Simulate Bayesian posterior distributions across experimental sample sizes

Draws sims experimental results from a normal data-generating process with true PATE tau and possible sampling bias, computes the posterior mean for each draw using posterior_mean_fn(), and returns a tidy tibble. Used in Chapter 11 to illustrate how sampling-bias uncertainty limits learning even as sample size grows.

Usage

simulate_posteriors(
  N,
  sigma_B,
  sims = 5000,
  tau = 0.1,
  sigma_Y = 1,
  sigma_g = 0.2,
  g = 0,
  beta = 0
)

Arguments

N

Integer. Experimental sample size.

sigma_B

Numeric. Standard deviation of the sampling-bias distribution. Set to 0 for no bias uncertainty.

sims

Integer. Number of simulated experimental results. Default 5000.

tau

Numeric. True PATE. Default 0.1.

sigma_Y

Numeric. Outcome standard deviation. Default 1.

sigma_g

Numeric. Prior SD on the PATE. Default 0.2.

g

Numeric. Prior mean on the PATE. Default 0.

beta

Numeric. Prior mean on sampling bias. Default 0.

Value

A tibble::tibble() with columns N, sigma_B, and posterior_mean.