Mixture models: After a posterior analysis on data from a population of squash plants, it was...

 

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Mixture models: After a posterior analysis on data from a population of squash plants, it was determined that the total vegetable weight of a given plant could be modeled with the following distribution: p(yl0, 02) = .31dnorm(y, 0, ơ) + .46dnorm(201, 20) + .23dnorm(y, 301, 30) where the posterior distributions of the parameters have been calculated as 1/02 - gamma(10, 2.5), and ejo 2 normal(4.1, 02/20). a) Sample at least 5,000 y values from the posterior predictive distribution. b) Form a 75% quantile-based confidence interval for a new value of Y. Mixture models: After a posterior analysis on data from a population of squash plants, it was determined that the total vegetable weight of a given plant could be modeled with the following distribution: p(yl0, 02) = .31dnorm(y, 0, ơ) + .46dnorm(201, 20) + .23dnorm(y, 301, 30) where the posterior distributions of the parameters have been calculated as 1/02 - gamma(10, 2.5), and ejo 2 normal(4.1, 02/20). a) Sample at least 5,000 y values from the posterior predictive distribution. b) Form a 75% quantile-based confidence interval for a new value of Y.

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