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Semi Markov chain Monte CarloPrimeFaces.cw("AccordionPanel","widget_formSmash_some",{id:"formSmash:some",widgetVar:"widget_formSmash_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_all",{id:"formSmash:all",widgetVar:"widget_formSmash_all",multiple:true});
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PrimeFaces.cw("AccordionPanel","widget_formSmash_responsibleOrgs",{id:"formSmash:responsibleOrgs",widgetVar:"widget_formSmash_responsibleOrgs",multiple:true}); 1999 (English)Doctoral thesis, comprehensive summary (Other academic)
##### Abstract [en]

##### Place, publisher, year, edition, pages

Uppsala: Acta Universitatis Upsaliensis , 1999. , 131 p.
##### Series

Uppsala Dissertations in Mathematics, ISSN 1401-2049 ; 13
##### Keyword [en]

Mathematics, Adaptive simulation, error-in-the-variables, Kullback-Leibler divergence, Markov chain simulation, Markov chain Monte Carlo, semi-regenerative
##### Keyword [sv]

MATEMATIK
##### National Category

Mathematics
##### Research subject

Mathematical Statistics
##### Identifiers

URN: urn:nbn:se:uu:diva-1217ISBN: 91-506-1344-8OAI: oai:DiVA.org:uu-1217DiVA: diva2:160774
##### Public defence

1999-05-20, Room 247, Building 2, Polacksbacken, Uppsala University, Uppsala, 10:15
#####

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Available from: 1999-04-29 Created: 1999-04-29Bibliographically approved

The first paper introduces a new simulation technique, called semi Markov chain Monte Carlo, suitable for estimating the expectation of a fixed function over a distribution π, E_{π}*f*(χ). Given a Markov chain with stationary distribution p, for example a Markov chain corresponding to a Markov chain Monte Carlo algorithm, an embedded Markov renewal process is used to divide the trajectory into different parts. The parts are then used to estimate E_{π}*f*(χ) with a ratio estimator, *g*. An adaptive algorithm chooses the number of times the different parts are to be run, such that the asymptotic variance of *g* is minimized.

The Kullback-Leibler information divergence between univariate Student *t* and normal distributions are studied in the second paper. Explicit expressions, in terms of manageable functions, are derived for the Kullback-Leibler divergences. The expressions are obtained by taking the limits of the corresponding Renyi'sa -informations.

In the third paper, a logistic regression model having continuous independent variables measured with error is constructed. The measurement error process, the process which gives the error prone independent variables, is modelled using a multivariate linear regression model. The model uses information from a validation study, where the true independent variables and the independent variables measured with error are observed simultaneously, for a subgroup of the individuals. This results in a prediction model for the true independent variables. The model is developed using the Bayesian paradigm and the posterior is analyzedusing Gibbs sampling.

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