Regularized Aggregation of One-Off Probability Predictions

Published Online:https://doi.org/10.1287/opre.2021.2224

References

  • Albert JH, Chib S (1993) Bayesian analysis of binary and polychotomous response data. J. Amer. Statist. Assoc. 88(422):669–679.CrossrefGoogle Scholar
  • Arieli I, Babichenko Y, Smorodinsky R (2018) Robust forecast aggregation. Proc. National Acad. Sci. USA 115(52):E12135–E12143.CrossrefGoogle Scholar
  • Atanasov P, Joseph R, Feijoo F, Marshall M, Siddiqui S (2021) Human forest vs. random forest in time-sensitive covid-19 clinical trial prediction. Preprint, submitted December 9, http://dx.doi.org/10.2139/ssrn.3981732.Google Scholar
  • Atanasov P, Rescober P, Stone E, Swift SA, Servan-Schreiber E, Tetlock P, Ungar L, et al. (2017) Distilling the wisdom of crowds: Prediction markets vs. prediction polls. Management Sci. 63(3):691–706.LinkGoogle Scholar
  • Balasubramanian V (2006) MDL, Bayesian inference, and the geometry of the space of probability distributions. Grünwald P, Myung IJ, Pitt M, eds. Advances in Minimum Description Length: Theory and Applications (MIT Press, Cambridge, MA), 81–98.Google Scholar
  • Bhattacharya RN, Waymire EC (2007) A Basic Course in Probability Theory, vol. 69 (Springer, Berlin).Google Scholar
  • Bordley RF (1982) A multiplicative formula for aggregating probability assessments. Management Sci. 28(10):1137–1148.LinkGoogle Scholar
  • Brier GW (1950) Verification of forecasts expressed in terms of probability. Monthly Weather Rev. 78:1–3.CrossrefGoogle Scholar
  • Budescu DV, Por H-H, Broomell SB, Smithson M (2014) The interpretation of ipcc probabilistic statements around the world. Natural Climate Change 4(6):508–512.CrossrefGoogle Scholar
  • Burdzy K, Pal S (2021) Can coherent predictions be contradictory? Adv. Appl. Probabilities 53(1):133–161.CrossrefGoogle Scholar
  • Clarke BS, Barron AR (1994) Jeffreys’ prior is asymptotically least favorable under entropy risk. J. Statist. Planning Inference 41(1):37–60.CrossrefGoogle Scholar
  • Clemen RT (1987) Combining overlapping information. Management Sci. 33(3):373–380.LinkGoogle Scholar
  • Clemen RT, Winkler RL (1999) Combining probability distributions from experts in risk analysis. Risk Anal. 19(2):187–203.CrossrefGoogle Scholar
  • Dawid A, DeGroot M, Mortera J (1995) Coherent combination of experts’ opinions. TEST 4(2):263–313.CrossrefGoogle Scholar
  • Dietrich F (2010) Bayesian group belief. Soc. Choice Welfare 35(4):595–626.CrossrefGoogle Scholar
  • Dobbin K, Simon R (2005) Sample size determination in microarray experiments for class comparison and prognostic classification. Biostatistics 6(1):27–38.CrossrefGoogle Scholar
  • Erev I, Wallsten TS, Budescu DV (1994) Simultaneous over- and underconfidence: The role of error in judgment processes. Psych. Rev. 101(3):519–527.CrossrefGoogle Scholar
  • Ernst P, Pemantle R, Satopää V, Ungar L (2016) Bayesian aggregation of two forecasts in the partial information framework. Statist. Probability. Lett. 119:170–180.CrossrefGoogle Scholar
  • Everett B (2013) An Introduction to Latent Variable Models (Springer Science & Business Media, New York).Google Scholar
  • Fischhoff B, Beyth-Marom R (1983) Hypothesis evaluation from a Bayesian perspective. Psych. Rev. 90(3):239.CrossrefGoogle Scholar
  • Friedman JA, Baker JD, Mellers BA, Tetlock PE, Zeckhauser R (2018) The value of precision in probability assessment: Evidence from a large-scale geopolitical forecasting tournament. Internat. Stud. Quart. 62(2):410–422.Google Scholar
  • Gelman A, Stern HS, Carlin JB, Dunson DB, Vehtari A, Rubin DB (2013) Bayesian Data Analysis (Chapman and Hall/CRC).CrossrefGoogle Scholar
  • Ghosh M, et al.. (2011) Objective priors: An introduction for frequentists. Statist. Sci. 26(2):187–202.CrossrefGoogle Scholar
  • Gneiting T, Raftery AE (2007) Strictly proper scoring rules, prediction, and estimation. J. Amer. Statist. Assoc. 102(477):359–378.CrossrefGoogle Scholar
  • Hilbert M (2012) Toward a synthesis of cognitive biases: How noisy information processing can bias human decision making. Psych. Bull. 138(2):211.CrossrefGoogle Scholar
  • Hora SC, Fransen BR, Hawkins N, Susel I (2013) Median aggregation of distribution functions. Decision Anal. 10(4):279–291.LinkGoogle Scholar
  • Jeffreys H (1946) An invariant form for the prior probability in estimation problems. Proc. Royal Soc. London A Math. Phys. Sci. 186(1007):453–461.Google Scholar
  • Jeffreys H (1961) The Theory of Probability (Oxford University Press, Oxford, UK).Google Scholar
  • Jose VRR, Grushka-Cockayne Y, Lichtendahl KC Jr (2013) Trimmed opinion pools and the crowd’s calibration problem. Management Sci. 60(2):463–475.LinkGoogle Scholar
  • Kahana MJ, Aggarwal EV, Phan TD (2018) The variability puzzle in human memory. J. Experiment. Psych. Learn. Memory Cognition 44(12):1857.CrossrefGoogle Scholar
  • Kahneman D, Tversky A (1973) On the psychology of prediction. Psych. Rev. 80(4):237.CrossrefGoogle Scholar
  • Karvetski C, Meinel C, Maxwell D, Lu Y, Mellers B, Tetlock P (2021) Forecasting the accuracy of forecasters from properties of forecasting rationales. Preprint, submitted February 4, https://dx.doi.org/10.2139/ssrn.3779404.Google Scholar
  • Lee MD, Danileiko I (2014) Using cognitive models to combine probability estimates. Judgment Decision Making 9(3):259.CrossrefGoogle Scholar
  • Lichtendahl KC Jr, Winkler RL (2007) Probability elicitation, scoring rules, and competition among forecasters. Management Sci. 53(11):1745–1755.LinkGoogle Scholar
  • Lindley D (1985) Reconciliation of discrete probability distributions. Bayesian Statist. 2:375–390.Google Scholar
  • Malagò L, Pistone G (2015) Information geometry of the gaussian distribution in view of stochastic optimization. Proc. ACM Conf. on Foundations of Genetic Algorithms XIII (Association for Computing Machinery, New York), 150–162.Google Scholar
  • Matheny J, Rieber S (2015) Aggregative contingent estimation (ACE). Accessed July 20, 2020, https://www.iarpa.gov/index.php/research-programs/ace.Google Scholar
  • Mellers B, Ungar L, Baron J, Ramos J, Gurcay B, Fincher K, Scott SE, et al.. (2014) Psychological strategies for winning a geopolitical forecasting tournament. Psych. Sci. 25(5):1106–1115.CrossrefGoogle Scholar
  • Morrison DF, Marshall LC, Sahlin HL (1976) Multivariate Statistical Methods, 2nd ed. (McGraw-Hill, New York).Google Scholar
  • Murphy AH (1973) A new vector partition of the probability score. J. Appl. Meteorology 12(4):595–600.CrossrefGoogle Scholar
  • Myung IJ, Balasubramanian V, Pitt MA (2000) Counting probability distributions: Differential geometry and model selection. Proc. National Acad. Sci. USA 97(21):11170–11175.CrossrefGoogle Scholar
  • Neal RM (2003) Slice sampling. Ann. Statist. 31:705–741.CrossrefGoogle Scholar
  • O’Hagan A, Buck CE, Daneshkhah A, Eiser JR, Garthwaite PH, Jenkinson DJ, Oakley JE, et al. (2006) Uncertain Judgements: Eliciting Experts’ Probabilities (John Wiley & Sons, Chichester, UK).CrossrefGoogle Scholar
  • Owen DB (1980) A table of normal integrals. Comm. Statist. Simulation Comput. 9(4):389–419.CrossrefGoogle Scholar
  • Palley A, Satopää V (2021) Boosting the wisdom of crowds within a single judgment problem: Weighted averaging based on peer predictions. Preprint, submitted September 1, https://dx.doi.org/10.2139/ssrn.3504286.Google Scholar
  • Paulo R (2005) Default priors for Gaussian processes. Ann. Statist. 33(2):556–582.CrossrefGoogle Scholar
  • Ranjan R, Gneiting T (2010) Combining probability forecasts. J. Royal Statist. Soc. Series B Statist. Methodology 72(1):71–91.CrossrefGoogle Scholar
  • Ravishanker N, Dey DK (2001) A First Course in Linear Model Theory (CRC Press, Boca Raton, FL).Google Scholar
  • Reichenbach H (1971) The Theory of Probability (University of California Press).Google Scholar
  • Satopää VA (2021) Improving the wisdom of crowds with analysis of variance of predictions of related outcomes. Internat. J. Forecasting. 37(4):1728–1747.CrossrefGoogle Scholar
  • Satopää VA, Pemantle R, Ungar LH (2016) Modeling probability forecasts via information diversity. J. Amer. Statist. Assoc. 111(516):1623–1633.CrossrefGoogle Scholar
  • Satopää VA, Salikhov M, Tetlock PE, Mellers B (2021) Bias, information, noise: The BIN model of forecasting. Management Sci. 67(12):7599–7618.LinkGoogle Scholar
  • Satopää VA, Baron J, Foster DP, Mellers BA, Tetlock PE, Ungar LH (2014) Combining multiple probability predictions using a simple logit model. Internat. J. Forecasting 30(2):344–356.CrossrefGoogle Scholar
  • Satopää VA, Jensen ST, Pemantle R, Ungar LH (2017) Partial information framework: Model-based aggregation of estimates from diverse information sources. Electronic J. Statist. 11(2):3781–3814.CrossrefGoogle Scholar
  • Stone M (1961) The opinion pool. Ann. Math. Statist. 32:1339–1342.CrossrefGoogle Scholar
  • Ungar L, Mellers B, Satopää V, Tetlock P, Baron J (2012) The good judgment project: A large scale test of different methods of combining expert predictions. Technical report FS-12-06, Association for the Advancement of Artificial Intelligence, Palo Alto, CA.Google Scholar
  • Van Der Bles AM, van der Linden S, Freeman AL, Spiegelhalter DJ (2020) The effects of communicating uncertainty on public trust in facts and numbers. Proc. National Acad. Sci. USA 117(14):7672–7683.CrossrefGoogle Scholar
  • Venn J (1888) The Logic of Chance: An Essay on the Foundations and Province of the Theory of Probability, with Especial Reference to Its Logical Bearings and Its Application to Moral and Social Science, and to Statistics (Macmillan, London).Google Scholar
  • Winkler RL (1981) Combining probability distributions from dependent information sources. Management Sci. 27(4):479–488.LinkGoogle Scholar
  • Winkler RL, Poses RM (1993) Evaluating and combining physicians’ probabilities of survival in an intensive care unit. Management Sci. 39(12):1526–1543.LinkGoogle Scholar
  • Wyart V, De Gardelle V, Scholl J, Summerfield C (2012) Rhythmic fluctuations in evidence accumulation during decision making in the human brain. Neuron 76(4):847–858.CrossrefGoogle Scholar
  • Yates JF (1990) Judgment and Decision Making (Prentice-Hall, Upper Saddle River, NJ).Google Scholar
INFORMS site uses cookies to store information on your computer. Some are essential to make our site work; Others help us improve the user experience. By using this site, you consent to the placement of these cookies. Please read our Privacy Statement to learn more.