Spectral density estimation of stochastic processes under missing data and uncertainty quantification with Bayesian deep learning

Chen, Yu and Patelli, Edoardo and Edwards, Benjamin and Beer, Michael; Papadrakakis, M. and Papadopoulos, V. and Stefanou, G., eds. (2023) Spectral density estimation of stochastic processes under missing data and uncertainty quantification with Bayesian deep learning. In: UNCECOMP 2023: 5th International Conference on Uncertainty Quantification in Computational Science and Engineering. National Technical University of Athens, GRC, pp. 745-754. ISBN 9786185827021 (https://2023.uncecomp.org/proceedings/)

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Abstract

Stochastic processes are widely adopted in many domains to deal with problems which are stochastic in nature and involve strong nonlinearity, nonstationarity and uncertain system parameters. However, the uncertainties of spectral representation of the underlying stochastic processes have not been adequately acknowledged due to the data problems in practice, for instance, missing data. Therefore, this paper proposes a novel method for uncertainty quantification of spectral representation in the presence of missing data using Bayesian deep learning models. A range of missing levels are tested. An example in stochastic dynamics is employed for illustration.

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