Assume that we want to put a prior distribution on and perform Bayesian estimation. Your prior...

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Assume that we want to put a prior distribution on and perform Bayesian estimation. Your prior on is a gamma distribution ba p(0) = Ga(0|a, b) = -0-1 exp(-60)1(0 > 0). r(a) Derive the posterior distribution of 0. Consider two sets of values for a, b: (1) a= 0.1,6=0.1, which corresponds to a non-informative prior, and (2) a = 2,b= 5, which corresponds to an informative prior. Plot the prior, likelihood, and posterior, and arrange the plots from (1) and (2) in two panels in a row. Derive the expression of the marginal likelihood with the Ga(a, b) prior on 9. Derive the expression of the posterior predictive distribution with the Ga(a, b) prior on 0. Assume that we want to put a prior distribution on and perform Bayesian estimation. Your prior on is a gamma distribution ba p(0) = Ga(0|a, b) = -0-1 exp(-60)1(0 > 0). r(a) Derive the posterior distribution of 0. Consider two sets of values for a, b: (1) a= 0.1,6=0.1, which corresponds to a non-informative prior, and (2) a = 2,b= 5, which corresponds to an informative prior. Plot the prior, likelihood, and posterior, and arrange the plots from (1) and (2) in two panels in a row. Derive the expression of the marginal likelihood with the Ga(a, b) prior on 9. Derive the expression of the posterior predictive distribution with the Ga(a, b) prior on 0.

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To derive the posterior distribution of theta we need to use Bayes theorem pthetay fracpytheta pthet... View the full answer