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Related Experiment Video

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Measuring the Subjective Value of Risky and Ambiguous Options using Experimental Economics and Functional MRI Methods

Measuring the Subjective Value of Risky and Ambiguous Options using Experimental Economics and Functional MRI Methods

Published on: September 19, 2012

Bayesian Forecasting of Extreme Values in an Exchangeable Sequence.

¹Department of Statistics, University of Michigan, Ann Arbor, MI 48109.

Journal of Research of the National Institute of Standards and Technology

|July 5, 2023

Summary

This summary is machine-generated.

This study enhances extreme value forecasting for long-tailed distributions by modifying the Hill tail index estimator. Finite domain models offer more realistic predictions for future record values.

Keywords:

Bayesian forecasting exchangeability long-tailed distributions record values tail-index estimator

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Area of Science:

Statistics
Probability Theory

Background:

Forecasting extreme and record values in exchangeable sequences presents theoretical challenges.
Standard idealized models for long-tailed distributions can yield unrealistic predictions when assuming unbounded data.

Purpose of the Study:

To develop novel theory and methodology for predicting extreme and record values.
To adapt the Hill tail index estimator for improved forecasting accuracy.
To reconcile idealized models with finite observable data for practical prediction.

Main Methods:

Modification of the Hill tail index estimator for prediction.
Analysis of finite versus infinite idealized models for long-tailed distributions.
Application of posterior expectations for forecasting in long-tailed contexts.

Main Results:

The modified Hill estimator provides appropriate predictions for future variables.
Finite domain modeling resolves unrealistic predictions from unbounded idealized models.
Predictions for the next record value are shown to be within a few multiples of the current record.

Conclusions:

Finite domain models are compatible with sensible prediction methods for long-tailed distributions.
Posterior expectations are suitable for forecasting in long-tailed distributions, analogous to other scientific contexts.
The developed methodology is effective for forecasting extreme and record values, as demonstrated by simulations.