bayesian-modelinglisted

# Bayesian Modeling in R ## Overview Comprehensive Bayesian statistical modeling using Stan-based packages (brms, rstanarm), covering prior specification, posterior analysis, model comparison, and Bayesian workflow best practices. ## brms: Bayesian Regression Models ### Basic Models ```r library(brms) # Linear regression fit <- brm( formula = y ~ x1 + x2, data = df, family = gaussian(), seed = 123 ) # Logistic regression fit_logit <- brm( y ~ x1 + x2, data = df, family = bernoulli(link = "logit") ) # Poisson regression fit_pois <- brm( count ~ x1 + x2 + offset(log(exposure)), data = df, family = poisson() ) ``` ### Prior Specification ```r # View default priors get_prior(y ~ x1 + x2, data = df, family = gaussian()) # Set custom priors custom_priors <- c( prior(normal(0, 10), class = "Intercept"), prior(normal(0, 2), class = "b"), # All regression coefficients prior(normal(0, 1), class = "b", coef = "x1"), # Specific coefficient prior(exponential(1), class = "sigma") # Error SD ) fit <- brm( y ~ x1 + x2, data = df, family = gaussian(), prior = custom_priors, seed = 123 ) ``` ### Prior Predictive Checks ```r # Sample from prior only fit_prior <- brm( y ~ x1 + x2, data = df, family = gaussian(), prior = custom_priors, sample_prior = "only", # Prior predictive seed = 123 ) # Visualize prior predictions pp_check(fit_prior, type = "dens_overlay", ndraws = 100) ``` ### Mixed Effects Models ```r # Random intercept