copre: Tools for Nonparametric Martingale Posterior Sampling
Performs 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.
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>.
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