A set of tools for Bayesian nonparametric density estimation using Martingale posterior distributions and including the Copula Resampling (CopRe) algorithm. Also included are a Gibbs sampler for the marginal Mixture of Dirichlet Process (MDP) model and an extension to include full uncertainty quantification via a new Polya completion algorithm for the MDP. The CopRe and Polya samplers generate random nonparametric distributions as output, leading to complete nonparametric inference on posterior summaries. Routines for calculating arbitrary functionals from the sampled distributions are included as well as an important algorithm for finding the number and location of modes, which can then be used to estimate the clusters in the data using, for example, k-means.
You can install the development version of CopRe from GitHub with:
# install.packages("devtools")
devtools::install_github("blakemoya/copre")The basic usage of CopRe for density estimation is to supply a data vector, a number of forward simulations per sample, and a number of samples to draw:
library(copre)
data <- c(rnorm(100, mean = -2), rnorm(100, mean = 2))
res_cop <- copre(data, 100, 100)
plot(res_cop) +
ggplot2::geom_function(
fun = function(x) (dnorm(x, mean = -2) + dnorm(x, mean = 2)) / 2
)