A Bayesian Nonparametric Regression Model With Normalized Weights: A Study of Hippocampal Atrophy in Alzheimer’s Disease

Antoniano-Villalobos, Isadora; Wade, Sara; Walker, Stephen G.

doi:10.1080/01621459.2013.879061

Cited by 11 publications

(10 citation statements)

References 22 publications

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“…Given the complex nature of the application that we are considering and the lack of theory justifying transformations that would simplify the shape of the relation between the variables, we have decided to consider a linear predictor approach. Therefore, in this work, we build on the construction of the covariate-dependent weights developed by Antoniano-Villalobos et al (2014), which allows for combinations of continuous and discrete covariates and favors interpretability.…”

Section: Bayesian Nonparametric Density Regressionmentioning

confidence: 99%

“…As previously discussed, this parametric model is not flexible enough to capture the complex dependence structures contained in the data. We therefore extend the nonparametric density regression framework introduced by Antoniano- Villalobos et al (2014) to model the R d -valued latent variable Y:…”

Section: Bayesian Nonparametric Density Regressionmentioning

confidence: 99%

“…We propose a Bayesian multivariate density regression model that extends the univariate model of Antoniano-Villalobos et al (2014) to the case of multiple mixed-type responses with censoring and constraints. This approach is promising for our data, due to its ability to capture their peculiar features.…”

Section: Introductionmentioning

confidence: 99%

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Colombian Women’s Life Patterns: A Multivariate Density Regression Approach

Wade¹,

Piccarreta²,

Cremaschi³

et al. 2021

Bayesian Anal.

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Women in Colombia face difficulties related to the patriarchal traits of their societies and well-known conflict afflicting the country since 1948. In this critical context, our aim is to study the relationship between baseline sociodemographic factors and variables associated to fertility, partnership patterns, and work activity. To best exploit the explanatory structure, we propose a Bayesian multivariate density regression model, which can accommodate mixed responses with censored, constrained, and binary traits. The flexible nature of the models allows for nonlinear regression functions and non-standard features in the errors, such as asymmetry or multi-modality. The model has interpretable covariatedependent weights constructed through normalization, allowing for combinations of categorical and continuous covariates. Computational difficulties for inference are overcome through an adaptive truncation algorithm combining adaptive Metropolis-Hastings and sequential Monte Carlo to create a sequence of automatically truncated posterior mixtures. For our study on Colombian women's life patterns, a variety of quantities are visualised and described, and in particular, our findings highlight the detrimental impact of family violence on women's choices and behaviors.

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Section: Bayesian Nonparametric Density Regressionmentioning

confidence: 99%

Section: Bayesian Nonparametric Density Regressionmentioning

confidence: 99%

See 1 more Smart Citation

Colombian Women’s Life Patterns: A Multivariate Density Regression Approach

Wade¹,

Piccarreta²,

Cremaschi³

et al. 2021

Bayesian Anal.

Self Cite

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“…Such density regression model, where the weights w in ( 23) follow the stick-breaking representation of ( 19) and the extended parameters (θ , ψ ) are i.i.d. from some adequate base measure, G, was proposed by Antoniano-Villalobos et al (2014), to which we refer the reader for additional details on the role and choice of hyper parameters, as well as the algorithm used for inference. We adopt this construction to estimate the conditional density f Y |X i (y|x i ) as a mixture of linear regression models:…”

Section: Conditional Density-based Estimationmentioning

confidence: 99%

Nonparametric estimation of probabilistic sensitivity measures

Antoniano-Villalobos

Borgonovo

2019

Stat Comput

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Computer experiments are becoming increasingly important in scientific investigations.In the presence of uncertainty, analysts employ probabilistic sensitivity methods to identify the key-drivers of change in the quantities of interest. Simulation complexity, large dimensionality and long running times may force analysts to make statistical inference at small sample sizes. Methods designed to estimate probabilistic sensitivity measures at relatively low computational costs are attracting increasing interest. We propose a fully Bayesian approach to the estimation of probabilistic sensitivity measures based on a one-sample design. We discuss, first, new estimators based on placing piecewise constant priors on the conditional distributions of the output given each input, by partitioning the input space. We then present two alternatives, based on Bayesian non-parametric density estimation, which bypass the need for predefined partitions. In all cases, the Bayesian paradigm guarantees the quantification of uncertainty in the estimation process through the posterior distribution over the sensitivity measures, without requiring additional simulator evaluations. The performance of the proposed methods is compared to that of traditional point estimators in a series of numerical experiments comprising synthetic but challenging simulators, as well as a realistic application.Probabilistic (or global) sensitivity measures are an indispensable complement of uncertainty quantification, as they highlight which areas should be given priority when planning data collection or further modelling efforts. International agencies such as the US Environmental Protection Agency (U.S. Environmental Protection Agency, 2009) or the British National Institute for Health Care Excellence (NICE, 2013) and the European Commission (2009) have issued guidelines recommending the use of probabilistic sensitivity analysis methods as the gold standard for ensuring reliability and transparency when using the output of a computer code for decision-making under uncertainty. Over the years, several probabilistic sensitivity measures have been proposed. Different measures enjoy alternative properties making them preferable in different contexts and for different purposes. We recall regression-based (Helton and Sallaberry, 2009), variance-based (Saltelli and Tarantola, 2002;Jiménez Rugama and Gilquin, 2018) and moment-independent measures (Borgonovo et al., 2014), all of which offer alternative ways to quantify the degree of statistical dependence between the simulator inputs and the output. A transversal issue in realistic applications is that analytical expressions of these measures are unavailable and analysts must resort to estimation. This, however, is a challenging task, especially for simulators with a high number of inputs (the curse of dimensionality) or with long running times (high computational cost).Recent results (Strong et al., 2012;Strong and Oakley, 2013) evidence the one-sample (or given-data) approach as an attractive design, which allows ...

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“…This form requires x 1:n to be standardized for good performance, and we find that specifying independent bandwidths for each dimension in x works well. This method is similar to the normalized covariate-dependent weights of Antoniano-Villalobos et al (2014).…”

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confidence: 99%

Martingale posterior distributions

Fong¹,

Holmes²,

Walker³

2021

Preprint

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The prior distribution on parameters of a likelihood is the usual starting point for Bayesian uncertainty quantification. In this paper, we present a different perspective. Given a finite data sample Y 1:n of size n from an infinite population, we focus on the missing Y n+1:∞ as the source of statistical uncertainty, with the parameter of interest being known precisely given Y 1:∞ . We argue that the foundation of Bayesian inference is to assign a predictive distribution on Y n+1:∞ conditional on Y 1:n , which then induces a distribution on the parameter of interest. Demonstrating an application of martingales, Doob shows that choosing the Bayesian predictive distribution returns the conventional posterior as the distribution of the parameter. Taking this as our cue, we relax the predictive machine, avoiding the need for the predictive to be derived solely from the usual prior to posterior to predictive density formula. We introduce the martingale posterior distribution, which returns Bayesian uncertainty directly on any statistic of interest without the need for the likelihood and prior, and this distribution can be sampled through a computational scheme we name predictive resampling. To that end, we introduce new predictive methodologies for multivariate density estimation, regression and classification that build upon recent work on bivariate copulas.

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A Bayesian Nonparametric Regression Model With Normalized Weights: A Study of Hippocampal Atrophy in Alzheimer’s Disease

Cited by 11 publications

References 22 publications

Colombian Women’s Life Patterns: A Multivariate Density Regression Approach

Colombian Women’s Life Patterns: A Multivariate Density Regression Approach

Nonparametric estimation of probabilistic sensitivity measures

Martingale posterior distributions

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