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2024 | OriginalPaper | Chapter

On the Collaboration Between Bayesian and Hilbertian Approaches

Authors : Eduardo Souza de Cursi, Adriano Fabro

Published in: Proceedings of the 6th International Symposium on Uncertainty Quantification and Stochastic Modelling

Publisher: Springer International Publishing

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Abstract

The chapter delves into the intersection of Bayesian inference and Hilbertian approaches, focusing on the determination of distributions from observed data. It begins by comparing Maximum Likelihood Estimation (MLE) and Bayesian Inference (BI), then introduces the Hilbert Approach (HA) as a tool for Uncertainty Quantification (UQ). The text explores how HA can generate priors and likelihoods, enhancing Bayesian inference and providing more accurate parameter estimations. It also discusses the use of De Finetti’s theorem for exchangeable sequences and demonstrates how HA can improve the estimation process. The chapter concludes by highlighting the potential of combining HA and BI for more robust statistical analysis, with examples showcasing the practical advantages of this collaboration.
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Metadata
Title
On the Collaboration Between Bayesian and Hilbertian Approaches
Authors
Eduardo Souza de Cursi
Adriano Fabro
Copyright Year
2024
Book
Proceedings of the 6th International Symposium on Uncertainty Quantification and Stochastic Modelling

Print ISBN: 978-3-031-47035-6

Electronic ISBN: 978-3-031-47036-3

Copyright Year: 2024

DOI
https://doi.org/10.1007/978-3-031-47036-3_16

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