Abstract: We propose a Bayesian nonparametric model for density estimation on the product of simplex 
spaces and the hypercube. The model is particularly useful for cases where the available data consist 
of multiple compositional features alongside variables that take on values within bounded intervals.
A compositional feature is a vector of non-negative components whose sum of values remains constant,
such as the time an individual spends on different activities during the day or the fraction of different 
types of food consumed as part of a person's diet. Our approach relies on a generalization of random multivariate 
Bernstein polynomials and corresponds to a Dirichlet process mixture of products of Dirichlet and beta densities.
Theoretical properties such as prior support and posterior consistency are studied. We evaluate the model's 
performance through a simulation study and a real-world application using data from the 2005–2006 cycle of the U.S. 
National Health and Nutrition Examination Survey (NHANES). Furthermore, the conditional densities derived under this
modeling strategy can be used for regression analyses where both the response and predictors take values on the simplex 
space and/or hypercube.
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Joint work with Claudia Wehrhahn and Alejandro Jara.