Cs294-2 Markov Chain Monte Carlo: Foundations & Applications 2.1 Applications of Markov Chain Monte Carlo (continued) 2.1.1 Statistical Inference
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چکیده
where Pr(Θ) is the prior distribution and refers to the information previously known about Θ, Pr(X | Θ) is the probability that X is obtained with the assumed model, and Pr(X) is the unconditioned probability that X is observed. Pr(Θ | X) is commonly called the posterior distribution and can be written in the form π(Θ) = w(Θ)/Z, where the weight w(Θ) = Pr(X | Θ)Pr(Θ) is easy to compute but the normalizing factor Z = Pr(X) is unknown. MCMC can then be used to sample from Pr(Θ | X). We can further use the sampling in the following applications:
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