Prior Distribution

Prior distributions are crucial in Bayesian inference, encoding prior knowledge or beliefs about the parameters of a model before observing data. Current research focuses on developing sophisticated prior distributions, including those based on deep generative models (like score-based diffusion models and variational autoencoders), structured tensors, and even language models, to improve the accuracy and efficiency of Bayesian inference across diverse applications. These advancements are particularly impactful in addressing challenges like high-dimensional optimization, uncertainty quantification in complex models (e.g., neural networks), and handling distributional shifts in data. The resulting improvements in model accuracy, uncertainty estimation, and computational efficiency have broad implications for fields ranging from materials science and medical diagnosis to astrophysics and robotics.