Related papers: Wavelet shrinkage based on the raised cosine prior
When developing risk prediction models, shrinkage methods are recommended, especially when the sample size is limited. Several earlier studies have shown that the shrinkage of model coefficients can reduce overfitting of the prediction…
A new shrinkage-based construction is developed for a compressible vector $\boldsymbol{x}\in\mathbb{R}^n$, for cases in which the components of $\xv$ are naturally associated with a tree structure. Important examples are when $\xv$…
Accurate and precise covariance matrices will be important in enabling planned cosmological surveys to detect new physics. Standard methods imply either the need for many N-body simulations in order to obtain an accurate estimate, or a…
We consider nonparametric Bayesian inference in a reflected diffusion model $dX_t = b (X_t)dt + \sigma(X_t) dW_t,$ with discretely sampled observations $X_0, X_\Delta, \dots, X_{n\Delta}$. We analyse the nonlinear inverse problem…
We present a proposal to deal with the non-normality issue in the context of regression models with measurement errors when both the response and the explanatory variable are observed with error. We extend the normal model by jointly…
Completely automatic and adaptive non-parametric inference is a pie in the sky. The frequentist approach, best exemplified by the kernel estimators, has excellent asymptotic characteristics but it is very sensitive to the choice of…
Bayesian image restoration has had a long history of successful application but one of the limitations that has prevented more widespread use is that the methods are generally computationally intensive. The authors recently addressed this…
In this paper, we propose the application of shrinkage strategies to estimate coefficients in the Bell regression models when prior information about the coefficients is available. The Bell regression models are well-suited for modeling…
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…
Spatial concurrent linear models, in which the model coefficients are spatial processes varying at a local level, are flexible and useful tools for analyzing spatial data. One approach places stationary Gaussian process priors on the…
Decomposition of digital signals and images into other basis or dictionaries than time or space domains is a very common approach in signal and image processing and analysis. Such a decomposition is commonly obtained using fixed transforms…
Wave Kinetic Equations (WKEs) are often used to describe the evolution of ensemble averaged wave amplitudes for nonlinear wave systems. In the present manuscript we describe a new approach to direct numerical simulation of solutions to…
For signals belonging to balls in smoothness classes and noise with enough moments, the asymptotic behavior of the minimax quadratic risk among soft-threshold estimates is investigated. In turn, these results, combined with a median…
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…
The problem of imaging extended targets (sources or scatterers) is formulated in the framework of compressed sensing with emphasis on subwavelength resolution. The proposed formulation of the problems of inverse source/scattering is…
In this paper, a methodology is investigated for signal recovery in the presence of non-Gaussian noise. In contrast with regularized minimization approaches often adopted in the literature, in our algorithm the regularization parameter is…
We propose a kernel mixture of polynomials prior for Bayesian nonparametric regression. The regression function is modeled by local averages of polynomials with kernel mixture weights. We obtain the minimax-optimal rate of contraction of…
A new thresholding strategy for the estimation of a deterministic image immersed in noise is introduced. The threshold is combined with a wavelet decomposition, where the wavelet coefficient of the image at any fixed value of the…
Within Bayesian state estimation, considerable effort has been devoted to incorporating constraints into state estimation for process optimization, state monitoring, fault detection and control. Nonetheless, in the domain of state-space…
Unlike the ordinary least-squares (OLS) estimator for the linear model, a ridge regression linear model provides coefficient estimates via shrinkage, usually with improved mean-square and prediction error. This is true especially when the…