#posterior inference under a binomial model #example pag 39 sec 2.5 binomial.beta_function(w=1,theta=seq(0.3,.6,.001),alpha=1,beta=1){ if (w == 1) postscript("/users/faculty/fdominic/teaching/BM/binomialbeta.ps") plot(theta,dbeta(theta,438,544),type="l",xlab="theta",ylab="", xaxs="i",yaxs="i",yaxt="n",bty="n",cex=2) lines(theta,dbeta(theta,alpha,beta),lty=2) lines(theta,dbeta(theta,437+alpha,543+beta),lty=2) abline(v=.485) CI_quantile(rbeta(1000,437+alpha,543+beta),probs=c(.025,.975)) abline(v=CI[1],lty=2) abline(v=CI[2],lty=2) par(oma=c(0,0,0,0)) par(mfrow=c(1,1)) if (w == 1) dev.off()} ##########sensitity analysis binomial.beta1_function(w=1,theta=seq(0,1,.001)){ if (w == 1) postscript("/users/faculty/fdominic/teaching/BM/binomialbeta1.ps") par(mfrow=c(3,2)) ccc_c(2,5,10,20,100,200) alpha_.485*ccc beta_ccc-alpha for(i in 1:length(ccc)){ plot(theta,dbeta(theta,438,544),type="l",xlab="theta",ylab="", xaxs="i",yaxs="i",yaxt="n",bty="n",ylim=c(0,27.6)) lines(theta,dbeta(theta,alpha[i],beta[i]),lty=3) lines(theta,dbeta(theta,438,544)) lines(theta,dbeta(theta,437+alpha[i],543+beta[i]),lty=2) abline(v=.485) CI_quantile(rbeta(1000,437+alpha[i],543+beta[i]),probs=c(.025,.975)) abline(v=CI[1],lty=2) abline(v=CI[2],lty=2) } par(oma=c(0,0,0,0)) par(mfrow=c(1,1)) if (w == 1) dev.off()}