Related papers: Bayesian priors and nuisance parameters

We apply Bayesian statistics to the estimation of correlation functions. We give the probability distributions of auto- and cross-correlations as functions of the data. Our procedure uses the measured data optimally and informs about the…

We study frequentist asymptotic properties of Bayesian procedures for high-dimensional Gaussian sparse regression when unknown nuisance parameters are involved. Nuisance parameters can be finite-, high-, or infinite-dimensional. A mixture…

Bayesian methods are actively used for parameter identification and uncertainty quantification when solving nonlinear inverse problems with random noise. However, there are only few theoretical results justifying the Bayesian approach.…

In high-dimensional Bayesian statistics, various methods have been developed, including prior distributions that induce parameter sparsity to handle many parameters. Yet, these approaches often overlook the rich spectral structure of the…

We study the application of a Bayesian method to extract relevant information from data for the case of a signal consisting of two or more decaying particles and its background. The method takes advantage of the dependence that exists in…

A new method of extracting the low-lying energy spectrum from Monte Carlo estimates of Euclidean-space correlation functions which incorporates Bayesian inference is described and tested. The procedure fully exploits the information present…

Additive or multiplicative stationary noise recently became an important issue in applied fields such as microscopy or satellite imaging. Relatively few works address the design of dedicated denoising methods compared to the usual white…

This paper addresses the problem of separating spectral sources which are linearly mixed with unknown proportions. The main difficulty of the problem is to ensure the full additivity (sum-to-one) of the mixing coefficients and…

We derive an exact and efficient Bayesian regression algorithm for piecewise constant functions of unknown segment number, boundary location, and levels. It works for any noise and segment level prior, e.g. Cauchy which can handle outliers.…

We seek to conduct statistical inference for a large collection of primary parameters, each with its own nuisance parameters. Our approach is partially Bayesian, in that we treat the primary parameters as fixed while we model the nuisance…

Many imaging systems are used to estimate a vector of parameters associated with the object being imaged. In many cases there are other parameters in the model for the imaging data that are not of interest for the task at hand. We refer to…

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 address the common problem of calculating intervals in the presence of systematic uncertainties. We aim to investigate several approaches, but here describe just a Bayesian technique for setting upper limits. The particular example we…

Exposure assessment models are deterministic models derived from physical-chemical laws. In real workplace settings, chemical concentration measurements can be noisy and indirectly measured. In addition, inference on important parameters…

Estimation problems in the presence of deterministic linear nuisance parameters arise in a variety of fields. To cope with those, three common methods are widely considered: (1) jointly estimating the parameters of interest and the nuisance…

Three independent techniques are used to separate fine structure from the absorption spectra, the background function in which is approximated by (i) smoothing spline. We propose a new reliable criterion for determination of smoothing…

Design of experiments has traditionally relied on the frequentist hypothesis testing framework where the optimal size of the experiment is specified as the minimum sample size that guarantees a required level of power. Sample size…

Prior distributions elicited for modelling the natural fluctuations or the uncertainty on parameters of Bayesian fishery population models, can be chosen among a vast range of statistical laws. Since the statistical framework is defined by…

The extraction of any physical information from quasielastic neutron scattering spectra is generally done by fitting a model to the data by means of chi-square minimization procedure. However, as pointed out by the pioneering work of D.S.…

Bayesian analyses require that all variable model parameters are given a prior probability distribution. This can pose a challenge for analyses where multiple experiments are combined if these experiments use different parametrisations for…