A full Bayesian approach for inverse problems

Details A full Bayesian approach for inverse problems A full Bayesian approach for inverse problems

2001-11-14

arxiv.org/abs/physics/0111123v1

Physics

Data Analysis, Statistics and Probability

Presented at MaxEnt95. Appeared in Maximum Entropy and Bayesian Methods, K. Hanson and R. Silver (Ed.), Kluwer Academic Publis

Scientific paper

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 $\yb$ related to the unknown parameters $\xb$ by $\yb=\Ab \xb+\nb$ and where we can assign the probability laws $p(\xb|\thetab)$, $p(\yb|\xb,\betab)$, $p(\betab)$ and $p(\thetab)$. The main discussion is then how to infer $\xb$, $\thetab$ and $\betab$ either individually or any combinations of them. Different situations are considered and discussed. As an important example, we consider the case where $\theta$ and $\beta$ 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.

Affiliated with

Also associated with

No associations

Rating

A full Bayesian approach for inverse problems does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with A full Bayesian approach for inverse problems, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and A full Bayesian approach for inverse problems will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-355851