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Semi Markov chain Monte Carlo
Uppsala University, Teknisk-naturvetenskapliga vetenskapsområdet, Mathematics and Computer Science, Department of Mathematics.
1999 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

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, Eπf(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 Eπf(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.

Place, publisher, year, edition, pages
Uppsala: Acta Universitatis Upsaliensis , 1999. , 131 p.
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]
National Category
Research subject
Mathematical Statistics
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
Available from: 1999-04-29 Created: 1999-04-29Bibliographically approved

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