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(a) Do you believe that the MCMC sample size of 3 chains, each with 2500 iterations after a burn-in of 500 iterations, is adequate? Why or why not? If you feel it is inadequate, than rerun WinBUGS with a larger MCMC sample size. If you use a larger MCMC sample size, then you may wish to use a value of n.thin greater than 1. Is the length of the burn-in periods adequate?

(b) Explain the purpose of the lines mu[1]

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(c) Construct time series and ACF plots of the parameters theta, sigma, ypred[1], and ypred[2]. What do the plots tell us about MCMC mixing and convergence? Include your plots and the R output with your work.

(d) Find a 90% posterior interval for the next observation after the observed data.

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