Epsilon Open Archive

Abstract

This thesis deals with application of several methods of computational statistics to the estimation of parameters in various models in remote sensing and environmental applications. The considered methods and applications are the following: - mapping of the spatial distribution of reindeer in the case of the incomplete ground survey by the Gibbs sampler - detection of small-sized tracks in aerial photos and satellite images with help of the Gibbs sampler - contextual classification of multispectral images with spatially correlated noise using Markov chain Monte Carlo methods and Markov random field prior - maximum likelihood estimation of the parameters of forest growth models with measurement errors - maximum spacing estimation based on Dirichlet tesselation for univariate and multivariate observations. In paper I we try to answer the following question. In mapping of animal distributions what is the minimum adequate number of plots one must survey to maintain a high accuracy of prediction? We use the Gibbs sampler to simulate the data for unsurveyed plots, and then use the simulated data to fit the autologistic model. In paper II we propose an algorithm for extracting small tracks from remotely sensed images. We specify several prior distributions of varying complexity, and calculate a maximum a posteriori estimate of the map of tracks using the Gibbs sampler. Paper III deals with classification of multispectral imagery in presence of autocorrelated noise. By means of simulation study we show how the classification results of conventional algorithms can be improved by adopting the Markov random field prior model. In paper IV the forest growth model with measurement errors is introduced. We establish some asymptotic properties for maximum likelihood estimates of the parameters of this model. Paper V is devoted to maximum spacing estimation based on Dirichlet tesselation. We prove consistency of such maximum spacing estimate in univariate case and conjecture it holds in higher dimensions.