Seminarium  i matematisk statistik
måndagen den 9. oktober 13.15  i MH230
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Linda Werner presenterar sitt examensarbete

A Hierarchical Bayesian Model for Spatial Data.


Abstract

In the environmental sciences many spatial datasets appear. In this
study we have suggested a hierarchical model for a spatial stochastic
field. The variation of the stochastic field is modelled as linear trend
plus microvariation in the form of a Gaussian Markov random field,
defined on a lattice. To use non-lattice observations we have used a
linear binning technique to map the observational points to the lattice
points. To estimate the model parameters we have adopted a Bayesian
perspective, and have specified priors for all parameters. Instead of
analytical estimation we use Monte Carlo integration over samples made
with Markov Chain Monte Carlo simulations, in particular Gibbs sampling.

We have used simulated datasets to study how and under what restrictions
the estimation procedures perform well. We found some restrictions for
the model parameters, and that some of the model parameters are
impossible to estimate with small datasets. Also the size of the
artificial grid on which the model is set have influence on the quality
of the estimation, and must be chosen in consideration of the number of
observations. We also suggest ways to continue the investigation.

Key-words: MCMC, GMF, Bayesian inference

Alla hälsas välkomna!