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# assa - STATS 390 SS Department of Statistics Assignment 3...

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Department of Statistics STATS 390 SS Assignment 3 Due: 9 February 2009 Please answer all questions. Remember this assignment is worth 10%. Make sure that you place all answers and output into a word document and store in a safe area till finished. 1. [ 34 marks ] Regression and DIC The data set provided contains variables x 1 , x 2 , x 3 and y in a file called regress data.txt the model file is called regress model.txt . The object of this question is for you to construct different models by taking different x variables, running each model and checking the DIC so that an appreciation of model checking and DIC is made. model { for (i in 1:100) { y[i] ~ dnorm(..., tau) mu[i] <- beta0+beta1*(x1[i]-mean(x1[]))+beta2*(x2[i]-mean(x2[])) +beta3*(x3[i]-mean(x3[])) } tau ~ dgamma(0.001,0.001) sigma <- 1/sqrt(...) beta0 ~ dnorm(0,1.0E-6) beta1 ~ dnorm(0,1.0E-6) beta2 ~ dnorm(0,1.0E-6) beta3 ~ dnorm(0,1.0E-6) } (a) [2 mark(s)] If y i = μ i + epsilon1 i where epsilon1 i N (0 , τ ) then fill in the gaps y[i] dnorm(...,...) (b) [2 mark(s)] Fill in the two gaps in the above model. (c) [2 mark(s)] What type of priors are assigned? (d) [1 mark(s)] Why has the mean of the x’s been subtracted in the line that defines mu[i]? (e) [3 mark(s)] Make suitable inits and run 3 chains using WinBUGS only (no R ), check conver- gence with the bgr plot. Paste the final bgr plot into your answers once you are satisfied that the distribution is stationary. Explain what the three different lines are and how they indicate convergence. STATS 390 SS Assignment 3 Page 1 of 7

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(f) [8 mark(s)] In Table 1 there are 4 models made up of different combinations of x’s. Run these as above by changing the model file, for example to make model 2 just replace the beta3 prior with beta3<-0 . Copy and fill in Table 1 in your answers. Model x-variables pD DIC 1 x 1 , x 2 , x 3 2 x 1 , x 2 3 x 2 , x 3 4 x 3 , x 1 Table 1: DIC checks on 4 Models (g) [8 mark(s)] Use R2WinBUGS to run model 1 and put the output into an R object called regress.sim . Print and plot the object pasting the output into your answers along with the bugs() command you used. (h) [8 mark(s)] Alter the model file regress model.txt by placing an informative prior on beta1 i.e use beta1 dnorm(0,16) (make sure the rest of the code is for Model 1 ) and use debug=T in the bugs() command.
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assa - STATS 390 SS Department of Statistics Assignment 3...

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