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A Bayesian non-parametric Potts model with application to pre-surgical FMRI data
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Johnson, T. D., Liu, Z., Bartsch, A. J. and Nichols, Thomas E. (2013) A Bayesian non-parametric Potts model with application to pre-surgical FMRI data. Statistical Methods in Medical Research , Volume 44 (Number 2). pp. 364-381. doi:10.1177/0962280212448970 ISSN 0962-2802.
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Official URL: http://dx.doi.org/10.1177/0962280212448970
Abstract
The Potts model has enjoyed much success as a prior model for image segmentation. Given the individual
classes in the model, the data are typically modeled as Gaussian random variates or as random variates
from some other parametric distribution. In this article, we present a non-parametric Potts model and
apply it to a functional magnetic resonance imaging study for the pre-surgical assessment of peritumoral
brain activation. In our model, we assume that the Z-score image from a patient can be segmented into
activated, deactivated, and null classes, or states. Conditional on the class, or state, the Z-scores are
assumed to come from some generic distribution which we model non-parametrically using a mixture of
Dirichlet process priors within the Bayesian framework. The posterior distribution of the model
parameters is estimated with a Markov chain Monte Carlo algorithm, and Bayesian decision theory is
used to make the final classifications. Our Potts prior model includes two parameters, the standard spatial
regularization parameter and a parameter that can be interpreted as the a priori probability that each
voxel belongs to the null, or background state, conditional on the lack of spatial regularization. We assume
that both of these parameters are unknown, and jointly estimate them along with other model
parameters. We show through simulation studies that our model performs on par, in terms of
posterior expected loss, with parametric Potts models when the parametric model is correctly
specified and outperforms parametric models when the parametric model in misspecified
| Item Type: | Journal Article | ||||
|---|---|---|---|---|---|
| Divisions: | Faculty of Science, Engineering and Medicine > Science > Statistics Faculty of Science, Engineering and Medicine > Engineering > WMG (Formerly the Warwick Manufacturing Group) |
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| Journal or Publication Title: | Statistical Methods in Medical Research | ||||
| Publisher: | Sage Publications Ltd. | ||||
| ISSN: | 0962-2802 | ||||
| Official Date: | August 2013 | ||||
| Dates: |
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| Volume: | Volume 44 | ||||
| Number: | Number 2 | ||||
| Page Range: | pp. 364-381 | ||||
| DOI: | 10.1177/0962280212448970 | ||||
| Status: | Peer Reviewed | ||||
| Publication Status: | Published | ||||
| Access rights to Published version: | Restricted or Subscription Access |
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