Calculating a joint distribution
The parts of the code we developed in the last video is displayed. It defines a grid over the underlying proportions of clicks (proportion_clicks
) and possible outcomes (n_visitors
) in pars
. It adds to it the prior
probability of each parameter combination and the likelihood that each proportion_clicks
would generate the corresponding n_visitors
.
This exercise is part of the course
Fundamentals of Bayesian Data Analysis in R
Exercise instructions
- Add the column
pars$probability
: The probability of eachproportion_clicks
andn_visitors
combination. As in the video, this should be calculated by multiplying thelikelihood
by theprior
- Make sure the column
pars$probability
sums to1.0
by normalizing it, that is, by dividingpars$probability
by the total sum ofpars$probability
.
Hands-on interactive exercise
Have a go at this exercise by completing this sample code.
n_ads_shown <- 100
proportion_clicks <- seq(0, 1, by = 0.01)
n_visitors <- seq(0, 100, by = 1)
pars <- expand.grid(proportion_clicks = proportion_clicks,
n_visitors = n_visitors)
pars$prior <- dunif(pars$proportion_clicks, min = 0, max = 0.2)
pars$likelihood <- dbinom(pars$n_visitors,
size = n_ads_shown, prob = pars$proportion_clicks)
# Add the column pars$probability and normalize it
pars$probability <- ___