Node-wise pseudo-marginal methods for spatial model selection

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Abstract

Motivated by problems from statistical analysis of neuroimaging data where current approaches make use of \mass univariate" analysis which neglects spatial structure entirely; A novel framework for incorporating spatial dependence within a large class of model-selection problems is introduced. Spatial dependence is encoded through a Markov random field model, enabling a variant of the pseudo-marginal Markov chain Monte Carlo algorithm to be developed. This method can then extended by a further augmentation of the underlying state space. The approach allows existing unbiased marginal likelihood estimator, used in settings in which spatial independence is assumed, to be readily exploited. This, therefore, allows the incorporation of spatial dependence using non-spatial estimates, with very minimal additional development effort. Numerical investigation on measured PET image data show notable improvements in revealing underlying spatial structure, when compared to current methods that assume spatial independence. This novel, accessible algorithm can be realistically used for analysis of smaller subsets of large image data sets such as 2

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