1. Rinderpest Virus in Rabbits with Missing Data. Temperatures (temp) were recorded in a rabbit at various times (time) after the rabbit was inoculated with rinderpest virus (the data modified from Carter and Mitchell, 1958). Rinderpest (RP) is an infectious viral disease of cattle, domestic buffalo, and some species of wildlife; it is commonly referred to as cattle plague. It is characterized by fever, oral erosions, diarrhea, lymphoid necrosis, and high mortality. Time after injection Temperature (time in hrs) (temp in ' F) 24 102.8 32 104.5 48 106.5 56 107.0 NA 107.1 70 105.1 72 103.9 75 NA 80 103.2 96 102.1 (a) Using an MCMC modeling library such as BUGS or PyMC and properly accounting for the missing data, demonstrate that a linear regression with one predictor (time) gives relatively low Bayesian R". What are estimators of the missing data? Does the 95% Credible Set for the slope contain 0? Comment on how you chose your priors and the results of your model. (b) Include time2 (squared time) as the second predictor, making the regression quadratic in variables, but still linear in coefficients. What are the estimators of missing data? Do the 95% Credible Sets for parameters in the quadratic model contain 0? Comment on how you Course Material for ISyE6420 by Brani Vidakovic is licensed under a Creative Commons Attribution- NonCommercial 4.0 International License. chose your priors and the results of your model. Is the Bayesian R2 better or worse than the model from 1(a)? Hint: If using BUGS, it is recommended to do the modeling in (a) and (b) in two separate BUGS programs. The linear regression is not good for part (a). Given the missing data, the estimator for o is large, and SSE = (n - p) . o' is bigger than SST, making the R2 negative. For the single predictor model, please consider BR2-max(0, 1-SSE/SST) in your BUGS code. The quadratic regression is fine without any modification of BR2