One aspect of the algorithmic lens in theoretical computer science is a view on other scientific disciplines that focuses on satisfactory solutions that adhere to real-world constraints, as opposed to solutions that would be optimal ignoring such constraints. The algorithmic lens has provided a unique and important perspective on many academic fields, including molecular biology, ecology, neuroscience, quantum physics, economics, and social science. This thesis applies the algorithmic lens to Bayesian epistemology. Traditional Bayesian epistemology provides a comprehensive framework for how an individual's beliefs should evolve upon receiving new information. However, these methods typically assume an exhaustive model of such information, including the correlation structure between different pieces of evidence. In reality, individuals might lack such an exhaustive model, while still needing to form beliefs. Beyond such informational constraints, an individual may be bounded by limited computation, or by limited communication with agents that have access to information, or by the strategic behavior of such agents. Even when these restrictions prevent the formation of a *perfectly* accurate belief, arriving at a *reasonably* accurate belief remains crucial. In this thesis, we establish fundamental possibility and impossibility results about belief formation under a variety of restrictions, and lay the groundwork for further exploration.

翻译：理论计算机科学中的算法视角，关注的是在现实约束下提供满意解而非忽略约束的最优解，这一视角已为分子生物学、生态学、神经科学、量子物理、经济学和社会科学等诸多学术领域提供了独特而重要的洞见。本论文将算法视角应用于贝叶斯认识论。传统贝叶斯认识论为个体信念在新信息出现时应如何演化提供了全面框架，但这类方法通常假定信息具有完备模型，包括不同证据之间的相关结构。现实中，个体可能缺乏此类完备模型，却仍需形成信念。除信息约束外，个体还可能受限于有限的计算能力、与信息获取主体的有限通信，或此类主体的策略行为。即便这些限制阻碍了形成*完全*精确的信念，获得*合理*精确的信念依然至关重要。本论文确立了在多种限制条件下信念形成的基本可能性与不可能性结论，并为后续探索奠定基础。