Bayesian multivariate mixed-scale density estimation

@article{Canale2011BayesianMM,
  title={Bayesian multivariate mixed-scale density estimation},
  author={Antonio Canale and David B. Dunson},
  journal={arXiv: Statistics Theory},
  year={2011}
}
Although continuous density estimation has received abundant attention in the Bayesian nonparametrics literature, there is limited theory on multivariate mixed scale density estimation. In this note, we consider a general framework to jointly model continuous, count and categorical variables under a nonparametric prior, which is induced through rounding latent variables having an unknown density with respect to Lebesgue measure. For the proposed class of priors, we provide sufficient conditions… 
View PDF on arXiv
10 Citations
Highly Influential Citations
1
Background Citations
8
Methods Citations
2

10 Citations

Citation Type

Citation Type

Adaptive Bayesian Estimation of Mixed Discrete-Continuous Distributions under Smoothness and Sparsity
TLDR
Bayesian mixture of normals models can be used for optimal adaptive estimation of mixed discrete-continuous distributions under anisotropic smoothness conditions and possibly increasing number of support points for the discrete part of the distribution.
Bayesian density regression for discrete outcomes
TLDR
The paper presents a Markov chain Monte Carlo algorithm for posterior sampling, sufficient conditions for weak consistency, and illustrations on density, mean and quantile regression utilising simulated and real datasets.
Copula based factorization in Bayesian multivariate infinite mixture models
Bayesian nonparametric modeling and theory for complex data
The dissertation focuses on solving some important theoretical and methodological problems associated with Bayesian modeling of infinite dimensional ‘objects’, popularly called nonparametric Bayes.…
Bayesian Nonparametric Modeling for Multivariate Ordinal Regression
TLDR
A Bayesian nonparametric modeling approach for univariate and multivariate ordinal regression is introduced, which is based on mixture modeling for the joint distribution of latent responses and covariates, and achieves inferential flexibility, while avoiding these difficulties.
The how and why of Bayesian nonparametric causal inference
TLDR
A comprehensive overview of Bayesian nonparametric applications to causal inference is presented and it is argued that most of the time it is necessary to model both the selection and outcome processes.
BNPmix: An R Package for Bayesian Nonparametric Modeling via Pitman-Yor Mixtures
TLDR
BNPmix is an R package for Bayesian nonparametric multivariate density estimation, clustering, and regression, using Pitman-Yor mixture models, a flexible and robust generalization of the popular class of Dirichlet process mixture models.
Hierarchically Coupled Mixture Models with Local Dependence, with Application to Imputing Mixed Data
TLDR
It is demonstrated that as a default imputation engine the HCMM-LD outperforms the most popular sequential imputation alternative.
A Bayesian nonparametric model for data on different scales of measure; an application to customer base management of telecommunications companies.
To analyse telecommunications marketing data which are usually made of discrete and continuous observations we consider a general framework to jointly model continuous, count and categorical…
Model-based approach for household clustering with mixed scale variables
TLDR
A Bayesian nonparametric mixture model is proposed that jointly models a set of latent variables, as in an underlying variable response approach, associated to the observed mixed scale data and accommodates for the different sampling probabilities.

References

SHOWING 1-10 OF 17 REFERENCES
Adaptive Bayesian multivariate density estimation with Dirichlet mixtures
We show that rate-adaptive multivariate density estimation can be performed using Bayesian methods based on Dirichlet mixtures of normal kernels with a prior distribution on the kernel's covariance…
Nonparametric estimation of the anisotropic probability density of mixed variables
Bayesian Kernel Mixtures for Counts
TLDR
Focusing on the rounded Gaussian case, this work generalizes the modeling framework to account for multivariate count data, joint modeling with continuous and categorical variables, and other complications, and proposes broad class of alternative models, nonparametric mixtures of rounded continuous kernels.
Bayesian Density Estimation and Inference Using Mixtures
Abstract We describe and illustrate Bayesian inference in models for density estimation using mixtures of Dirichlet processes. These models provide natural settings for density estimation and are…
Nonparametric estimation of distributions with categorical and continuous data
Nonparametric Estimation of Conditional CDF and Quantile Functions With Mixed Categorical and Continuous Data
We propose a new nonparametric conditional cumulative distribution function kernel estimator that admits a mix of discrete and categorical data along with an associated nonparametric conditional…
POSTERIOR CONSISTENCY OF DIRICHLET MIXTURES IN DENSITY ESTIMATION
A Dirichlet mixture of normal densities is a useful choice for a prior distribution on densities in the problem of Bayesian density estimation. In the recent years, efficient Markov chain Monte Carlo…
Bayesian modeling of joint and conditional distributions
Cross-validation and the estimation of probability distributions with categorical data
In this paper, we consider the problem of estimating a joint distribution that is defined over a set of discrete variables. We use a smoothing kernel estimator to estimate the joint distribution. We…
Cross-Validation and the Estimation of Conditional Probability Densities
TLDR
This article shows that cross-validation produces asymptotically optimal smoothing for relevant components, while eliminating irrelevant components by oversmoothing in the problem of nonparametric estimation of a conditional density.
...
1
2
...