Bayesian Density Regression

Dunson, David B.; Pillai, Natesh S.; Park, Juhyun

doi:10.1111/j.1467-9868.2007.00582.x

Cited by 191 publications

(163 citation statements)

References 25 publications

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“…There is an increasing literature on such conditional modeling approaches [12,11,15,6,25], though they remain to be developed for general predictors X, including shapes and predictors with support on a variety of manifolds. We plan to pursue this and to develop theory of large support, posterior consistency and rates of convergence in ongoing work.…”

Section: Discussionmentioning

confidence: 99%

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Nonparametric Bayes Regression and Classification Through Mixtures of Product Kernels

Dunson¹,

Bhattacharya²

2011

Bayesian Statistics 9

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SUMMARYIt is routine in many fields to collect data having a variety of measurement scales and supports. For example, in biomedical studies for each patient one may collect functional data on a biomarker over time, gene expression values normalized to lie on a hypersphere to remove artifacts, clinical and demographic covariates and a health outcome. A common interest focuses on building predictive models, with parametric assumptions seldom supported by prior knowledge. Hence, it is most appropriate to define a prior with large support allowing the conditional distribution of the response given predictors to be unknown and changing flexibly across the predictor space not just in the mean but also in the variance and shape.Building on earlier work on Dirichlet process mixtures, we describe a simple and general strategy for inducing models for conditional distributions through discrete mixtures of product kernel models for joint distributions of predictors and response variables. Computation is straightforward and the approach can easily accommodate combining of widely disparate data types, including vector data in a Euclidean space, categorical observations, functions, images and manifold data.

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Section: Discussionmentioning

confidence: 99%

“…This results in a simple method for density regression [12], which can easily accommodate a rich variety of predictors.…”

Section: Classification From Functional Predictorsmentioning

confidence: 99%

Nonparametric Bayes Regression and Classification Through Mixtures of Product Kernels

Dunson¹,

Bhattacharya²

2011

Bayesian Statistics 9

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“…The conditional BMI distribution was not assumed to be normally distributed, but could be regarded as a mixture of conditional normal densities because mixtures of a sufficiently large number of normal densities can be used to approximate any smooth density accurately. Where the weights w k could or could not depend on x, and could be inference by classical methods or Bayesian methods, although Dunson et al 42 assumed their dependency of x and used nonparametric Bayesian inference. …”

Section: Density Regression Approachmentioning

confidence: 99%

“…Dunson et al 42 proposed a density regression to study the association between Luteinizing hormone (LH) and BMI in randomly selected women defined by:…”

Section: Density Regression Approachmentioning

confidence: 99%

Statistical methods for body mass index: A selective review

Liu

Alhamzawi

et al. 2016

Stat Methods Med Res

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Abstract:Obesity rates have been increasing over recent decades, causing significant concern among policy makers. Excess body fat, commonly measured by body mass index (BMI), is a major risk factor for several common disorders including diabetes and cardiovascular disease, placing a substantial burden on health care systems. To guide effective public health action, we need to understand the complex system of intercorrelated influences on BMI. This paper, based on all eligible articles searched from Global health, Medline and Web of Science databases, reviews both classical and modern statistical methods for BMI analysis. We give a description of each of these methods, exploring the classification, links and differences between them and the reasons for choosing one over the others in different settings. We aim to provide a key resource and statistical library for researchers in public health and medicine to deal with obesity and BMI data analysis. AbstractObesity rates have been increasing over recent decades, causing significant concern among policy makers. Excess body fat, commonly measured by body mass index (BMI), is a major risk factor for several common disorders including diabetes and cardiovascular disease, placing a substantial burden on health care systems. To guide effective public health action, we need to understand the complex system of intercorrelated influences on BMI. This paper, based on all eligible articles searched from Global health, Medline and Web of Science databases, reviews both classical and modern statistical methods for BMI analysis. We give a description of each of these methods, exploring the classification, links and differences between them and the reasons for choosing one over the others in different settings. We aim to provide a key resource and statistical library for researchers in public health and medicine to deal with obesity and BMI data analysis.

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“…MacEachern (1999MacEachern ( , 2000 proposed a collection of dependent random probability measures with marginal distributions given by the DP. This idea has been extended and applied to the construction of various types of random probability measures such as the density regression (Dunson et al, 2007;Tokdar et al, 2010). A covariate-dependent extension was proposed by Müller et al, (2011) and some alternative extensions to build covariate-dependent random partition models can be found in Park and Dunson (2010), and Argiento et al, (2014).…”

Section: Introductionmentioning

confidence: 99%

Bayesian analysis of random partition models with Laplace distribution

Kyung

2017

CSAM

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We develop a random partition procedure based on a Dirichlet process prior with Laplace distribution. Gibbs sampling of a Laplace mixture of linear mixed regressions with a Dirichlet process is implemented as a random partition model when the number of clusters is unknown. Our approach provides simultaneous partitioning and parameter estimation with the computation of classification probabilities, unlike its counterparts. A full Gibbssampling algorithm is developed for an efficient Markov chain Monte Carlo posterior computation. The proposed method is illustrated with simulated data and one real data of the energy efficiency of Tsanas and Xifara (Energy and Buildings, 49, 560-567, 2012).

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Bayesian Density Regression

Cited by 191 publications

References 25 publications

Nonparametric Bayes Regression and Classification Through Mixtures of Product Kernels

Nonparametric Bayes Regression and Classification Through Mixtures of Product Kernels

Statistical methods for body mass index: A selective review

Bayesian analysis of random partition models with Laplace distribution

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