals for Probabilities of Default." Journal of Banking & Finance 30, no. 8 (August 2006).
  • 10 Dec 2015
  • Working Paper Summaries

The Probability of Rare Disasters: Estimation and Implications

Keywords: by Emil N. Siriwardane; Financial Services; Banking
  • 20 Jun 2016
  • Research & Ideas

When Predicting Other People's Preferences, You're Probably Wrong

terminally ill patient, based on the patient’s previous choices—neglecting to discuss more palliative options. And if you knew nothing of Leslie John other than her guilty pleasure of watching The Bachelor, you’d probably predict that she... View Details
Keywords: by Carmen Nobel; Retail
  • 2007
  • Other Unpublished Work

Probabilities as Similarity-Weighted Frequencies in Presence of Irrelevant Observations

By: Jacob Dov Leshno

A decision maker is asked to express her beliefs by assigning probabilities to certain possible states. We focus on the relationship between her database and her beliefs. BGSS\cite{BGSS} show that if beliefs given a union of two databases are a convex combination of... View Details

Keywords: Decision Making; Cognition and Thinking
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Leshno, Jacob Dov. "Probabilities as Similarity-Weighted Frequencies in Presence of Irrelevant Observations." 2007.
  • May 1974 (Revised December 1974)
  • Background Note

Assessing Probability Distributions for Uncertain Quantities

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Jackson, Barbara B. "Assessing Probability Distributions for Uncertain Quantities." Harvard Business School Background Note 174-193, May 1974. (Revised December 1974.)
  • 2015
  • Working Paper

The Probability of Rare Disasters: Estimation and Implications

By: Emil Siriwardane
I analyze a rare disasters economy that yields a measure of the risk neutral probability of a macroeconomic disaster, p*t. A large panel of options data provides strong evidence that p*t is the single factor driving option-implied jump risk measures in the cross... View Details
Keywords: Financial Markets; Forecasting and Prediction; Financial Crisis; Macroeconomics
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Siriwardane, Emil. "The Probability of Rare Disasters: Estimation and Implications." Harvard Business School Working Paper, No. 16-061, November 2015.
  • Article

Bringing Probability Judgments into Policy Debates via Forecasting Tournaments

By: Philip E. Tetlock, Barbara A. Mellers and J. Peter Scoblic
Political debates often suffer from vague-verbiage predictions that make it difficult to assess accuracy and improve policy. A tournament sponsored by the U.S. intelligence community revealed ways in which forecasters can better use probability estimates to make... View Details
Keywords: Tournaments; Politics; Depolarization; Knowledge Creation; Forecasting and Prediction; Government and Politics
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Tetlock, Philip E., Barbara A. Mellers, and J. Peter Scoblic. "Bringing Probability Judgments into Policy Debates via Forecasting Tournaments." Science 355, no. 6324 (February 3, 2017): 481–483.
  • 09 Aug 2017
  • Sharpening Your Skills

Productivity Tips You Probably Haven't Considered Before

Source: rawpixel Hit a wall trying to increase your productivity? Recent research by Harvard Business School professors might help. The following articles address some basic questions: Should we deal with easy tasks first? Do employees know better than management about... View Details
Keywords: by Sean Silverthorne
  • Teaching Interest

Overview

Graduate student instructor, Introduction to Statistics, 2002
Reader, Introduction to Time Series, 2003
Reader, Introductory Probability Theory, 2001 View Details
Keywords: Statistics; Probability
  • Article

Third-Party Punishment as a Costly Signal of High Continuation Probabilities in Repeated Games

By: Jillian J. Jordan and David G. Rand
Why do individuals pay costs to punish selfish behavior, even as third-party observers? A large body of research suggests that reputation plays an important role in motivating such third-party punishment (TPP). Here we focus on a recently proposed reputation-based... View Details
Keywords: Direct Reciprocity; Evolution; Dispersal; Cooperation; Trust; Reputation; Game Theory
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Jordan, Jillian J., and David G. Rand. "Third-Party Punishment as a Costly Signal of High Continuation Probabilities in Repeated Games." Journal of Theoretical Biology 421 (May 21, 2017): 189–202.
  • 02 Nov 2021
  • Research & Ideas

Why COVID-19 Probably Killed More People Than We Realize

As the number of casualties from COVID-19 ballooned at an alarming rate last year, some feared that government officials were failing to report several coronavirus-related losses and the actual death toll was much higher worldwide. While the official count shows more... View Details
Keywords: by Michael Blanding
  • November 1983
  • Article

Subjective Probability and the Theory of Games: Some Further Comment

By: A. E. Roth and F. Schoumaker
Keywords: Theory; Games, Gaming, and Gambling
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Roth, A. E., and F. Schoumaker. "Subjective Probability and the Theory of Games: Some Further Comment." Management Science 29, no. 11 (November 1983): 1337–1340.
  • summer 1970
  • Article

Marketing Strategy and Bank Service Interaction: A Probability Model

By: D. B. Crane
Keywords: Marketing; Strategy; Banks and Banking
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Crane, D. B. "Marketing Strategy and Bank Service Interaction: A Probability Model." Journal of Bank Research 1 (summer 1970).
  • February 2017
  • Background Note

Decision Analysis

By: George Wu and Kathleen McGinn
Describes decision analysis, a systematic approach for analyzing decision problems. A running example illustrates problem structuring (decision trees), probability assessment, endpoint evaluation, “folding back the tree” as a method of analysis, and sensitivity... View Details
Keywords: Decision Analysis; Decision Trees; Probability; Decision Making; Analysis
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Wu, George, and Kathleen McGinn. "Decision Analysis." Harvard Business School Background Note 917-018, February 2017.
  • Article

Your Sales Training Is Probably Lackluster. Here's How to Fix It

By: Frank V. Cespedes and Yuchun Lee
U.S. companies spend over $70 billion annually on training and an average of $1,459 per salesperson—almost 20% more than they spend on workers in all other functions. Yet, when it comes to equipping sales teams with relevant knowledge and skills, the ROI of sales... View Details
Keywords: Salesforce Management; Training
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Cespedes, Frank V., and Yuchun Lee. "Your Sales Training Is Probably Lackluster. Here's How to Fix It." Harvard Business Review (website) (June 12, 2017).
  • July 26, 2019
  • Article

You're Probably Making Incorrect Assumptions about Your Opposing Political Party

By: Arthur C. Brooks
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Brooks, Arthur C. "You're Probably Making Incorrect Assumptions about Your Opposing Political Party." Washington Post, On Leadership (July 26, 2019).
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