Simulation of uninformativ datasets for Bayesian t-tests

sim_uninformative_bf.R

n_bf <- 50

# Simulate data
library("BayesFactor")
previous_data <- rnorm(2, mean = 0, sd = 3)

uninformative_bf <- function(x, previous_data = NULL, mu = 0) {
  bf <- as.vector(ttestBF(c(previous_data, x), mu = mu))
  (1 - bf)^2
}

bfs <- as.vector(ttestBF(previous_data, mu = 0))

for(i in 1:(n_bf-1)) {
  next_observation <- optim(rnorm(2, mean = 0, sd = 5), uninformative_bf, previous_data = previous_data, method = "BFGS")
  previous_data <- c(previous_data, next_observation$par)
  bfs <- c(bfs, as.vector(ttestBF(previous_data, mu = 0)))
}

# Plot data
plot(
  NA
  , NA
  , xlim = c(1, n_bf)
  , ylim = c(1/10, 10)
  , axes = FALSE
  , xlab = "n"
  , ylab = bquote("BF"[10])
  , log = "y"
  , main = expression(paste("Bayesian t-test (", mu == 0, ", ", r == sqrt(2)/2, ")"))
)

for(i in c(1/10, 1/3, 1, 3, 10)) lines(x = c(0, n_bf), y = c(i, i), col = "grey", lty = "dashed")
lines(x = c(0, n_bf), y = c(1, 1), lwd = 2)
points(1:n_bf, bfs, pch = 21, col = "steelblue", bg = "lightblue")

axis(1)
axis(2, at = c(1/10, 1/3, 1, 3, 10), labels = c("1/10", "1/3", "1", "3", "10"), las = 1)

A particularly good example: