draw_stick_breaks: Draw stick-breaks depending on a concentration parameter

In alan-turing-institute/PosteriorBootstrap: Non-Parametric Sampling with Parallel Monte Carlo

Draw stick-breaks depending on a concentration parameter

Description

draw_stick_breaks returns a vector with the breaks of a stick of length 1.

Usage

draw_stick_breaks(
  concentration = 1,
  min_stick_breaks = 100,
  threshold = 1e-08,
  seed = NULL
)

Arguments

concentration	The parameter c in the paper (page 3, formula 3), which is an effective sample size.
min_stick_breaks	The minimal number of stick-breaks.
threshold	The threshold of stick remaining below which the function stops looking for more stick-breaks. It corresponds to epsilon in the paper, at the bottom of page 5 and in algorithm 2 in page 12.
seed	A seed to start the sampling.

Details

This function implements the stick-breaking process for non-parametric learning described in section 2 of the supplementary material. The name "stick-breaking" comes from a stick of unit length that we need to break into a number of items. This code implements algorithm 2 and the stick-breaking function calculates the parameter T in algorithm 1, which is the only difference between the two algorithms. The code uses the Beta distribution as that distribution is part of the definition of the stick-breaking process. The function draws from the beta distribution, e.g. b_1, b_2, b_3, ..., and computes the stick breaks as b_1, (1-b_1)*b_2, (1-b_1)*(1-b_2)*b_3, ... . The length remaining in the stick at each step is 1-b_1, (1-b_1)* (1-b_2), (1-b_1)*(1-b_2)*(1-b_3), ... so the latter converges to zero.

Value

A vector of stick-breaks summing to one.

Examples

draw_stick_breaks(1)
draw_stick_breaks(1, min_stick_breaks = 10)
draw_stick_breaks(1, min_stick_breaks = 10, threshold = 1e-8)

alan-turing-institute/PosteriorBootstrap documentation built on Sept. 12, 2023, 9:32 a.m.