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Bayesian inference for nonlinear diffusions, observed at discrete times, is a challenging task that has prompted the development of a number of algorithms, mainly within the computational statistics community. We propose a new direction,…

The success of diffusion probabilistic models in generative tasks, such as text-to-image generation, has motivated the exploration of their application to regression problems commonly encountered in scientific computing and various other…

Fiber tracking based on diffusion weighted Magnetic Resonance Imaging (dMRI) allows for noninvasive reconstruction of fiber bundles in the human brain. In this chapter, we discuss sources of error and uncertainty in this technique, and…

Bayesian neural networks (BNNs) have recently regained a significant amount of attention in the deep learning community due to the development of scalable approximate Bayesian inference techniques. There are several advantages of using a…

Brain cell structure and function reflect neurodevelopment, plasticity and ageing, and changes can help flag pathological processes such as neurodegeneration and neuroinflammation. Accurate and quantitative methods to non-invasively…

While Deep Neural Networks (DNNs) achieve state-of-the-art accuracy in various applications, they often fall short in accurately estimating their predictive uncertainty and, in turn, fail to recognize when these predictions may be wrong.…

The modeling and uncertainty quantification of closed curves is an important problem in the field of shape analysis, and can have significant ramifications for subsequent statistical tasks. Many of these tasks involve collections of closed…

Uncertainty quantification is an important task in machine learning - a task in which standardneural networks (NNs) have traditionally not excelled. This can be a limitation for safety-critical applications, where uncertainty-aware methods…

Detail features of magnetic resonance images play a cru-cial role in accurate medical diagnosis and treatment, as they capture subtle changes that pose challenges for doc-tors when performing precise judgments. However, the widely utilized…

Magnetic Resonance Imaging (MRI) offers unparalleled soft-tissue contrast but is fundamentally limited by long acquisition times. While deep learning-based accelerated MRI can dramatically shorten scan times, the reconstruction from…

The displacement distribution of a water molecular is characterized mathematically as Gaussianity without considering potential diffusion barriers and compartments. However, this is not true in real scenario: most biological tissues are…

Deep generative models have emerged as promising tools for detecting arbitrary anomalies in data, dispensing with the necessity for manual labelling. Recently, autoregressive transformers have achieved state-of-the-art performance for…

Collective insights from a group of experts have always proven to outperform an individual's best diagnostic for clinical tasks. For the task of medical image segmentation, existing research on AI-based alternatives focuses more on…

Recently, combinations of generative and Bayesian machine learning have been introduced in particle physics for both fast detector simulation and inference tasks. These neural networks aim to quantify the uncertainty on the generated…

Diffusion models have recently emerged as powerful generative models in medical imaging. However, it remains a major challenge to combine these data-driven models with domain knowledge to guide brain imaging problems. In neuroimaging,…

Statistical shape modeling (SSM) has recently taken advantage of advances in deep learning to alleviate the need for a time-consuming and expert-driven workflow of anatomy segmentation, shape registration, and the optimization of…

Diffusion-weighted imaging (DWI) is a powerful non-invasive tool which is widely used in clinical routine. Mostly, apparent diffusion coefficient maps are acquired, which cannot be directly related to cellular structure. More recently it…

Diffusion models are the current state-of-the-art for solving inverse problems in imaging. Their impressive generative capability allows them to approximate sampling from a prior distribution, which alongside a known likelihood function…

We present a novel approach for training deep neural networks in a Bayesian way. Classical, i.e. non-Bayesian, deep learning has two major drawbacks both originating from the fact that network parameters are considered to be deterministic.…

Many developmental processes, such as plasticity and aging, or pathological processes such as neurological diseases are characterized by modulations of specific cellular types and their microstructures. Diffusion-weighted Magnetic Resonance…