We consider a data set of locations where people in Central Bohemia have been infected by tick-borne encephalitis (TBE), and where population census data and covariates concerning vegetation and altitude are available. The aims are to estimate the risk map of the disease and to study the dependence of the risk on the covariates. Instead of using the common area level approaches we base the analysis on a Bayesian approach for a log Gaussian Cox point process with covariates. Posterior characteristics for a discretized version of the log Gaussian Cox process are computed using Markov chain Monte Carlo methods. A particular problem which is thoroughly discussed is to determine a model for the background population density. The risk map shows a clear dependency with the population intensity models and the basic model which is adopted for the population intensity determines what covariates influence the risk of TBE. Model validation is based on the posterior predictive distribution of various summary statistics.
The paper is devoted to the stereological unfolding problem of bivariate size-orientation distribution of platelike particles in metallography. Gokhale (1996) derived an integral equation which relates this bivariate distribution in three-dimensional (3D) space to the corresponding size-orientation distribution of planar sections of the specimen. The present paper yields a numerical algorithm which enables to transform a bivariate histogram of observed quantities to the histogram of 3D characteristics. The use of the method is demonstrated in examples with simulated data, where an easy analytical solution is available and can be compared with the results of estimation. The spectrum of unfolding problems solved numerically (cf. Ohser and Muecklich, 2000) is thus extended
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