The “vb” Function in R

• Package: rstan

• Purpose: Performs variational Bayesian inference on a Stan model

• General class: Bayesian inference

• Required argument(s):

• object: A stan model compiled with a function like “stan_model”.

• data: List or environment containing data for the Stan model.

• Notable optional arguments:

• pars: Names of parameters to monitor and return estimates for.

• algorithm: The algorithm to use for variational inference, such as “meanfield” or “fullrank”.

• iter: Number of iterations for the variational algorithm.

• tol_rel_obj: Relative tolerance for the convergence criterion.

• seed: Random seed for reproducibility.

• Example:

• # Load the rstan library
  library(rstan)
  
  # Define the Stan model code
  model_code <- '
  data {
  int<lower=0> N;
  real y[N];
  }
  parameters {
  real mu;
  real<lower=0> sigma;
  }
  model {
  y ~ normal(mu, sigma);
  }
  '
  
  # Compile the Stan model
  model <- stan_model(model_code = model_code)
  
  # Perform variational Bayesian inference
  N = 1000
  fit <- vb(model, data = list(N = N, y = rnorm(N)))
  
  # View summary of variational estimates
  summary(fit)

• This example demonstrates how to use the “vb” function from the rstan package to perform variational Bayesian inference on a compiled Stan model. The function requires the result of fitting a Stan model (stanfit object) as input and allows specifying various optional arguments like parameters to monitor, the variational algorithm, convergence criteria, and random seed.