This work is motivated by a pilot study on the change in tumor/brain contrast uptake induced by radiation via quantitative Magnetic Resonance Imaging. The results inform the optimal timing of administering chemotherapy in the context of radiotherapy. A noticeable feature of the data is spatial heterogeneity. The tumor is physiologically and pathologically distinct from surrounding healthy tissue. Also, the tumor itself is usually highly heterogeneous. We employ a Gaussian Hidden Markov Random Field model that respects the above features. The model introduces a latent layer of discrete labels from an Markov Random Field (MRF) governed by a spatial regularization parameter. We further assume that conditional on the hidden labels, the observed data are independent and normally distributed, We treat the regularization parameter of the MRF, as well as the number of states of the MRF as parameters, and estimate them via the Reversible Jump Markov chain Monte Carlo algorithm. We propose a novel and nontrivial implementation of the Reversible Jump moves. The performance of the method is examined in both simulation studies and real data analysis. We report the pixel-wise posterior mean and standard deviation of the change in contrast uptake marginalized over the number of states and hidden labels. We also compare the performance with a Markov chain with fixed number of states and a parallel Expectation-Maximization approach from a frequentist perspective.



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