Inner spike and slab Bayesian nonparametric models

by   Antonio Canale, et al.

Discrete Bayesian nonparametric models whose expectation is a convex linear combination of a point mass at some point of the support and a diffuse probability distribution allow to incorporate strong prior information, while still being extremely flexible. Recent contributions in the statistical literature have successfully implemented such a modelling strategy in a variety of applications, including density estimation, nonparametric regression and model-based clustering. We provide a thorough study of a large class of nonparametric models we call inner spike and slab hNRMI models, which are obtained by considering homogeneous normalized random measures with independent increments (hNRMI) with base measure given by a convex linear combination of a point mass and a diffuse probability distribution. In this paper we investigate the distributional properties of these models and our results include: i) the exchangeable partition probability function they induce, ii) the distribution of the number of distinct values in an exchangeable sample, iii) the posterior predictive distribution, and iv) the distribution of the number of elements that coincide with the only point of the support with positive probability. Our findings are the main building block for an actual implementation of Bayesian inner spike and slab hNRMI models by means of a generalized Pólya urn scheme.


Random taste heterogeneity in discrete choice models: Flexible nonparametric finite mixture distributions

This study proposes a mixed logit model with multivariate nonparametric ...

Marginally Constrained Nonparametric Bayesian Inference through Gaussian Processes

Nonparametric Bayesian models are used routinely as flexible and powerfu...

Nonparametric Estimation of Uncertainty Sets for Robust Optimization

We investigate a data-driven approach to constructing uncertainty sets f...

Geometric Sensitivity Measures for Bayesian Nonparametric Density Estimation Models

We propose a geometric framework to assess global sensitivity in Bayesia...

Asymptotic behavior of the number of distinct values in a sample from the geometric stick-breaking process

Discrete random probability measures are a key ingredient of Bayesian no...

Density estimation on small datasets

How might a smooth probability distribution be estimated, with accuratel...

Bayesian nonparametric modelling of sequential discoveries

We aim at modelling the appearance of distinct tags in a sequence of lab...

Please sign up or login with your details

Forgot password? Click here to reset