Is It Better to Average Probabilities or Quantiles?

References

• Abbas AE, Budescu DV, Yu H-T, Haggerty R. A comparison of two probability encoding methods: Fixed probability vs. fixed variable values. Decision Anal. (2008) 5:190–202Link, Google Scholar
• Armstrong SJ. Combining forecasts. Principles of Forecasting: A Handbook for Researchers and Practitioners (2001) (Kluwer Academic, Norwell, MA) 417–439Crossref, Google Scholar
• Balanda KP, MacGillivray HL. Kurtosis: A critical review. Amer. Statistician (1988) 42:111–119Google Scholar
• Budescu DV, Du N. Coherence and consistency of investors' probability judgments. Management Sci. (2007) 53:1731–1744Link, Google Scholar
• Casella G, Berger RL. Statistical Inference (2002) 2nd ed.(Duxbury, Pacific Grove, CA) Google Scholar
• Clemen RT, Winkler RL. Combining economic forecasts. J. Bus. Econom. Statist. (1986) 4:39–46Crossref, Google Scholar
• Clements MP. Explanations of the inconsistencies in survey respondents' forecasts. Eur. Econom. Rev. (2010) 54:536–549Crossref, Google Scholar
• Croushore D. Introducing: The survey of professional forecasters. Federal Reserve Bank of Philadelphia Bus. Rev. (1993) November/December):3–13Google Scholar
• Dawid AP. Statistical theory: The prequential approach (with discussion). J. Roy. Statist. Soc. A (1984) 147:278–292Crossref, Google Scholar
• Diebold FX, Gunther TA, Tay AS. Evaluating density forecasts, with applications to financial risk management. Internat. Econom. Rev. (1998) 39:863–883Crossref, Google Scholar
• Diebold FX, Tay AS, Wallis KF, Engle R, White H. Evaluating density forecasts of inflation: The survey of profession of forecasters. Festschrift in Honor of C.W.J. Granger (1999) (Oxford University Press, Oxford, UK) 76–90Google Scholar
• Engelberg J, Manski CF, Williams J. Comparing the point predictions and subjective probability distributions of professional forecasters. J. Bus. Econom. Statist. (2009) 27:30–41Crossref, Google Scholar
• Fildes R, Makridakis S. The impact of empirical accuracy studies on time series analysis and forecasting. Internat. Statist. Rev. (1995) 63:289–308Crossref, Google Scholar
• Gneiting T, Raftery AE. Strictly proper scoring rules, prediction, and estimation. J. Amer. Statist. Assoc. (2007) 102:359–378Crossref, Google Scholar
• Gneiting T, Balabdaoui F, Raftery AE. Probabilistic forecasts, calibration and sharpness. J. Roy. Statist. Soc. B (2007) 69:243–268Crossref, Google Scholar
• Hora SC. Probability judgments for continuous quantities: Linear combinations and calibration. Management Sci. (2004) 50:597–604Link, Google Scholar
• Hora SC. An analytic method for evaluating the performance of aggregation rules for probability densities. Oper. Res. (2010) 58:1440–1449Link, Google Scholar
• Larrick RP, Soll JB. Intuitions about combining opinions: Misappreciation of the averaging principle. Management Sci. (2006) 52:111–127Link, Google Scholar
• Larrick RP, Mannes AE, Soll JB, Krueger JI. The social psychology of the wisdom of crowds. Frontiers in Social Psychology: Social Judgment and Decision Making (2011) (Psychology Press, New York) 227–242Google Scholar
• Matheson JE, Winkler RL. Scoring rules for continuous probability distributions. Management Sci. (1976) 22:1087–1096Link, Google Scholar
• Mitchell DW. More on spreads and non-arithmetic means. Math. Gazette (2004) 88:142–144Google Scholar
• Mitchell J, Wallis KF. Evaluating density forecasts: Forecast combinations, model mixtures, calibration and sharpness. J. Appl. Econometrics (2011) 26:1023–1040Crossref, Google Scholar
• Morris PA. Combining expert judgments: A Bayesian approach. Management Sci. (1977) 23:679–693Link, Google Scholar
• Müller A, Stoyan D. Comparison Methods for Stochastic Models and Risks (2002) (John Wiley & Sons, Chichester, UK) Google Scholar
• O'Hagan AO, Buck CE, Daneshkhah A, Eiser JR, Garthwaite PH, Jenkinson DJ, Oakley JE, Rakow T. Uncertain Judgements: Eliciting Experts' Probabilities (2006) (John Wiley & Sons, Chichester, UK) Crossref, Google Scholar
• Ranjan R. Combining and evaluating probabilistic forecasts. (2009) . Ph.D. dissertation, University of Washington, SeattleGoogle Scholar
• Ranjan R, Gneiting T. Combining probability forecasts. J. Roy. Statist. Soc. B. (2010) 72:71–91Crossref, Google Scholar
• Ratcliff R. Group reaction time distributions and an analysis of distribution statistics. Psych. Bull. (1979) 86:446–461Crossref, Google Scholar
• Rubin DB. Bayesianly justifiable and relevant frequency calculations for the applied statistician. Ann. Statist. (1984) 12:1151–1172Crossref, Google Scholar
• Shuford EH, Albert A, Massengill HE. Admissible probability measurement procedures. Psychometrika (1966) 31:125–145Crossref, Google Scholar
• Smith JQ. Diagnostic checks of non-standard time series models. J. Forecasting (1985) 4:283–291Crossref, Google Scholar
• Stone M. The opinion pool. Ann. Math. Statist. (1961) 32:1339–1342Crossref, Google Scholar
• Thomas EAC, Ross BH. On appropriate procedures for combining probability distributions with the same family. J. Math. Psych. (1980) 21:136–152Crossref, Google Scholar
• Wallis KF. Combining forecasts—Forty years later. Appl. Financial Econom. (2011) 21:33–41Crossref, Google Scholar
• Wang J, Peters BA, Smith JS, Medeiros DJ, Roohrer MW. Generating daily changes in market variables using a multivariate mixture of normal distributions. Proc. 2001 Winter Simulation Conf. (2001) (ACM, Arlington, VA) 283–289Google Scholar
• Winkler RL. Scoring rules and the evaluation of probability assessors. J. Amer. Statist. Assoc. (1969) 64:1073–1077Crossref, Google Scholar
• Winkler RL. Scoring rules and the evaluation of probabilities. Test (1996) 5:1–60Crossref, Google Scholar