1887
Volume 36 Number 8
  • E-ISSN: 1365-2478

Abstract

ABSTRACT

This paper gives a review of Bayesian parameter estimation. The Bayesian approach is fundamental and applicable to all kinds of inverse problems. Its basic formulation is probabilistic. Information from data is combined with information on model parameters. The result is called the probability density function and it is the solution to the inverse problem. In practice an estimate of the parameters is obtained by taking its maximum. Well‐known estimation procedures like least‐squares inversion or norm inversion result, depending on the type of noise and information given. Due to the information the maximum will be unique and the estimation procedures will be stable except (in theory) for the most pathological problems which are very unlikely to occur in practice. The approach of Tarantola and Valette can be derived within classical probability theory.

The Bayesian approach allows a full resolution and uncertainty analysis which is discussed in Part II of the paper.

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2006-04-27
2024-03-28
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