A conditional density estimation partition model using logistic Gaussian processes

Payne, Richard D.; Guha, Nilabja; Ding, Yu; Mallick, Bani K.

doi:10.1093/biomet/asz064

Cited by 7 publications

(3 citation statements)

References 46 publications

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“…An important direction for future research is to extend the proposed Bayesian sum of trees model to accommodate additional data features commonly encountered in practice, such as time‐ and covariate‐dependent time series (Bertolacci et al., 2022), extra spectral variability due to clustering effects (Krafty, 2016), and missingness in covariate vectors. Alternative partitioning frameworks, such Voronoi tessellations (Payne et al., 2020) and binary space partitioning trees (Fan et al., 2019), and soft‐decision trees (Linero & Yang, 2018) that better adapt to smooth effects may also be considered for capturing covariate effects in an even more flexible and parsimonious manner.…”

Section: Discussionmentioning

confidence: 99%

Adaptive Bayesian Sum of Trees Model for Covariate-Dependent Spectral Analysis

Wang

Bruce

2022

Biometrics

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This paper introduces a flexible and adaptive nonparametric method for estimating the association between multiple covariates and power spectra of multiple time series. The proposed approach uses a Bayesian sum of trees model to capture complex dependencies and interactions between covariates and the power spectrum, which are often observed in studies of biomedical time series. Local power spectra corresponding to terminal nodes within trees are estimated nonparametrically using Bayesian penalized linear splines. The trees are considered to be random and fit using a Bayesian backfitting Markov chain Monte Carlo (MCMC) algorithm that sequentially considers tree modifications via reversible‐jump MCMC techniques. For high‐dimensional covariates, a sparsity‐inducing Dirichlet hyperprior on tree splitting proportions is considered, which provides sparse estimation of covariate effects and efficient variable selection. By averaging over the posterior distribution of trees, the proposed method can recover both smooth and abrupt changes in the power spectrum across multiple covariates. Empirical performance is evaluated via simulations to demonstrate the proposed method's ability to accurately recover complex relationships and interactions. The proposed methodology is used to study gait maturation in young children by evaluating age‐related changes in power spectra of stride interval time series in the presence of other covariates.

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Section: Discussionmentioning

confidence: 99%

Adaptive Bayesian Sum of Trees Model for Covariate-Dependent Spectral Analysis

Wang

Bruce

2022

Biometrics

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“…An important direction for future research is to extend the proposed Bayesian sum of trees model to accommodate additional data features commonly encountered in practice, such as time-and covariate-dependent time series (Bertolacci et al, 2019), extra spectral variability due to clustering effects (Krafty, 2016), and missingness in covariate vectors. Alternative partitioning frameworks, such Voronoi tesselations (Payne et al, 2020) and binary space partitioning trees (Fan et al, 2019), may also be considered for capturing covariate effects in an even more flexible and parsimonious manner.…”

Section: Discussionmentioning

confidence: 99%

Adaptive Bayesian Sum of Trees Model for Covariate Dependent Spectral Analysis

Wang¹,

Li²,

Bruce³

2021

Preprint

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This article introduces a flexible and adaptive nonparametric method for estimating the association between multiple covariates and power spectra of multiple time series. The proposed approach uses a Bayesian sum of trees model to capture complex dependencies and interactions between covariates and the power spectrum, which are often observed in studies of biomedical time series. Local power spectra corresponding to terminal nodes within trees are estimated nonparametrically using Bayesian penalized linear splines. The trees are considered to be random and fit using a Bayesian backfitting Markov chain Monte Carlo (MCMC) algorithm that sequentially considers tree modifications via reversible-jump MCMC techniques. For high-dimensional covariates, a sparsity-inducing Dirichlet hyperprior on tree splitting proportions is considered, which provides sparse estimation of covariate effects and efficient variable selection. By averaging over the posterior distribution of trees, the proposed method can recover both smooth and abrupt changes in the power spectrum across multiple covariates. Empirical performance is evaluated via simulations to demonstrate the proposed method's ability to accurately recover complex relationships and interactions.The proposed methodology is used to study gait maturation in young children by evaluating age-related changes in power spectra of stride interval time series in the presence of other covariates.

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“…The statistics literature on univariate density estimation is enormous; and the problem of covariate density estimation, sometimes referred to as density regression, has also received attention (see, e.g., Payne et al, 2020, and the references therein). The literature on multivariate density estimation, in contrast, is small and the literature on multivariate density regression almost non-existent.…”

Section: Supplementary Materials Formentioning

confidence: 99%

Bayesian Semiparametric Covariate Informed Multivariate Density Deconvolution

Sarkar¹

2022

Preprint

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Estimating the marginal and joint densities of the long-term average intakes of different dietary components is an important problem in nutritional epidemiology. Since these variables cannot be directly measured, data are usually collected in the form of 24-hour recalls of the intakes. The problem of estimating the density of the latent long-term average intakes from their observed but error contaminated recalls then becomes a problem of multivariate deconvolution of densities. The underlying densities could potentially vary with the subjects' demographic characteristics such as sex, ethnicity, age, etc. The problem of density deconvolution in the presence of associated precisely measured covariates has, however, never been considered before, not even in the univariate setting. We present a flexible Bayesian semiparametric approach to covariate informed multivariate deconvolution. Building on recent advances on copula deconvolution and conditional tensor factorization techniques, our proposed method not only allows the joint and the marginal densities to vary flexibly with the associated predictors but also allows automatic selection of the most influential predictors. Importantly, the method also allows the density of interest and the density of the measurement errors to vary with potentially different sets of predictors. We design Markov chain Monte Carlo algorithms that enable efficient posterior inference, appropriately accommodating uncertainty in all aspects of our analysis. The empirical efficacy of the proposed method is illustrated through simulation experiments. Its practical utility is demonstrated in the afore-described nutritional epidemiology applications in estimating covariate adjusted long term intakes of different dietary components. An important by-product of the approach is a solution to covariate informed ordinary multivariate density estimation. Supplementary materials include substantive additional details and R codes are also available online.

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A conditional density estimation partition model using logistic Gaussian processes

Cited by 7 publications

References 46 publications

Adaptive Bayesian Sum of Trees Model for Covariate-Dependent Spectral Analysis

Adaptive Bayesian Sum of Trees Model for Covariate-Dependent Spectral Analysis

Adaptive Bayesian Sum of Trees Model for Covariate Dependent Spectral Analysis

Bayesian Semiparametric Covariate Informed Multivariate Density Deconvolution

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