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Abstract:
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In this application, we use a Gaussian Hidden Markov Random Field to model the changes in brain/tumor vascular permeability induced by radiation as a noisy observation of an underlying Random Field. In the missing data scenario, the change in permeability is the observed outcome, and the hidden state label is the missing observation. The conditional expectation in the E-step requires summation over all possible realizations of the Random Field, the size of which increases exponentially. We thereby propose a stochastic approximation of the expectation. We use Louis's method to obtain the standard errors of parameter estimates for future comparison with their Bayesian posterior counterparts. Furthermore, the number of states in the Random Field can be selected using information criteria, AIC, BIC, etc. With satisfactory simulation results, we are now working on the real dataset.
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