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Conference Papers Year : 2023

Reparameterization of extreme value framework for improved Bayesian workflow

Abstract

Combining extreme value theory with Bayesian methods offers several advantages, such as a quantification of uncertainty on parameter estimation or the ability to study irregular models that cannot be handled by frequentist statistics. However, it comes with many options that are left to the user concerning model building, computational algorithms, and even inference itself. Among them, the parameterization of the model induces a geometry that can alter the efficiency of computational algorithms, in addition to making calculations involved. We focus on the Poisson process characterization of extremes and outline two key benefits of an orthogonal parameterization addressing both issues. First, several diagnostics show that Markov chain Monte Carlo convergence is improved compared with the original parameterization. Second, orthogonalization also helps deriving Jeffreys and penalized complexity priors, and establishing posterior propriety. The analysis is supported by simulations, and our framework is then applied to extreme level estimation on river flow data.
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Dates and versions

hal-04170162 , version 1 (25-07-2023)

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  • HAL Id : hal-04170162 , version 1

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Julyan Arbel, Anne Dutfoy-Lebrun, Stéphane Girard, Théo Moins. Reparameterization of extreme value framework for improved Bayesian workflow. EVA 2023 - 13th International Conference on Extreme Value Analysis, Probabilistic and Statistical Models and their Applications, Jun 2023, Milan, Italy. ⟨hal-04170162⟩
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