[Bayesian prior distribution and its determination]

The prior distribution refers to a probabilistic description of the uncertainty of unknown parameters by researchers before observing sample data. It is a prerequisite and key step in Bayesian statistical methods, as well as a major challenge encountered in practical applications. Based on four dimensions-information content, probabilistic characteristics, relationship with the likelihood function, and structural hierarchy-this paper comprehensively sorts out the types of prior distributions, illustrates the impact of prior distributions on results through a combination of theory and case studies, and discusses in depth the key issues that need to be prioritized when selecting prior distributions. In addition, this paper elaborates on the importance and implementation methods of sensitivity analysis for prior distributions and introduces key points for reporting Bayesian statistical inference results. Only by rationally selecting prior distributions and standardizing Bayesian statistical inference can the scientific value of Bayesian statistics be fully realized.