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the most important questions in lifeare indeed, for the most part, only problems in probability. One may even say, strictly speaking, that almost all of our knowledge is only probable.

Pierre-Simon Laplace, Philosophical Essay on Probabilities

Over 200 years ago, French mathematician Pierre-Simon Laplace recognized that most problems we face are inherently probabilistic and that most of our knowledge is based on probabilities rather than absolute certainties. With this premise, he fully developed Bayes theorem, a fundamental theory of probability, without being aware that the English reverend Thomas Bayes (also a statistician and philosopher) had described the theorem sixty years ago. The theorem, therefore, was named after Bayes, although Laplace did most of the mathematical work to complete it.

In contrast to its long history, Bayes theorem has come into the spotlight only in recent decades, finding a prominent surge in its applications in diverse disciplines, with the growing realization that the theorem more closely aligns with our perception and cognitive processes. It manifests the dynamic adjustment of probabilities informed by both new data and pre-existing knowledge. Moreover, it explains the iterative and evolving nature of our knowledge-acquiring and decision-making.

In addition, Bayesian inference has become a powerful technique for building predictive models and making model selections, applied broadly in various fields in scientific research and data science. Using Bayesian statistics in deep learning is also a vibrant area under active study.

This article will first review the basics of Bayes theorem and its application in Bayesian inference and statistics. We will next explore how the Bayesian framework unifies our understanding of perception, human cognition, and decision-making. Ultimately, we will gain insights into the current state and challenges of Bayesian intelligence and the interplay between human and artificial intelligence in the near future.

Bayes theorem begins with the mathematical notion of conditional probability, the probability

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Bayesian Inference: A Unified Framework for Perception, Reasoning, and Decision-making - Towards Data Science