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On Gibbs sampler and Metrolopolis-Hastings applied to pairwise poisson and car crash data
Linköpings universitet.ORCID iD: 0000-0002-9164-9221
(English)Manuscript (preprint) (Other academic)
Abstract [en]

We address the use of MCMC methods in the presence of incidental parameters. Two different models are studied, one pairwise Poisson model and a model for car crash data. In both models, a Bayesian analysis is made where the posterior density is obtained by MCMC methods. The empirical KL-measure is used to diagnose convergence. Credible intervals for structural parameters are computed in both models and compared to the corresponding confidence intervals obtained by frequentist analysis. Although some differences are observed, the methods give qualitatively the same conclusions.

Keyword [en]
Accident rate, Statistics, Analysis (math), Method
National Category
Probability Theory and Statistics
Research subject
80 Road: Traffic safety and accidents, 812 Road: Collation of accident statistics
Identifiers
URN: urn:nbn:se:vti:diva-7101OAI: oai:DiVA.org:vti-7101DiVA: diva2:747458
Available from: 2013-01-07 Created: 2014-09-16 Last updated: 2016-02-22Bibliographically approved
In thesis
1. Computer based statistical treatment in models with incidental parameters: inspired by car crash data
Open this publication in new window or tab >>Computer based statistical treatment in models with incidental parameters: inspired by car crash data
2003 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

Bootstrap and Markov chain Monte Carlo methods have received much attention in recent years. We study computer intensive methods that can be used in complex situations where it is not possible to express the likelihood estimates or the posterior analytically. The work is inspired by a set of car crash data from real traffic.

We formulate and develop a model for car crash data that aims to estimate and compare the relative collision safety among different car models. This model works sufficiently well, although complications arise due to a growing vector of incidental parameters. The bootstrap is shown to be a useful tool for studying uncertainties of the estimates of the structural parameters. This model is further extended to include driver characteristics. In a Poisson model with similar, but simpler structure, estimates of the structural parameter in the presence of incidental parameters are studied. The profile likelihood, bootstrap and the delta method are compared for deterministic and random incidental parameters. The same asymptotic properties, up to first order, are seen for deterministic as well as random incidental parameters.

The search for suitable methods that work in complex model structures leads us to consider Markov chain Monte Carlo (MCMC) methods. In the area of MCMC, we consider particularly the question of how and when to claim convergence of the MCMC run in situations where it is only possible to analyse the output values of the run and also how to compare different MCMC modellings. In Metropolis-Hastings algorithm, different proposal functions lead to different realisations. We develop a new convergence diagnostic, based on the Kullback-Leibler distance, which is shown to be particularly useful when comparing different runs. Comparisons with established methods turn out favourably for the KL.

In both models, a Bayesian analysis is made where the posterior distribution is obtained by MCMC methods. The credible intervals are compared to the corresponding confidence intervals from the bootstrap analysis and are shown to give the same qualitative conclusions.

Place, publisher, year, edition, pages
Linköping: Linköpings universitet, 2003. 34 p.
Series
Linköping Studies in Science and Technology. Dissertations, ISSN 0345-7524 ; 814
Keyword
Mathematical model, Accident, Statistics, Analysis, Driver, Characteristics
National Category
Mathematics
Research subject
80 Road: Traffic safety and accidents, 812 Road: Collation of accident statistics
Identifiers
urn:nbn:se:vti:diva-7106 (URN)1377 (Local ID)91-7373-625-2 (ISBN)1377 (Archive number)1377 (OAI)
Public defence
2003-05-09, Sal Visionen, Hus B, Linköpings Universitet, 13:15 (Swedish)
Opponent
Available from: 2009-10-07 Created: 2014-09-16 Last updated: 2016-02-22Bibliographically approved

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CiteExportLink to record
Permanent link

Direct link
Cite
Citation style
  • apa
  • harvard1
  • ieee
  • modern-language-association-8th-edition
  • vancouver
  • Other style
More styles
Language
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Other locale
More languages
Output format
  • html
  • text
  • asciidoc
  • rtf