Lecture 2: August 29 2.1 Applications of Random Sampling (continued) 2.1.1 Statistical Inference 2.2 Basic Definitions and the Fundamental Theorem
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چکیده
Sampling from the posterior distribution is a natural goal, as it gives us essentially the best possible information about the parameters given the data. We can also use this sampling to solve other related problems, such as inference, where the goal is to compute the probability of a future event Y given data from the past X . This can be reduced to computing the expectation of Pr[Y |Θ] with respect to the posterior distribution:
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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 ...
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