Elaborate on the details of the R program in Example 11.6.1.

Data from in Example 11.6.1

The prior probability prior_weights is extended over a prior grid as required in this approach. A very elementary function getc helps in this task along with the sapply function. The likelihood function is computed in the usual way. The posterior_grid as given in the program accomplishes the third step of the approach, while the sample function in the final step is obtained.

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> p < seq (0, 1, length=100) > X <- 11; n <- 27 > lower_limit <- seq (0,0.9,0.1); upper_limit <- seq (0.1, 1,0.1) > prior_intervals <- cbind (lower_limit, upper_limit) > prior_weights <- c(1, 5.2, 8, 7.2, 4.6, 2.1, 0.7, 0.1, 0, 0) > names (prior_weights) <- paste (prior_intervals [, 1], "-", + prior_intervals [, 2], sep="") > prior_interval_weights <- prior_weights/sum (prior_weights) > getc <- function (a,b,c) c [a>= b[,1] & a<=b[, 2]] > p_prior <- unlist (sapply (p, getc, b=prior_intervals, + c-prior_interval_weights)) > likelihood <- p^x* (1-p) ^ (n-x) > posterior_grid <- p_prior* likelihood > posterior_grid <- posterior_grid/sum (posterior_grid) > posterior_sample <- sample (p, size=500, replace=TRUE, + prob=posterior_grid) > par (mfrow=c (1,2)) > barplot (prior_weights, main="Histogram Prior",xlab="p") > hist (posterior_sample, main="Posterior Distribution",xlab="p")