Related papers: Fully Bayesian Estimation and Variable Selection i…
In the usual Bayesian setting, a full probabilistic model is required to link the data and parameters, and the form of this model and the inference and prediction mechanisms are specified via de Finetti's representation. In general, such a…
We propose the Bayesian adaptive Lasso (BaLasso) for variable selection and coefficient estimation in linear regression. The BaLasso is adaptive to the signal level by adopting different shrinkage for different coefficients. Furthermore, we…
Bayesian approach, as a useful tool for quantifying uncertainties, has been widely used for solving inverse problems of partial differential equations (PDEs). One of the key difficulties for employing Bayesian approach for the issue is how…
Implicit sampling is a weighted sampling method that is used in data assimilation, where one sequentially updates estimates of the state of a stochastic model based on a stream of noisy or incomplete data. Here we describe how to use…
Statistical models are central to machine learning with broad applicability across a range of downstream tasks. The models are controlled by free parameters that are typically estimated from data by maximum-likelihood estimation or…
In discriminative settings such as regression and classification there are two random variables at play, the inputs X and the targets Y. Here, we demonstrate that the Variational Information Bottleneck can be viewed as a compromise between…
Density estimation is a classical problem in statistics and has received considerable attention when both the data has been fully observed and in the case of partially observed (censored) samples. In survival analysis or clinical trials, a…
A variational Bayesian inference for measured wave intensity, such as X-ray intensity, is proposed in this paper. The data is popular to obtain information about unobservable features of an object, such as a material sample and the…
Few Bayesian methods for analyzing high-dimensional sparse survival data provide scalable variable selection, effect estimation and uncertainty quantification. Such methods often either sacrifice uncertainty quantification by computing…
We propose a novel Bayesian model selection technique on linear mixed-effects models to compare multiple treatments with a control. A fully Bayesian approach is implemented to estimate the marginal inclusion probabilities that provide a…
This study proposes a mathematical programming-based algorithm for the integrated selection of variable subsets and bandwidth estimation in geographically weighted regression, a local regression method that allows the kernel bandwidth and…
Hierarchical statistical models are widely employed in information science and data engineering. The models consist of two types of variables: observable variables that represent the given data and latent variables for the unobservable…
We study methods for simultaneous analysis of many noisy and biased estimates, each paired with an even noisier estimate of its own bias. The analyst's goal is to construct short calibrated intervals for each parameter. The standard…
In this paper, we present an approach for modeling bio-tissues that incorporates the variability in properties as part of their characteristics. This is achieved by considering the parameters of the model of a biomaterial to themselves be…
Neural network based generative models with discriminative components are a powerful approach for semi-supervised learning. However, these techniques a) cannot account for model uncertainty in the estimation of the model's discriminative…
Given discrete time observations over a fixed time interval, we study a nonparametric Bayesian approach to estimation of the volatility coefficient of a stochastic differential equation. We postulate a histogram-type prior on the volatility…
We propose a new wavelet-based method for density estimation when the data are size-biased. More specifically, we consider a power of the density of interest, where this power exceeds 1/2. Warped wavelet bases are employed, where warping is…
In this paper, we consider the problem of blind signal and image separation using a sparse representation of the images in the wavelet domain. We consider the problem in a Bayesian estimation framework using the fact that the distribution…
In wavelet shrinkage and thresholding, most of the standard techniques do not consider information that wavelet coefficients might be bounded, although information about bounded energy in signals can be readily available. To address this,…
In this paper, we propose a class of efficient, accurate, and general methods for solving state-estimation problems with equality and inequality constraints. The methods are based on recent developments in variable splitting and partially…