Bayesian Inversion and Inference of Categorical Markov Models with Likelihood Functions Including Dependence and Convolution
MetadataShow full item record
A convolutional two-level Markov model is studied in this thesis. The bottom level contains a latent Markov chain, and given the variables, the middle contains a latent Gaussian random field. We observe the second level through a convolution with additive Gaussian noise. Previously studied models are extended by including additional spatial correlation in the middle layer. We propose two different approximations of the likelihood function, namely the truncation and projection approximation, of varying order. These approximate models are exactly assessed by the Forward-Backward algorithm. Properties of various predictors are studied in different approximate posterior models. The predictors are seen to be stable with respect to an increase of the spatial correlation in the response model. An increase of $k$, being the approximation order, is not seen to have a great effect on the predictors. The approximate posterior models are used as proposal densities in a Metropolis-Hastings algorithm to assess the correct posterior model, and we quantify the quality of each approximation by the acceptance rate. The acceptance rate is observed to be an increasing function of $k$. We observed higher acceptance rates when the proportion of the acquisition convolution was high, relative to the spatial correlation. A high class response variance also increased the acceptance rate. Estimation of the transition matrix, using the EM-algorithm and simulation based inference, is found to be feasible under certain conditions. A univariate maximum marginal likelihood estimation of the model parameter in the Ricker acquisition convolution kernel is considered.