Tools for Nonparametric Martingale Posterior Sampling // Performs
Bayesian nonparametric density estimation using Martingale
posterior distributions including the Copula Resampling (CopRe)
algorithm. Also included are a Gibbs sampler for the marginal
Gibbs-type mixture model and an extension to include full
uncertainty quantification via a predictive sequence resampling
(SeqRe) algorithm. The CopRe and SeqRe 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. Implements work developed in Moya B., Walker S. G.
(2022). doi:10.48550/arxiv.2206.08418, Fong, E., Holmes, C.,
Walker, S. G. (2021) doi:10.48550/arxiv.2103.15671, and Escobar
M. D., West, M. (1995) doi:10.1080/01621459.1995.10476550.