copre - 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>.