Related papers: Bayesian Quantile Estimation and Regression with M…
Bayesian inference provides a flexible way of combining data with prior information. However, quantile regression is not equipped with a parametric likelihood, and therefore, Bayesian inference for quantile regression demands careful…
Quantile regression is a powerful data analysis tool that accommodates heterogeneous covariate-response relationships. We find that by coupling the asymmetric Laplace working likelihood with appropriate shrinkage priors, we can deliver…
The martingale posterior framework is a generalization of Bayesian inference where one elicits a sequence of one-step ahead predictive densities instead of the likelihood and prior. Posterior sampling then involves the imputation of unseen…
The predictive Bayesian view involves eliciting a sequence of one-step-ahead predictive distributions in lieu of specifying a likelihood function and prior distribution. Recent methods have leveraged predictive distributions which are…
A Neural Process (NP) estimates a stochastic process implicitly defined with neural networks given a stream of data, rather than pre-specifying priors already known, such as Gaussian processes. An ideal NP would learn everything from data…
Crossing of fitted conditional quantiles is a prevalent problem for quantile regression models. We propose a new Bayesian modelling framework that penalises multiple quantile regression functions toward the desired non-crossing space. We…
Bayesian inference provides principled uncertainty quantification but is often limited by the challenges of prior and likelihood elicitation. The martingale posterior (MGP) (Fong et al., 2023) offers an alternative by replacing these…
We introduce scalable algorithms for online learning of neural network parameters and Bayesian sequential decision making. Unlike classical Bayesian neural networks, which induce predictive uncertainty through a posterior over model…
Federated Bayesian neural networks require fixing a prior on the model parameters together with a likelihood. Eliciting meaningful priors on the weight space of modern overparameterized models is notoriously difficult, and misspecification…
The prior distribution on parameters of a sampling distribution is the usual starting point for Bayesian uncertainty quantification. In this paper, we present a different perspective which focuses on missing observations as the source of…
Flexible estimation of multiple conditional quantiles is of interest in numerous applications, such as studying the effect of pregnancy-related factors on low and high birth weight. We propose a Bayesian non-parametric method to…
Bayesian modelling allows for the quantification of predictive uncertainty which is crucial in safety-critical applications. Yet for many machine learning (ML) algorithms, it is difficult to construct or implement their Bayesian…
In this paper, we consider Bayesian methods for non-parametric quantile regressions with multiple continuous predictors ranging values in the unit interval. In the first method, the quantile function is assumed to be smooth over the…
Classic Bayesian methods with complex models are frequently infeasible due to an intractable likelihood. Simulation-based inference methods, such as Approximate Bayesian Computing (ABC), calculate posteriors without accessing a likelihood…
This study extends the Bayesian nonparametric instrumental variable regression model to determine the structural effects of covariates on the conditional quantile of the response variable. The error distribution is nonparametrically…
There is a growing interest in the so-called Bayesian Predictive Inference approach, which allows to perform Bayesian inference without specifying the likelihood and prior of the model, or the need of any MCMC. Instead, only a sequence of…
Bayesian inference typically relies on specifying a parametric model that approximates the data-generating process. However, misspecified models can yield poor convergence rates and unreliable posterior calibration. Bayesian empirical…
In this article, we develop a semiparametric Bayesian estimation and model selection approach for partially linear additive models in conditional quantile regression. The asymmetric Laplace distribution provides a mechanism for Bayesian…
We develop quantile regression models in order to derive risk margin and to evaluate capital in non-life insurance applications. By utilizing the entire range of conditional quantile functions, especially higher quantile levels, we detail…
We develop a multivariate posterior sampling procedure through deep generative quantile learning. Simulation proceeds implicitly through a push-forward mapping that can transform i.i.d. random vector samples from the posterior. We utilize…