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The advent of convolutional neural networks has led to remarkable progress in dense stereo labeling problem, achieving superior performance over the traditional methods. However, the ill-posed nature of stereo matching makes noise (outliers)in winner-takes-all (WTA) disparity maps inevitable. This paper presents a robust statistical approach to noise detection and refinement of WTA disparity maps. In the context of noise detection, the input noisy WTA disparity map is segmented into regular grid cells (regions) with the aim of leveraging Markov random field (MRF) to infer candidate disparity labels.However, there are two key problems: there can be large severe outliers in the regions; second, the regular partition process may produce regions with mixed disparity distributions. To overcome these problems, we optimize a robust objective function over the segmented disparity map. By obtaining the optimal solution of the objective function through a maximum a posteriori estimation in a probabilistic model, we are able to infer MRF candidate disparity labels. We then apply a soft-segmentation constraint on the estimated MRF candidate disparity labels to describe and detect outliers in the disparity map. Next, an edge-preserving statistical inference that leverages the joint statistics of the disparity map and its guidance reference image is used to select correct candidate disparity for each detected outlier. Finally, a weighted median filter is applied to remove small spikes and irregularities in the resulting disparity map. Rigorous and comprehensive experiments showed that the proposed method is distributionally robust and outlier resistant, and can effectively detect and correct outliers in disparity maps. Middlebury evaluation benchmark validated the competitive performance of the proposed method.