2.6 Example Pop vs Soda vs Coke

Define the prior probability model.

prior <- c("midwest" = 0.21, "northeast" = 0.17, "south" = 0.38, "west" = 0.24)

Prior probability model
region	midwest	northeast	south	west
probability	21.0%	17.0%	38.0%	24.0%

likelihood <- pop_vs_soda |> 
  tabyl(pop, region) |> 
  adorn_percentages("col") |> 
  filter(pop) |> 
  select(-pop)

Data model (likelihoods)
region	midwest	northeast	south	west
likelihood	64.5%	27.3%	7.9%	29.4%

posterior <- prior * likelihood / sum(prior * likelihood)

Posterior porbability model
	midwest	northeast	south	west
prior	21.0%	17.0%	38.0%	24.0%
likelihood	64.5%	27.3%	7.9%	29.4%
posterior	47.9%	16.4%	10.7%	25.0%

We can summarize the key observations from this analysis is the form of the below graph.