Neural networks have achieved remarkable performance across various problem domains, but their widespread applicability is hindered by inherent limitations such as overconfidence in predictions, lack of interpretability, and vulnerability to adversarial attacks. To address these challenges, Bayesian neural networks (BNNs) have emerged as a compelling extension of conventional neural networks, integrating uncertainty estimation into their predictive capabilities. This comprehensive primer presents a systematic introduction to the fundamental concepts of neural networks and Bayesian inference, elucidating their synergistic integration for the development of BNNs. The target audience comprises statisticians with a potential background in Bayesian methods but lacking deep learning expertise, as well as machine learners proficient in deep neural networks but with limited exposure to Bayesian statistics. We provide an overview of commonly employed priors, examining their impact on model behavior and performance. Additionally, we delve into the practical considerations associated with training and inference in BNNs. Furthermore, we explore advanced topics within the realm of BNN research, acknowledging the existence of ongoing debates and controversies. By offering insights into cutting-edge developments, this primer not only equips researchers and practitioners with a solid foundation in BNNs, but also illuminates the potential applications of this dynamic field. As a valuable resource, it fosters an understanding of BNNs and their promising prospects, facilitating further advancements in the pursuit of knowledge and innovation.

翻译：神经网络已在各类问题领域展现出卓越性能，但其广泛适用性仍受制于固有局限，如预测过度自信、可解释性缺失及对抗攻击脆弱性。为解决这些挑战，贝叶斯神经网络（BNNs）作为传统神经网络的有力扩展应运而生，将不确定性估计融入其预测能力。本综合性入门文章系统介绍了神经网络与贝叶斯推断的基本概念，阐释了二者协同整合以构建BNNs的原理。目标读者包括具备贝叶斯方法基础但缺乏深度学习专长的统计学者，以及精通深度神经网络但鲜有接触贝叶斯统计的机器学习研究者。我们概述了常用先验分布，剖析其对模型行为与性能的影响；深入探讨了BNNs训练与推理中的实践考量；并进一步探究了BNN研究领域的前沿议题，承认已有争议与讨论的存在。通过提供对前沿进展的洞见，本文不仅为研究人员与实践者奠定BNNs的坚实基础，更揭示了这一动态领域的潜在应用前景。作为重要参考文献，本文促进了对BNNs及其广阔前景的理解，为知识探索与创新进程中的进一步突破提供助力。