In greta-dev/greta: Simple and Scalable Statistical Modelling in R

Ridge prior

Here we estimate a simple, one-variable Bayesian linear regression model that uses a ridge prior. The ridge prior has a frequentist interpretation where it is used as a penalty for regression coefficients. Among other effects, the penalty shrinks the coefficients towards zero to reduce variance without setting them to zero. The Bayesian version uses a normal distribution for the slopes and a inverse gamma prior for the strength of the penalty. Note that since the prior in our intercept is still improper, the joint prior is also improper.

# variables & priors
int <- variable()
sd <- cauchy(0, 3, truncation = c(0, Inf))

tau <- inverse_gamma(1, 1)
coef <- normal(0, tau)

# linear predictor
mu <- int + coef * attitude$complaints

# observation model
distribution(attitude$rating) <- normal(mu, sd)