Uncertainty Quantification Over Spectral Estimation of Stochastic Processes Subject to Gapped Missing Data Using Variational Bayesian Inference

Yu Chen*, Edoardo Patelli, Michael Beer, Ben Edwards

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingConference contribution book

Abstract

In this work we quantify the uncertainty over Power Spectral Density estimation of stochastic processes based on realizations with gapped missing data. For the purpose of imputation, a fully-connected neural network architecture that works in an autoregressive manner is firstly constructed to probabilistically capture the temporal patterns in the time series data. Particularly, under the Bayesian scheme, uncertainties with respect to the parameters of the neural network model (i.e. weights) are introduced by multivariate Gaussian distribution. During training, the posteriors are learnt through variational inference approach. As a result, the missing gaps can be recursively imputed via our neural network in each realization, and thanks to the probabilistic merit of Bayesian inference, an ensemble of reconstructed realizations can then be obtained. Further, by resorting to a Fourier-based spectral estimation method, a probabilistic power spectrum could be derived, with each frequency component represented by a probability distribution.

Original languageEnglish
Title of host publicationProceedings of the 8th International Symposium on Reliability Engineering and Risk Management, ISRERM 2022
EditorsMichael Beer, Enrico Zio, Kok-Kwang Phoon, Bilal M. Ayyub
Pages173-178
Number of pages6
DOIs
Publication statusPublished - 4 Sept 2024
Event8th International Symposium on Reliability Engineering and Risk Management, ISRERM 2022 - Hannover, Germany
Duration: 4 Sept 20227 Sept 2022

Conference

Conference8th International Symposium on Reliability Engineering and Risk Management, ISRERM 2022
Country/TerritoryGermany
CityHannover
Period4/09/227/09/22

Keywords

  • Bayesian neural network
  • missing data
  • spectral estimation
  • stochastic process
  • Variational Bayesian inference

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