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Exercise

Updating by Bayes' rule

Suppose Madison constructs a prior for proportion of female college students who believe they are overweight, where the possible values are contained in P and the respective probabilities in Prior:

P <- c(0.5, 0.6, 0.7, 0.8, 0.9)
Prior <- c(0.3, 0.3, 0.2, 0.1, 0.1)

Imagine that a sample of n = 20 female students is selected and y = 16 of these students consider themselves to be overweight. The likelihood of 16 so-called "successes" in a sample of size 20 is given by the binomial density function:

dbinom(16, size = 20, prob = P)

where P is the binomial probability of success.

Now you can compute Madison's posterior probabilities for the unknown proportion P!

The vector of proportions P and the vector of probabilities Prior are both available in your workspace.

Remember: you can use the bayesian_crank() function to implement Bayes' rule!

Instructions

100 XP
  • Use the dbinom() function to compute the vector of likelihoods. Store the result in Likelihood.
  • Create a Bayesian data frame called bayes_df with variables P, Prior, and Likelihood.
  • Use the bayesian_crank() function to compute the posterior probabilities. Save the result in bayes_df and print it to the console.
  • Pass bayes_df to the prior_post_plot() function to graph the prior and posterior probabilities contained in bayes_df.