Mixture of Sequential Quantile Array Random Probability Measures for Nonparametric Bayesian Density Estimation

We introduce a mixture of Sequential Quantile Array (SQA) Random Probability Measures. The SQA prior is dual to the Polya tree (PT) prior and exhibits similar practical limitations. We propose a mixture extension (MSQA), analogous to mixtures of Polya trees, that combines random weights and random partitions, increasing flexibility while preserving large support. We provide the main theoretical properties of MSQA and illustrate their use in density estimation, comparing them with PT and mixture Polya tree models.