Combining Probability Distributions: A Critique and an Annotated Bibliography

Genest, Christian; Zidek, James V.

doi:10.1214/ss/1177013825

Cited by 791 publications

(553 citation statements)

References 81 publications

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“…Since there are many equivalence classes (provided j j > 1), there are many generalized geometric pooling functions. discussion and comparison of linear and geometric pooling, see Genest and Zidek (1986).…”

Section: How Can Geometric Pooling Be Justi…ed?mentioning

confidence: 99%

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Probabilistic Opinion Pooling

Dietrich

List

2017

Oxford Handbooks Online

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Suppose several individuals (e.g., experts on a panel) each assign probabilities to some events. How can these individual probability assignments be aggregated into a single collective probability assignment? This chapter is a review of several proposed solutions to this problem, focusing on three salient proposals: linear pooling (the weighted or unweighted linear averaging of probabilities), geometric pooling (the weighted or unweighted geometric averaging of probabilities), and multiplicative pooling (where probabilities are multiplied rather than averaged). Axiomatic characterizations of each class of pooling functions are presented (most characterizations are classic results, but one is new), with the argument that linear pooling can be justified “procedurally” but not “epistemically”, while the other two pooling methods can be justified “epistemically”. The choice between them, in turn, depends on whether the individuals' probability assignments are based on shared information or on private information. In conclusion a number of other pooling methods are mentioned.

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Section: How Can Geometric Pooling Be Justi…ed?mentioning

confidence: 99%

“…There is a growing interdisciplinary literature on probabilistic opinion pooling; some references are given below (for a classic review, see Genest and Zidek 1986). While a complete review of the literature is beyond the scope of this article, we aim to give a ‡avour of the variety of possible approaches.…”

Section: Introductionmentioning

confidence: 99%

Probabilistic Opinion Pooling

Dietrich

List

2017

Oxford Handbooks Online

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“…This rule for aggregation of probabilistic assessments has been dubbed linear opinion pool by Stone [37], and is attributed to Laplace (see [2,29,16], for a survey).…”

Section: The Bayesian Casementioning

confidence: 99%

Aggregation of multiple prior opinions

Crès

Gilboa

Vieille

2011

Journal of Economic Theory

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Experts are asked to provide their advice in a situation of uncertainty. They adopt the decision maker's utility function, but each has a potentially different set of prior probabilities, and so does the decision maker. The decision maker and the experts maximize the minimal expected utility with respect to their sets of priors. We show that a natural Pareto condition is equivalent to the existence of a set Λ of probability vectors over the experts, interpreted as possible allocations of weights to the experts, such that (i) the decision maker's set of priors is precisely all the weighted-averages of priors, where an expert's prior is taken from her set and the weight vector is taken from Λ; (ii) the decision maker's valuation of an act is the minimal weighted valuation, over all weight vectors in Λ, of the experts' valuations.

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“…Hall and Mitchell (2007) combine two inflation density forecasts from two institutions. 5 The restriction that each weight is positive could be relaxed; for discussion see Genest and Zidek (1986). 6 The logarithmic score of the i-th density forecast, ln g(π τ,h | I i,τ ), is the logarithm of the probability density function g(.…”

Section: Recursive Weights (Rw)mentioning

confidence: 99%

Real-Time Inflation Forecast Densities from Ensemble Phillips Curves

et al. 2010

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A popular macroeconomic forecasting strategy takes combinations across many models to hedge against model instabilities of unknown timing; see (among others) Stock and Watson (2004) and Clark and McCracken (2009). In this paper, we examine the effectiveness of recursive-weight and equal-weight combination strategies for density forecasting using a time-varying Phillips curve relationship between inflation and the output gap. The densities reflect the uncertainty across a large number of models using many statistical measures of the output gap, allowing for a single structural break of unknown timing. We use real-time data for the US, Australia, New Zealand and Norway. Our main finding is that the recursive-weight strategy performs well across the real-time data sets, consistently giving well-calibrated forecast densities. The equal-weight strategy generates poorly-calibrated forecast densities for the US and Australian samples. There is little difference between the two strategies for our New Zealand and Norwegian data. We also find that the ensemble modeling approach performs more consistently with real-time data than with revised data in all four countries.

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Combining Probability Distributions: A Critique and an Annotated Bibliography

Cited by 791 publications

References 81 publications

Probabilistic Opinion Pooling

Probabilistic Opinion Pooling

Aggregation of multiple prior opinions

Real-Time Inflation Forecast Densities from Ensemble Phillips Curves

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