Related papers: Bayesian Quantile Regression for Single-Index Mode…
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 propose a new family of error distributions for model-based quantile regression, which is constructed through a structured mixture of normal distributions. The construction enables fixing specific percentiles of the distribution while,…
This article introduces a Bayesian neural network estimation method for quantile regression assuming an asymmetric Laplace distribution (ALD) for the response variable. It is shown that the posterior distribution for feedforward neural…
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…
Laplace approximations are a standard tool for computationally efficient inference in latent Gaussian models, but they fail for quantile regression with the asymmetric Laplace likelihood because the observed Hessian vanishes almost…
Quantile regression, a robust method for estimating conditional quantiles, has advanced significantly in fields such as econometrics, statistics, and machine learning. In high-dimensional settings, where the number of covariates exceeds…
Gaussian latent variable models are a key class of Bayesian hierarchical models with applications in many fields. Performing Bayesian inference on such models can be challenging as Markov chain Monte Carlo algorithms struggle with the…
The Bayesian paradigm has the potential to solve core issues of deep neural networks such as poor calibration and data inefficiency. Alas, scaling Bayesian inference to large weight spaces often requires restrictive approximations. In this…
A method for sequential inference of the fixed parameters of a dynamic latent Gaussian models is proposed and evaluated that is based on the iterated Laplace approximation. The method provides a useful trade-off between computational…
Bayesian inference on non-Gaussian data is often non-analytic and requires computationally expensive approximations such as sampling or variational inference. We propose an approximate inference framework primarily designed to be…
Regression classes modeling more than the mean of the response have found a lot of attention in the last years. Expectile regression is a special and computationally convenient case of this family of models. Expectiles offer a quantile-like…
We introduce a random partition model for Bayesian nonparametric regression. The model is based on infinitely-many disjoint regions of the range of a latent covariate-dependent Gaussian process. Given a realization of the process, the…
We develop a Bayesian median autoregressive (BayesMAR) model for time series forecasting. The proposed method utilizes time-varying quantile regression at the median, favorably inheriting the robustness of median regression in contrast to…
Gaussian graphical model is one of the powerful tools to analyze conditional independence between two variables for multivariate Gaussian-distributed observations. When the dimension of data is moderate or high, penalized likelihood methods…
Envelope models provide a sufficient dimension reduction framework for multivariate regression analysis. Bayesian inference for these models has been developed primarily using Markov chain Monte Carlo (MCMC) methods. Specifically, Gibbs…
Gaussian processes are a natural way of defining prior distributions over functions of one or more input variables. In a simple nonparametric regression problem, where such a function gives the mean of a Gaussian distribution for an…
This work introduces Bayesian quantile regression modeling framework for the analysis of longitudinal count data. In this model, the response variable is not continuous and hence an artificial smoothing of counts is incorporated. The…
This work is motivated by the analysis of ecological interaction networks. Poisson stochastic blockmodels are widely used in this field to decipher the structure that underlies a weighted network, while accounting for covariate effects.…
The paper introduces a Bayesian estimation method for quantile regression in univariate ordinal models. Two algorithms are presented that utilize the latent variable inferential framework of Albert and Chib (1993) and the normal-exponential…
Nonparametric Bayesian models are used routinely as flexible and powerful models of complex data. Many times, a statistician may have additional informative beliefs about data distribution of interest, e.g., its mean or subset components,…