相关论文: Shrinkage priors for Bayesian prediction

Modern applications of Bayesian inference involve models that are sufficiently complex that the corresponding posterior distributions are intractable and must be approximated. The most common approximation is based on Markov chain Monte…

We develop a novel Empirical Bayes methodology for prediction under check loss in high-dimensional Gaussian models. The check loss is a piecewise linear loss function having differential weights for measuring the amount of underestimation…

Loss-based priors assign probability mass to parameter values according to the inferential loss incurred when they are excluded from the parameter space, and provide a general solution for discrete parameters. Extending this idea to…

Bayesian parameter inference depends on a choice of prior probability distribution for the parameters in question. The prior which makes the posterior distribution maximally sensitive to data is called the Jeffreys prior, and it is…

This work proposes a wavelet shrinkage rule under asymmetric LINEX loss function and a mixture of a point mass function at zero and the logistic distribution as prior distribution to the wavelet coefficients in a nonparametric regression…

The training of high-dimensional regression models on comparably sparse data is an important yet complicated topic, especially when there are many more model parameters than observations in the data. From a Bayesian perspective, inference…

Datasets in engineering applications are often limited and contaminated, mainly due to unavoidable measurement noise and signal distortion. Thus, using conventional data-driven approaches to build a reliable discriminative model, and…

Bayesian inference --- although becoming popular in physics and chemistry --- is hampered up to now by the vagueness of its notion of prior probability. Some of its supporters argue that this vagueness is the unavoidable consequence of the…

We propose a general algorithm for approximating nonstandard Bayesian posterior distributions. The algorithm minimizes the Kullback-Leibler divergence of an approximating distribution to the intractable posterior distribution. Our method…

We investigate the use of normalizing flow (NF) models as flexible priors in Bayesian inference via Markov Chain Monte Carlo (MCMC) sampling for iterative Bayesian calibration. Trained on posteriors from previous analyses, these models can…

Directional data emerges in a wide array of applications, ranging from atmospheric sciences to medical imaging. Modeling such data, however, poses unique challenges by virtue of their being constrained to non-Euclidean spaces like…

Estimating boundary curves has many applications such as economics, climate science, and medicine. Bayesian trend filtering has been developed as one of locally adaptive smoothing methods to estimate the non-stationary trend of data. This…

Variational Bayesian inference is an important machine-learning tool that finds application from statistics to robotics. The goal is to find an approximate probability density function (PDF) from a chosen family that is in some sense…

Bayesian neural networks (BNNs) are state-of-the-art machine learning methods that can naturally regularize and systematically quantify uncertainties using their stochastic parameters. Kullback-Leibler (KL) divergence-based variational…

In the present work, we consider variable selection and shrinkage for the Gaussian dynamic linear regression within a Bayesian framework. In particular, we propose a novel method that allows for time-varying sparsity, based on an extension…

Wavelet shrinkage estimators are widely applied in several fields of science for denoising data in wavelet domain by reducing the magnitudes of empirical coefficients. In nonparametric regression problem, most of the shrinkage rules are…

Let $X$ be a random vector with distribution $P_{\theta}$ where $\theta$ is an unknown parameter. When estimating $\theta$ by some estimator $\varphi(X)$ under a loss function $L(\theta,\varphi)$, classical decision theory advocates that…

In the value-added literature, it is often claimed that regressing on empirical Bayes shrinkage estimates corrects for the measurement error problem in linear regression. We clarify the conditions needed; we argue that these conditions are…

It can be important in Bayesian analyses of complex models to construct informative prior distributions which reflect knowledge external to the data at hand. Nevertheless, how much prior information an analyst can elicit from an expert will…

Estimating time-varying correlation matrices is challenging because existing methods may adapt slowly to structural changes, impose insufficient regularization, or produce diffuse posterior uncertainty. In moderate dimensions, an additional…