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Performance of convolutional neural networks (CNNs) in image analysis tasks is often marred in the presence of acquisition-related distribution shifts between training and test images. Recently, it has been proposed to tackle this problem by fine-tuning trained CNNs for each test image. Such test-time-adaptation (TTA) is a promising and practical strategy for improving robustness to distribution shifts as it requires neither data sharing between institutions nor annotating additional data. Previous TTA methods use a helper model to increase similarity between outputs and/or features extracted from a test image with those of the training images. Such helpers, which are typically modeled using CNNs, can be task-specific and themselves vulnerable to distribution shifts in their inputs. To overcome these problems, we propose to carry out TTA by matching the feature distributions of test and training images, as modelled by a field-of-experts (FoE) prior. FoEs model complicated probability distributions as products of many simpler expert distributions. We use 1D marginal distributions of a trained task CNN's features as experts in the FoE model. Further, we compute principal components of patches of the task CNN's features, and consider the distributions of PCA loadings as additional experts. We validate the method on 5 MRI segmentation tasks (healthy tissues in 4 anatomical regions and lesions in 1 one anatomy), using data from 17 clinics, and on a MRI registration task, using data from 3 clinics. We find that the proposed FoE-based TTA is generically applicable in multiple tasks, and outperforms all previous TTA methods for lesion segmentation. For healthy tissue segmentation, the proposed method outperforms other task-agnostic methods, but a previous TTA method which is specifically designed for segmentation performs the best for most of the tested datasets. Our code is publicly available.