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Isotropic probability measures in infinite dimensional spaces: Inverse problems/prior information/stochastic inversionLet R be the real numbers, R(n) the linear space of all real n-tuples, and R(infinity) the linear space of all infinite real sequences x = (x sub 1, x sub 2,...). Let P sub n :R(infinity) approaches R(n) be the projection operator with P sub n (x) = (x sub 1,...,x sub n). Let p(infinity) be a probability measure on the smallest sigma-ring of subsets of R(infinity) which includes all of the cylinder sets P sub n(-1) (B sub n), where B sub n is an arbitrary Borel subset of R(n). Let p sub n be the marginal distribution of p(infinity) on R(n), so p sub n(B sub n) = p(infinity)(P sub n to the -1(B sub n)) for each B sub n. A measure on R(n) is isotropic if it is invariant under all orthogonal transformations of R(n). All members of the set of all isotropic probability distributions on R(n) are described. The result calls into question both stochastic inversion and Bayesian inference, as currently used in many geophysical inverse problems.
Document ID
19880004554
Acquisition Source
Legacy CDMS
Document Type
Contractor Report (CR)
Authors
Backus, George (California Univ., San Diego La Jolla, CA, United States)
Date Acquired
September 5, 2013
Publication Date
September 4, 1987
Subject Category
Statistics And Probability
Report/Patent Number
NAS 1.26:181555
NASA-CR-181555
Accession Number
88N13936
Funding Number(s)
CONTRACT_GRANT: NAG5-818
CONTRACT_GRANT: NSF EAR-85-21543
Distribution Limits
Public
Copyright
Work of the US Gov. Public Use Permitted.

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