Details
| Original language | English |
|---|---|
| Title of host publication | 9th Hotine-Marussi Symposium on Mathematical Geodesy - Proceedings of the Symposium in Rome, 2018 |
| Editors | Pavel Novák, Mattia Crespi, Nico Sneeuw, Fernando Sansò |
| Place of Publication | Cham |
| Publisher | Springer Science and Business Media Deutschland GmbH |
| Pages | 127-135 |
| Number of pages | 9 |
| ISBN (Electronic) | 978-3-030-54267-2 |
| ISBN (Print) | 9783030542665 |
| Publication status | Published - 2019 |
| Event | 9th Hotine-Marussi Symposium on Mathematical Geodesy, 2018 - Rome, Italy Duration: 18 Jun 2018 → 22 Jun 2018 Conference number: 9 |
Publication series
| Name | International Association of Geodesy Symposia |
|---|---|
| Volume | 151 |
| ISSN (Print) | 0939-9585 |
| ISSN (Electronic) | 2197-9359 |
Abstract
In this contribution, a robust Bayesian approach to adjusting a nonlinear regression model with t-distributed errors is presented. In this approach the calculation of the posterior model parameters is feasible without linearisation of the functional model. Furthermore, the integration of prior model parameters in the form of any family of prior distributions is demonstrated. Since the posterior density is then generally non-conjugated, Monte Carlo methods are used to solve for the posterior numerically. The desired parameters are approximated by means of Markov chain Monte Carlo using Gibbs samplers and Metropolis-Hastings algorithms. The result of the presented approach is analysed by means of a closed-loop simulation and a real world application involving GNSS observations with synthetic outliers.
Keywords
- Bayesian nonlinear regression model, Gibbs sampler, Markov Chain Monte Carlo, Metropolis-Hastings algorithm, Scaled t-distribution
ASJC Scopus subject areas
- Earth and Planetary Sciences(all)
- Computers in Earth Sciences
- Earth and Planetary Sciences(all)
- Geophysics
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9th Hotine-Marussi Symposium on Mathematical Geodesy - Proceedings of the Symposium in Rome, 2018. ed. / Pavel Novák; Mattia Crespi; Nico Sneeuw; Fernando Sansò. Cham: Springer Science and Business Media Deutschland GmbH, 2019. p. 127-135 (International Association of Geodesy Symposia; Vol. 151).
Research output: Chapter in book/report/conference proceeding › Conference contribution › Research › peer review
}
TY - GEN
T1 - A Bayesian Nonlinear Regression Model Based on t-Distributed Errors
AU - Dorndorf, Alexander
AU - Kargoll, Boris
AU - Paffenholz, Jens André
AU - Alkhatib, Hamza
N1 - Conference code: 9
PY - 2019
Y1 - 2019
N2 - In this contribution, a robust Bayesian approach to adjusting a nonlinear regression model with t-distributed errors is presented. In this approach the calculation of the posterior model parameters is feasible without linearisation of the functional model. Furthermore, the integration of prior model parameters in the form of any family of prior distributions is demonstrated. Since the posterior density is then generally non-conjugated, Monte Carlo methods are used to solve for the posterior numerically. The desired parameters are approximated by means of Markov chain Monte Carlo using Gibbs samplers and Metropolis-Hastings algorithms. The result of the presented approach is analysed by means of a closed-loop simulation and a real world application involving GNSS observations with synthetic outliers.
AB - In this contribution, a robust Bayesian approach to adjusting a nonlinear regression model with t-distributed errors is presented. In this approach the calculation of the posterior model parameters is feasible without linearisation of the functional model. Furthermore, the integration of prior model parameters in the form of any family of prior distributions is demonstrated. Since the posterior density is then generally non-conjugated, Monte Carlo methods are used to solve for the posterior numerically. The desired parameters are approximated by means of Markov chain Monte Carlo using Gibbs samplers and Metropolis-Hastings algorithms. The result of the presented approach is analysed by means of a closed-loop simulation and a real world application involving GNSS observations with synthetic outliers.
KW - Bayesian nonlinear regression model
KW - Gibbs sampler
KW - Markov Chain Monte Carlo
KW - Metropolis-Hastings algorithm
KW - Scaled t-distribution
UR - http://www.scopus.com/inward/record.url?scp=85074150240&partnerID=8YFLogxK
U2 - 10.1007/1345_2019_76
DO - 10.1007/1345_2019_76
M3 - Conference contribution
AN - SCOPUS:85074150240
SN - 9783030542665
T3 - International Association of Geodesy Symposia
SP - 127
EP - 135
BT - 9th Hotine-Marussi Symposium on Mathematical Geodesy - Proceedings of the Symposium in Rome, 2018
A2 - Novák, Pavel
A2 - Crespi, Mattia
A2 - Sneeuw, Nico
A2 - Sansò, Fernando
PB - Springer Science and Business Media Deutschland GmbH
CY - Cham
T2 - 9th Hotine-Marussi Symposium on Mathematical Geodesy, 2018
Y2 - 18 June 2018 through 22 June 2018
ER -