A Bayesian Nonlinear Regression Model Based on t-Distributed Errors

Alexander Dorndorf; Boris Kargoll; Jens André Paffenholz; Hamza Alkhatib

doi:10.1007/1345_2019_76

A Bayesian Nonlinear Regression Model Based on t-Distributed Errors

Alexander Dorndorf^*
, Boris Kargoll
, Jens André Paffenholz
, Hamza Alkhatib

^*Corresponding author for this work

Geodetic Institute

Research output: Chapter in book/report/conference proceeding › Conference contribution › Research › peer review

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.

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
DOIs	https://doi.org/10.1007/1345_2019_76
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

Conference

Conference	9th Hotine-Marussi Symposium on Mathematical Geodesy, 2018
Country/Territory	Italy
City	Rome
Period	18 Jun 2018 → 22 Jun 2018

Keywords

Bayesian nonlinear regression model
Gibbs sampler
Markov Chain Monte Carlo
Metropolis-Hastings algorithm
Scaled t-distribution

ASJC Scopus subject areas

Computers in Earth Sciences
Geophysics

Access to Document

10.1007/1345_2019_76

Cite this

Dorndorf, A., Kargoll, B., Paffenholz, J. A., & Alkhatib, H. (2019). A Bayesian Nonlinear Regression Model Based on t-Distributed Errors. In P. Novák, M. Crespi, N. Sneeuw, & F. Sansò (Eds.), 9th Hotine-Marussi Symposium on Mathematical Geodesy - Proceedings of the Symposium in Rome, 2018 (pp. 127-135). (International Association of Geodesy Symposia; Vol. 151). Springer Science and Business Media Deutschland GmbH. https://doi.org/10.1007/1345_2019_76

Dorndorf, Alexander ; Kargoll, Boris ; Paffenholz, Jens André et al. / A Bayesian Nonlinear Regression Model Based on t-Distributed Errors. 9th Hotine-Marussi Symposium on Mathematical Geodesy - Proceedings of the Symposium in Rome, 2018. editor / Pavel Novák ; Mattia Crespi ; Nico Sneeuw ; Fernando Sansò. Cham : Springer Science and Business Media Deutschland GmbH, 2019. pp. 127-135 (International Association of Geodesy Symposia).

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title = "A Bayesian Nonlinear Regression Model Based on t-Distributed Errors",

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",

author = "Alexander Dorndorf and Boris Kargoll and Paffenholz, \{Jens Andr{\'e}\} and Hamza Alkhatib",

year = "2019",

doi = "10.1007/1345\_2019\_76",

language = "English",

isbn = "9783030542665",

series = "International Association of Geodesy Symposia",

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pages = "127--135",

editor = "Pavel Nov{\'a}k and Mattia Crespi and Nico Sneeuw and Fernando Sans{\`o}",

booktitle = "9th Hotine-Marussi Symposium on Mathematical Geodesy - Proceedings of the Symposium in Rome, 2018",

address = "Germany",

note = "9th Hotine-Marussi Symposium on Mathematical Geodesy, 2018 ; Conference date: 18-06-2018 Through 22-06-2018",

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Dorndorf, A, Kargoll, B, Paffenholz, JA & Alkhatib, H 2019, A Bayesian Nonlinear Regression Model Based on t-Distributed Errors. in P Novák, M Crespi, N Sneeuw & F Sansò (eds), 9th Hotine-Marussi Symposium on Mathematical Geodesy - Proceedings of the Symposium in Rome, 2018. International Association of Geodesy Symposia, vol. 151, Springer Science and Business Media Deutschland GmbH, Cham, pp. 127-135, 9th Hotine-Marussi Symposium on Mathematical Geodesy, 2018, Rome, Italy, 18 Jun 2018. https://doi.org/10.1007/1345_2019_76

A Bayesian Nonlinear Regression Model Based on t-Distributed Errors. / Dorndorf, Alexander; Kargoll, Boris; Paffenholz, Jens André et al.
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

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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

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Dorndorf A, Kargoll B, Paffenholz JA, Alkhatib H. A Bayesian Nonlinear Regression Model Based on t-Distributed Errors. In Novák P, Crespi M, Sneeuw N, Sansò F, editors, 9th Hotine-Marussi Symposium on Mathematical Geodesy - Proceedings of the Symposium in Rome, 2018. Cham: Springer Science and Business Media Deutschland GmbH. 2019. p. 127-135. (International Association of Geodesy Symposia). Epub 2019 Jul 27. doi: 10.1007/1345_2019_76

A Bayesian Nonlinear Regression Model Based on t-Distributed Errors

Abstract

Publication series

Conference

Keywords

ASJC Scopus subject areas

Access to Document

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