In python - please use pandas, numpy, matplotlib, and seaborn packages

1. a) For this tasks we will use a medical advisor example. You are thinking about hiring a medical advisor for a liver transplant that had 100 cases and only 5 complications. The normal base rate of complications in North America is 10%. You are trying to decide between two hypotheses:

H0: The Consultant does not impact the complication rate (i.e. p=0.1)

H1: The Consultant halves the complication rate (i.e. p=0.05)

Write a function that again simulates data both under the H0 and H1. Then calculate the Bayes-Factor BF(H1/H0). Finally report the posterior probability of the H1, assuming the prior probability was 0.5. How would you interpret the BF and the posterior probability?

Below is the dataset called births.csv:

fAge,mAge,weeks,premature,visits,gained,weight,sexBaby,smoke 31,30,39,full term,13,1,6.88,male,smoker 34,36,39,full term,5,35,7.69,male,nonsmoker 36,35,40,full term,12,29,8.88,male,nonsmoker 41,40,40,full term,13,30,9,female,nonsmoker 42,37,40,full term,0,10,7.94,male,nonsmoker 37,28,40,full term,12,35,8.25,male,smoker 35,35,28,premie,6,29,1.63,female,nonsmoker 28,21,35,premie,9,15,5.5,female,smoker 22,20,32,premie,5,40,2.69,male,smoker 36,25,40,full term,13,34,8.75,female,nonsmoker 27,19,32,premie,5,32,6.5,female,nonsmoker 35,34,40,full term,15,20,7.44,male,nonsmoker 25,19,41,full term,13,47,8.38,male,smoker 36,33,38,full term,10,20,6,male,nonsmoker 27,27,39,full term,11,5,7.81,male,smoker 24,23,38,full term,13,22,7.81,female,nonsmoker 33,40,36,premie,13,23,7.81,female,nonsmoker 25,23,40,full term,10,30,7.31,male,nonsmoker 28,27,33,premie,6,18,4.75,male,smoker 25,22,34,premie,10,20,3.75,male,nonsmoker 35,31,37,full term,12,37,8.06,female,nonsmoker 33,38,32,premie,10,16,2.19,female,smoker 32,26,42,full term,15,30,7.38,male,smoker 29,30,39,full term,10,43,6.88,female,nonsmoker 24,22,40,full term,16,34,6.88,female,smoker 25,25,38,full term,19,13,7.63,female,nonsmoker 34,33,43,full term,13,25,9.13,male,smoker 33,20,39,full term,15,70,7.38,female,smoker 32,28,37,full term,13,35,8.25,female,nonsmoker 28,26,39,full term,15,45,7.19,female,nonsmoker 27,27,39,full term,14,31,7.56,female,nonsmoker 25,21,36,premie,15,10,6.81,male,nonsmoker 21,24,38,full term,16,50,3.75,female,nonsmoker 26,25,38,full term,11,27,8.75,male,nonsmoker 33,30,37,full term,10,57,6.56,male,nonsmoker 27,25,40,full term,11,26,7.44,male,nonsmoker 34,25,39,full term,5,37,6,female,smoker 29,21,39,full term,18,13,7.75,female,nonsmoker 33,30,39,full term,9,42,7.81,male,smoker 39,24,39,full term,6,30,5.8,female,smoker 24,23,42,full term,9,22,8.81,male,nonsmoker 29,26,39,full term,14,65,7.75,female,smoker 35,28,38,full term,10,25,6.88,male,nonsmoker 27,22,35,premie,12,30,4.69,male,nonsmoker 33,25,35,premie,15,18,6.75,male,nonsmoker 27,22,39,full term,12,30,6.94,female,smoker 30,25,35,premie,15,40,5.5,male,smoker 23,23,44,full term,4,55,6.8,female,smoker 21,22,40,full term,10,85,5.81,male,nonsmoker 22,32,37,full term,8,30,6.81,female,nonsmoker 34,34,38,full term,11,23,7.25,male,nonsmoker 22,22,39,full term,14,29,7.19,female,nonsmoker 35,31,40,full term,10,45,8,female,nonsmoker 25,26,39,full term,12,40,8.38,male,nonsmoker 22,26,39,full term,12,31,7.31,male,smoker 22,34,39,full term,12,57,9.69,male,nonsmoker 40,40,38,full term,13,38,7.31,male,nonsmoker 24,18,37,full term,8,25,6.19,male,smoker 42,38,41,full term,15,35,10.13,female,nonsmoker 30,28,39,full term,13,0,7.5,female,nonsmoker 35,31,40,full term,15,32,6.25,male,nonsmoker 39,27,39,full term,12,58,8.56,male,smoker 28,18,41,full term,10,11,6.5,female,nonsmoker 29,29,44,full term,12,51,8.5,male,nonsmoker 28,24,39,full term,11,23,7.5,female,nonsmoker 33,35,38,full term,10,20,5.2,female,smoker 29,31,36,premie,8,42,5.32,male,smoker 19,20,34,premie,13,6,4.5,male,nonsmoker 21,19,39,full term,11,48,7.3,female,smoker 43,31,41,full term,5,20,6.7,female,smoker 33,27,41,full term,15,38,7.8,male,smoker 27,21,41,full term,8,26,5.94,female,nonsmoker 29,30,39,full term,15,44,7.2,male,smoker 21,20,37,full term,10,26,5.38,female,smoker 23,16,40,full term,4,12,6,female,nonsmoker 34,34,37,full term,17,35,6.88,female,nonsmoker 26,26,41,full term,10,68,9.31,male,nonsmoker 22,22,40,full term,13,0,6.5,male,smoker 31,32,38,full term,6,27,6.75,female,nonsmoker 39,37,38,full term,5,45,5.13,male,nonsmoker 36,37,38,full term,3,23,7.5,male,smoker 34,36,38,full term,4,25,7.2,male,smoker 33,32,33,premie,10,60,5.06,male,nonsmoker 30,24,41,full term,12,40,8.13,male,smoker 30,29,39,full term,14,30,5.38,male,nonsmoker 27,24,40,full term,11,8,7.69,female,nonsmoker 23,23,41,full term,14,19,7.88,female,nonsmoker 24,21,41,full term,13,40,7.88,female,nonsmoker 34,29,39,full term,15,24,8.25,female,nonsmoker 32,25,41,full term,13,50,7.75,female,nonsmoker 26,25,40,full term,10,25,7,male,nonsmoker 45,41,33,premie,13,0,5.69,female,nonsmoker 26,23,42,full term,14,23,6.75,male,nonsmoker 25,34,41,full term,10,35,8.19,female,nonsmoker 24,19,40,full term,12,36,8.19,male,nonsmoker 35,31,39,full term,15,35,7.44,male,nonsmoker 35,36,38,full term,18,37,8.25,male,nonsmoker 28,25,40,full term,7,31,9.19,male,nonsmoker 34,31,40,full term,14,44,7.5,female,nonsmoker 35,33,40,full term,16,30,6.81,male,nonsmoker 30,25,40,full term,12,35,8.13,male,nonsmoker 26,20,41,full term,16,21,6.9,female,smoker 24,22,39,full term,12,32,8.38,male,nonsmoker 23,26,38,full term,14,40,8,male,smoker 34,27,39,full term,16,24,8.88,male,smoker 22,20,40,full term,17,39,9.06,male,smoker 26,17,38,full term,11,30,9.5,female,nonsmoker 22,18,40,full term,12,13,8.75,male,nonsmoker 34,33,39,full term,10,40,8.06,male,nonsmoker 20,23,39,full term,15,56,7.31,male,smoker 21,16,38,full term,15,75,7.56,male,smoker 22,20,38,full term,8,45,7.44,female,nonsmoker 32,35,38,full term,17,55,7.5,female,nonsmoker 37,35,40,full term,16,32,7.31,female,nonsmoker 36,30,39,full term,11,21,7.88,male,nonsmoker 31,23,44,full term,14,40,6.81,male,nonsmoker 20,20,37,full term,12,22,5.94,female,nonsmoker 46,39,38,full term,10,35,6.75,male,smoker 23,25,37,full term,8,53,7.69,female,nonsmoker 28,21,38,full term,12,40,7.38,male,nonsmoker 25,19,40,full term,16,37,7.94,male,smoker 33,24,39,full term,8,22,5,male,smoker 17,20,39,full term,16,35,5.63,female,nonsmoker 27,23,43,full term,15,30,7.81,female,nonsmoker 33,27,41,full term,14,58,8,male,nonsmoker 22,18,33,premie,7,40,1.69,male,smoker 26,23,38,full term,5,28,7.19,female,nonsmoker 37,33,36,premie,11,15,6.31,male,smoker 32,24,39,full term,8,23,6.88,male,smoker 24,22,42,full term,7,21,6.5,female,nonsmoker 17,17,29,premie,4,10,3.5,female,nonsmoker 18,15,37,full term,12,76,8.44,male,nonsmoker 24,20,41,full term,16,35,7.19,male,nonsmoker 22,21,41,full term,12,32,8.38,male,nonsmoker 20,17,40,full term,17,38,7.19,female,nonsmoker 25,22,39,full term,12,27,6.31,female,smoker 33,33,38,full term,15,60,6.56,male,nonsmoker 23,21,40,full term,15,38,7.63,female,nonsmoker 36,28,39,full term,15,40,8.38,male,nonsmoker 31,29,41,full term,12,30,7.69,male,smoker 23,23,36,premie,2,27,5.88,female,nonsmoker 22,19,39,full term,7,0,7.31,male,smoker 47,24,40,full term,12,46,6.88,male,nonsmoker 32,35,37,full term,10,25,5.63,male,smoker 30,29,38,full term,17,55,7,female,nonsmoker 25,17,40,full term,15,20,7.63,female,nonsmoker 38,37,39,full term,5,20,6.5,male,smoker 31,32,37,full term,12,22,6,female,nonsmoker 33,28,41,full term,10,30,8.13,male,nonsmoker 38,37,26,premie,5,25,3.63,male,nonsmoker