Discrete posterior
Great work! In comparing the effectiveness of the two drugs \(S\) and \(N\), you constructed a prior distribution for the pair (pS
, pN
), where pS
and pN
are the probabilities of relieving pain. The prior was called a "testing prior" where the probability the two drugs are equally effective is 0.5.
Suppose that in a clinical trial, 12 out of 20 patients with the standard drug experienced relief, and 17 of 20 patients with the new drug experienced relief.
You can use the two_p_update()
function to compute the posterior probabilities for (pS
, pN
) and the draw_two_p()
function to construct a graph of the probabilities.
The posterior of the difference in probabilities d_NS
= pN
- pS
is found using the two_p_summarize()
function.
Now it's your turn to compute posterior probabilities using a uniform prior on (pS
, pN
)!
This exercise is part of the course
Beginning Bayes in R
Exercise instructions
A uniform prior, stored in prior
, is defined such that each probability can take on the five values 0.1, 0.3, 0.5, 0.7, 0.9 and all possible (pS
, pN
) pairs are equally likely.
- Define vectors
s1f1
ands2f2
that contain the number of successes and number of failures for each of the two samples. - Use
two_p_update()
to compute the posterior distribution. - Use
draw_two_p()
to graph the posterior. - Use
two_p_summarize()
to find the posterior distribution ond_NS
=pN
-pS
, andprob_plot()
to graph this distribution.
Hands-on interactive exercise
Have a go at this exercise by completing this sample code.
# Define a uniform prior on all 25 pairs: prior
prior <- testing_prior(0.1, 0.9, 5, uniform = TRUE)
# Define the data: s1f1, s2f2
s1f1 <- ___
s2f2 <- ___
# Compute the posterior: post
# Graph the posterior
# Find the probability distribution of pN - pS: d_NS
# Graph this distribution