12.5 Prior Distribution
Assuming these priors are independent.
Yi|β0,β1,β2,β3,σ∼Pois(λi)β0c∼N(2,0.52)β1∼N(0,0.172)β2∼N(0,4.972)β3∼N(0,5.602)
- “typical state” λ=7
log(λ)=log(7)≈1.95≈2
- logged number of laws (2±2×0.5)
(e1,e3)≈(3,20)
prior_summary(equality_model_prior)
## Priors for model 'equality_model_prior'
## ------
## Intercept (after predictors centered)
## ~ normal(location = 2, scale = 0.5)
##
## Coefficients
## Specified prior:
## ~ normal(location = [0,0,0], scale = [2.5,2.5,2.5])
## Adjusted prior:
## ~ normal(location = [0,0,0], scale = [0.17,4.97,5.60])
## ------
## See help('prior_summary.stanreg') for more details
12.5.1 So Far
%>%
equality add_fitted_draws(equality_model_prior, n = 100) %>%
ggplot(aes(x = percent_urban, y = laws, color = historical)) +
geom_line(aes(y = .value, group = paste(historical, .draw))) +
labs(title = "Anti-Discrimination Laws",
subtitle = "Human Rights Campaign State Equality Index",
caption = "R4DS Bayes Rules book club") +
scale_color_manual(values = c("blue", "red", "purple")) +
theme_minimal() +
ylim(0, 100)