مقایسهٔ روش‌ها

	تحلیل پیشین مزدوج	زنجیره مارکوف مونت کارلو (MCMC)
حوزه	بیزی	بیزی
خانواده	Bayesian methods	Bayesian methods
سال پیدایش	1961	—
پدیدآور	Raiffa & Schlaifer (1961); DeGroot (1970)	—
نوع	Closed-form Bayesian model	Posterior sampling algorithm
منبع بنیادین	Raiffa, H. & Schlaifer, R. (1961). Applied Statistical Decision Theory. Harvard University Press. ISBN: 978-0-87584-017-8	Gelman, A., Carlin, J. B., Stern, H. S., Dunson, D. B., Vehtari, A. & Rubin, D. B. (2013). Bayesian Data Analysis (3rd ed.). CRC Press. ISBN: 978-1439840955
نام‌های دیگر	conjugate priors, conjugate Bayesian updating, closed-form posterior analysis, Beta-Binomial model	markov chain monte carlo, MCMC sampling, MCMC (Markov Zinciri Monte Carlo)
مرتبط	3	3
خلاصه	Conjugate prior analysis is a class of Bayesian inference methods in which the prior distribution and the likelihood belong to a matched family — called a conjugate pair — so that the posterior distribution has exactly the same functional form as the prior and can be derived in closed form. Introduced systematically by Raiffa and Schlaifer (1961) and consolidated by DeGroot (1970), conjugate analysis is the pedagogic backbone of introductory Bayesian statistics and a practical tool whenever analytical tractability is required.	Markov Chain Monte Carlo (MCMC) is a family of computational algorithms for sampling from complex probability distributions, most commonly the posterior distributions that arise in Bayesian inference. Rather than computing posteriors analytically — which is rarely possible for realistic models — MCMC constructs a Markov chain whose stationary distribution is the target posterior and draws dependent samples from it, enabling full probabilistic inference for virtually any model.