SeBR (version 1.1.0)

bb: Bayesian bootstrap posterior sampler for the CDF

Description

Compute one Monte Carlo draw from the Bayesian bootstrap (BB) posterior distribution of the cumulative distribution function (CDF).

Usage

bb(y)

Value

a function that can evaluate the sampled CDF at any argument(s)

Arguments

y

the data from which to infer the CDF (preferably sorted)

Details

Assuming the data y are iid from an unknown distribution, the Bayesian bootstrap (BB) is a nonparametric model for this distribution. The BB is a limiting case of a Dirichlet process prior (without any hyperparameters) that admits direct Monte Carlo (not MCMC) sampling.

This function computes one draw from the BB posterior distribution for the CDF Fy.

Examples

# Simulate data:
y = rnorm(n = 100)

# One draw from the BB posterior:
Fy = bb(y)

class(Fy) # this is a function
Fy(0) # some example use (for this one draw)
Fy(c(.5, 1.2))

# Plot several draws from the BB posterior distribution:
ys = seq(-3, 3, length.out=1000)
plot(ys, ys, type='n', ylim = c(0,1),
     main = 'Draws from BB posterior', xlab = 'y', ylab = 'F(y)')
for(s in 1:50) lines(ys, bb(y)(ys), col='gray')

# Add ECDF for reference:
lines(ys, ecdf(y)(ys), lty=2)