Tractable Bayesian density regression via logit stick-breaking priors

Rigon, Tommaso; Durante, Daniele

doi:10.1016/j.jspi.2020.05.009

Cited by 15 publications

(24 citation statements)

References 45 publications

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“…As such, equation (2) defines a truncated stick-breaking prior with H support points {Φ 0h } and covariate-dependent weights summing to 1. Similarly to Rigon and Durante (2021), we assume that the weights are generated via a logit stick-breaking construction, that is,…”

Section: Exploratory Data Analysismentioning

confidence: 99%

“…Posterior inference is performed through a Gibbs sampler algorithm, as detailed in Appendix B. However, it is worth noting that the full-conditional of the weights parameters {α h } in Equation (3) can be derived in closed-form with the introduction of auxiliary variables, using results in Polson et al (2013) and Rigon and Durante (2021). The full conditional distributions of b and γ are derived as in a standard multivariate Bayesian linear regression models.…”

Section: Exploratory Data Analysismentioning

confidence: 99%

“…Our contribution includes the design of an efficient Gibbs sampling algorithm to perform posterior inference, that exploits recent results on logit stick-breaking priors by Rigon and Durante (2021). Note that the this random probability measure is represented by a finite random probability with H support points, but, unlike the sparse mixture in Frühwirth-Schnatter and Malsiner-Walli ( 2019), (i) the weights depend on covariates and (ii) come from a stick-breaking construction, thus implying stochastic dominance of the sequence itself (for a fixed value of the covariate).…”

Section: Introductionmentioning

confidence: 99%

“…6. Since the update of α h is independent of the AR model, we can simply refer to Rigon and Durante (2021) where a latent variable ω ih is introduced. Defining ρ ih |z i ∼ B(ν h (z i )), the couple (ω ih , ρ ih ) is updated as in Polson et al (2013) from a Pólya-Gamma distribution.…”

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confidence: 99%

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Bayesian Nonparametric Vector Autoregressive Models via a Logit Stick-breaking Prior: an Application to Child Obesity

Beraha¹,

Guglielmi²,

Quintana³

et al. 2022

Preprint

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Overweight and obesity in adults are known to be associated with risks of metabolic and cardiovascular diseases. Because obesity is an epidemic, increasingly affecting children, it is important to understand if this condition persists from early life to childhood and if different patterns of obesity growth can be detected. Our motivation starts from a study of obesity over time in children from South Eastern Asia. Our main focus is on clustering obesity patterns after adjusting for the effect of baseline information. Specifically, we consider a joint model for height and weight patterns taken every 6 months from birth. We propose a novel model that facilitates clustering by combining a vector autoregressive sampling model with a dependent logit stick-breaking prior. Simulation studies show the superiority of the model to capture patterns, compared to other alternatives. We apply the model to the motivating dataset, and discuss the main features of the detected clusters. We also compare alternative models with ours in terms of predictive performances.

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Section: Exploratory Data Analysismentioning

confidence: 99%

Section: Exploratory Data Analysismentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

mentioning

confidence: 99%

See 2 more Smart Citations

Bayesian Nonparametric Vector Autoregressive Models via a Logit Stick-breaking Prior: an Application to Child Obesity

Beraha¹,

Guglielmi²,

Quintana³

et al. 2022

Preprint

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“…As part of the proposed method, AdaptSPEC is extended to handle a time varying mean, which avoids having to de-mean (center) the time series as a preliminary step. The covariates, which are assumed to be time-independent, are incorporated via the mixture using the logistic stick breaking process (LSBP) of Rigon and Durante (2017), where the log odds for each 'stick break' are modeled using a thin plate spline Gaussian process over the covariates. The model is formulated in a Bayesian framework, where Markov chain Monte Carlo (MCMC) methods are used for parameter estimation.…”

Section: Introductionmentioning

confidence: 99%

AdaptSPEC-X: Covariate Dependent Spectral Modeling of Multiple Nonstationary Time Series

Bertolacci¹,

Rosen²,

Cripps³

et al. 2019

Preprint

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We present a method for the joint analysis of a panel of possibly nonstationary time series. The approach is Bayesian and uses a covariate-dependent infinite mixture model to incorporate multiple time series, with mixture components parameterized by a time varying mean and log spectrum. The mixture components are based on AdaptSPEC, a nonparametric model which adaptively divides the time series into an unknown but finite number of segments and estimates the local log spectra by smoothing splines. We extend AdaptSPEC to handle multiple time series with time varying mean and missing values. Covariates, assumed to be time-independent, are incorporated via the mixture weights using the logistic stick breaking process. The resulting model can estimate time varying means and spectra at both observed and unobserved covariate values, allowing for predictive inference. Estimation is performed by Markov chain Monte Carlo (MCMC) methods, combining data augmentation, reversible jump, and Riemann manifold Hamiltonian Monte Carlo techniques. We evaluate the methodology using simulated data, and describe applications to Australian rainfall data and measles incidence in the US. Efficient software implementing the method proposed in this paper is available in the R package BayesSpec.

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A hierarchical constrained density regression model for predicting cluster‐level dose‐response

Pennell,

Wheeler,

Auerbach

2024

Environmetrics

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With the advent of new alternative methods for rapid toxicity screening of chemicals comes the need for new statistical methodologies which appropriately synthesize the large amount of data collected. For example, transcriptomic assays can be used to assess the impact of a chemical on thousands of genes, but current approaches to analyzing the data treat each gene separately and do not allow sharing of information among genes within pathways. Furthermore, the methods employed are fully parametric and do not account for changes in distribution shape that may occur at high exposure levels. To address the limitations of these methods, we propose Constrained Logistic Density Regression (COLDER) to model expression data from different genes simultaneously. Under COLDER, the dose‐response function for each gene is assigned a prior via a discrete logistic stick‐breaking process (LSBP) whose weights depend on gene‐level characteristics (e.g., pathway membership) and atoms consist of different dose‐response functions subject to a shape constraint that ensures biological plausibility. The posterior distribution for the benchmark dose among genes within the same pathways can be estimated directly from the model, which is another advantage over current methods. The ability of COLDER to predict gene‐level dose‐response is evaluated in a simulation study and the method is illustrated with data from a National Toxicology Program study of Aflatoxin B1.

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Tractable Bayesian density regression via logit stick-breaking priors

Cited by 15 publications

References 45 publications

Bayesian Nonparametric Vector Autoregressive Models via a Logit Stick-breaking Prior: an Application to Child Obesity

Bayesian Nonparametric Vector Autoregressive Models via a Logit Stick-breaking Prior: an Application to Child Obesity

AdaptSPEC-X: Covariate Dependent Spectral Modeling of Multiple Nonstationary Time Series

A hierarchical constrained density regression model for predicting cluster‐level dose‐response

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