Mapping of Probabilities: Theory for the Interpretation of Uncertain Physical Measurements

Here’s the abstract for a talk by Dr. Albert Tarantola, Institut de Physique du Globe de Paris:

While the conventional way for making inferences from observations goes through the use of conditional probabilities (via de Bayes identity), there is an alternative. It consists in introducing some new definitions in Probability Theory (image and reciprocal image of a probability, intersection of two probabilities), that are accompanied by a compatibility property. The resulting theory is simple, accepts a clear Bayesian interpretation, and naturally incorporates the Popperian notion of falsification (for us, falsification of models, not of theories). The applications of the theory in the domain of inverse problems shall be discussed.

Unfortunately I can’t make the talk. I can’t figure out what he’s saying in the abstract, but the topic interests me. If anybody knows more about this, please let me know.

P.S. Brian Borchers writes,

Tarantola has been writing about Bayesian approaches to geophysical inverse problems for some time. He has recently (2005) published a book on inverse problem theory (Inverse Problem Theory and Methods for Model Parameter Estimation, SIAM 2005) that you might find interesting.

The “image of a probability” doesn’t appear in the SIAM book, but it is the topic of Tarantola’s new book, “Mapping of Probabilities”. You can download a draft (or at least the first two chapters) from his web site at http://www.ipgp.jussieu.fr/~tarantola/

1 thought on “Mapping of Probabilities: Theory for the Interpretation of Uncertain Physical Measurements

  1. I went to the lecture. The topic seemed very interesting, but he had a lot of trouble explaining how it was different from a standard Bayesian approach. He seemed disappointed at how the lecture went, and said that the previous two times he gave it, it went better.

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