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Markov Chain Monte Carlo and the Application to Geodetic Time Series Analysis
OLIVARES PULIDO, German; TEFERLE, Felix Norman; HUNEGNAW, Addisu
2020In Montillet, Jean-Philippe; Bos, Machiel (Eds.) Geodetic Time Series Analysis in Earth Sciences
 

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Keywords :
Time Series Analysis; Stochastic Properties; Markov Chain Monte Carlo; Random Walk; Metropolis-Hasting; Parameter Estimation; Parameter Uncertainties; Geodesy; Earth Sciences
Abstract :
[en] The time evolution of geophysical phenomena can be characterised by stochastic time series. The stochastic nature of the signal stems from the geophysical phenomena involved and any noise, which may be due to, e.g., un-modelled effects or measurement errors. Until the 1990's, it was usually assumed that white noise could fully characterise this noise. However, this was demonstrated to be not the case and it was proven that this assumption leads to underestimated uncertainties of the geophysical parameters inferred from the geodetic time series. Therefore, in order to fully quantify all the uncertainties as robustly as possible, it is imperative to estimate not only the deterministic but also the stochastic parameters of the time series. In this regard, the Markov Chain Monte Carlo (MCMC) method can provide a sample of the distribution function of all parameters, including those regarding the noise, e.g., spectral index and amplitudes. After presenting the MCMC method and its implementation in our MCMC software we apply it to synthetic and real time series and perform a cross-evaluation using Maximum Likelihood Estimation (MLE) as implemented in the CATS software. Several examples as to how the MCMC method performs as a parameter estimation method for geodetic time series are given in this chapter. These include the applications to GPS position time series, superconducting gravity time series and monthly mean sea level (MSL) records, which all show very different stochastic properties. The impact of the estimated parameter uncertainties on sub-sequentially derived products is briefly demonstrated for the case of plate motion models. Finally, the MCMC results for weekly downsampled versions of the benchmark synthetic GNSS time series as provided in Chapter 2 are presented separately in an appendix.
Research center :
ULHPC - University of Luxembourg: High Performance Computing
Disciplines :
Computer science
Earth sciences & physical geography
Author, co-author :
OLIVARES PULIDO, German ;  University of Luxembourg > Faculty of Science, Technology and Communication (FSTC) > Engineering Research Unit ; Spire Global ; Geoscience Australia > National Positioning Infrastructure
TEFERLE, Felix Norman  ;  University of Luxembourg > Faculty of Science, Technology and Communication (FSTC) > Engineering Research Unit
HUNEGNAW, Addisu  ;  University of Luxembourg > Faculty of Science, Technology and Communication (FSTC) > Engineering Research Unit
External co-authors :
yes
Language :
English
Title :
Markov Chain Monte Carlo and the Application to Geodetic Time Series Analysis
Publication date :
2020
Main work title :
Geodetic Time Series Analysis in Earth Sciences
Author, co-author :
Montillet, Jean-Philippe
Bos, Machiel
Publisher :
Springer
Edition :
1st ed.
ISBN/EAN :
978-3-030-21718-1
Collection name :
Springer Geophysics
Pages :
53-138
Focus Area :
Computational Sciences
FnR Project :
FNR12909050 - Advanced Asymmetry Tropospheric Products For Meteorology From Gnss And Sar Observations, 2018 (01/02/2019-31/07/2022) - Norman Teferle
Funders :
University of Luxembourg - UL
FNR - Fonds National de la Recherche
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since 22 January 2020

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