Semi Markov chain Monte Carlo

Abstract: 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.