A full Bayesian approach for inverse problems
A. Mohammad-Djafari
Abstract
The main object of this paper is to present some general concepts of Bayesian inference and more specifically the estimation of the hyperparameters in inverse problems. We consider a general linear situation where we are given some data related to the unknown parameters by = + and where we can assign the probability laws p(|θb), p(|,βb), p(βb) and p(θb). The main discussion is then how to infer , θb and βb either individually or any combinations of them. Different situations are considered and discussed. As an important example, we consider the case where θ and β are the precision parameters of the Gaussian laws to whom we assign Gamma priors and we propose some new and practical algorithms to estimate them simultaneously. Comparisons and links with other classical methods such as maximum likelihood are presented. Keywords: Bayesian inference, Hyperparameter estimation, Inverse problems, Maximum likelihood.
Create a lesson
Related papers
Reduced latent leakage does not reliably predict lower likelihood bias in collider inference
Tong Pan
The Greedy Bump Bias: Local Profiling Geometry and the Look-Elsewhere Effect
Tommaso Dorigo
Multi-fidelity Monte Carlo estimation of floor response spectra under combined seismic and structural parameter uncertainties
Nils Baillie, Baptiste Kerleguer, Cyril Feau et al.
Parameter inference from a non-stationary unknown process using statistical feature-based slow feature analysis
Kieran S. Owens, Masako Tamaki, Ben D. Fulcher
A Probability Model for Pentagonal Prism Dice Rolls
Paul R. Hurst, J. Naleo Hyde
Geometry-native machine learning reconstruction of DSMC moment fields with support monitoring
Ehsan Roohi