Teaching Research on Conjugate Prior Distributions in Bayesian Statistics
The prior distribution plays a crucial role in Bayesian statistics,and conjugate priors are among the most important types.Students'understanding and mastery of conjugate prior distributions directly impact their learning outcomes in Bayesian statistical methods.Currently,most textbooks typically introduce some com-mon distributions with conjugate priors and then prove their conjugate properties.However,this teaching method lacks depth and flexibility.To address this issue,this article proposes a general expression for parameter conju-gate priors under a broader class of exponential family distributions.Subsequently,for some common distribu-tions,their conjugate priors for the parameters are derived from the structure of the exponential family,enabling students to not only gain a profound understanding of the essence of conjugate priors but also learn a more flexi-ble strategy for choosing conjugate priors.This teaching approach,transitioning from general to specific,helps enhance students'depth of understanding in Bayesian statistics and cultivates their ability to flexibly apply conju-gate priors.
Bayesian statisticsconjugate prior distributionexponential family distribution
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