Deep learning-based medical image segmentation models are trained using annotations that exhibit systematic bias and variability across raters. While probabilistic multi-rater approaches can emulate annotator-specific delineations, annotator characteristics are typically encoded implicitly in deep latent feature space, making direct analysis of their influence on predictive distributions less straightforward. We propose a logit-space probabilistic segmentation framework based on stochastic variational Gaussian Process that explicitly decomposes predictions into an image-dependent reference logit distribution and annotator specific perturbations parameterised by bias and variance. This formulation enables more explicit analysis on how intra- and inter-rater variability propagate to predictive distributions. We evaluate the method on a multi-annotator medical image dataset, which shows that explicitly modelling annotator specific perturbations improves uncertainty calibration while maintaining comparable segmentation accuracy, compared with state-of-the-art multi-rater probabilistic segmentation method. The learned bias and variance parameters quantitatively reflect annotator-specific behaviour. Furthermore, controlled perturbation experiments over bias and variance demonstrate how changes in annotator parameters systematically influence predictive performance. The code used in this paper is made publicly available at https://github.com/QiLi111/GPS-Var.

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