Related papers: Bayesian Wavelet Shrinkage with Beta Priors
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…
Statistical inference for sparse covariance matrices is crucial to reveal dependence structure of large multivariate data sets, but lacks scalable and theoretically supported Bayesian methods. In this paper, we propose beta-mixture…
Shrinkage prior has gained great successes in many data analysis, however, its applications mostly focus on the Bayesian modeling of sparse parameters. In this work, we will apply Bayesian shrinkage to model high dimensional parameter that…
Motivated by the increasing use of and rapid changes in array technologies, we consider the prediction problem of fitting a linear regression relating a continuous outcome $Y$ to a large number of covariates $\mathbf {X}$, for example,…
In inference problems involving a multi-dimensional parameter $\theta$, it is often natural to consider decision rules that have a risk which is invariant under some group $G$ of permutations of $\theta$. We show that this implies that the…
In all areas of human knowledge, datasets are increasing in both size and complexity, creating the need for richer statistical models. This trend is also true for economic data, where high-dimensional and nonlinear/nonparametric inference…
We consider a Bayesian approach to variable selection in the presence of high dimensional covariates based on a hierarchical model that places prior distributions on the regression coefficients as well as on the model space. We adopt the…
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…
It is increasingly being realised that many real world time series are not stationary and exhibit evolving second-order autocovariance or spectral structure. This article introduces a Bayesian approach for modelling the evolving wavelet…
We consider a high-dimensional sparse normal means model where the goal is to estimate the mean vector assuming the proportion of non-zero means is unknown. We model the mean vector by a one-group global-local shrinkage prior belonging to a…
As an alternative to variable selection or shrinkage in high dimensional regression, we propose to randomly compress the predictors prior to analysis. This dramatically reduces storage and computational bottlenecks, performing well when the…
This paper presents a novel Bayesian strategy for the estimation of smooth signals corrupted by Gaussian noise. The method assumes a smooth evolution of a succession of continuous signals that can have a numerical or an analytical…
The models used to describe the kinetics of ruminal degradation are usually nonlinear models where the dependent variable is the proportion of degraded food. The method of least squares is the standard approach used to estimate the unknown…
In this paper we propose a shrinkage wavelet-based method to estimate the signal in a nonparametric regression model with Autoregressive Fractionally Integrated Moving Average (ARFIMA) errors. Monte Carlo experiments indicate that the…
In recent years, a rich variety of shrinkage priors have been proposed that have great promise in addressing massive regression problems. In general, these new priors can be expressed as scale mixtures of normals, but have more complex…
In this paper we propose a wavelet-based methodology for estimation and variable selection in partially linear models. The inference is conducted in the wavelet domain, which provides a sparse and localized decomposition appropriate for…
We develop singular value shrinkage priors for the mean matrix parameters in the matrix-variate normal model with known covariance matrices. Our priors are superharmonic and put more weight on matrices with smaller singular values. They are…
This paper develops a class of Bayesian non- and semiparametric methods for estimating regression curves and surfaces. The main idea is to model the regression as locally linear, and then place suitable local priors on the local parameters.…
Shrinkage estimation usually reduces variance at the cost of bias. But when we care only about some parameters of a model, I show that we can reduce variance without incurring bias if we have additional information about the distribution of…
In this contribution, we consider the problem of blind source separation in a Bayesian estimation framework. The wavelet representation allows us to assign an adequate prior distribution to the wavelet coefficients of the sources. MCMC…