MIT15_097S12_lec15

For bernoulli beta we saw that the prior hyperparame

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Unformatted text preview: ikelihood model is used together with its conjugate prior, we know the posterior is from the same family of the prior, and moreover we have an explicit formula for the posterior hyperparameters. A table summarizing some of the useful conjugate prior relationships follows. There are many more conjugate prior relationships that are not shown in the following table but that can be found in reference books on Bayesian statistics1 . 1 Bayesian Data Analysis by Gelman, Carlin, Stern, and Rubin is an excellent choice. 11 Likelihood Conjugate Prior Prior Hyperparams Posterior Hyperparams m i=1 m i=1 m i=1 m i=1 yi , β + m − Bernoulli Beta α, β α+ Binomial Beta α, β α+ Poisson Gamma α, β α+ Geometric Beta α, β α + m, β + Uniform on [0, θ] Pareto xs , k max{max yi , xs }, k + m Exponential Gamma α, β α + m, β + Normal 2 µ 0 , σ0 Normal unknown mean known variance σ 2 µ0 2 σ0 + 1 σ2 m i=1 yi , β + yi m i=1 mi − yi yi , β + m m i=1 m i=1 m i=1 yi yi yi / 1 2 σ0 + m σ2 , 1 2 σ0 + m σ2 We will now discuss a f...
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This note was uploaded on 03/24/2014 for the course MIT 15.097 taught by Professor Cynthiarudin during the Spring '12 term at MIT.

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