Relation To Probabilistic Formulation
The probabilistic formulation of an inverse problem introduces (when all uncertainties are Gaussian) a covariance matrix representing the a priori uncertainties on the model parameters, and a covariance matrix representing the uncertainties on the observed parameters (see, for instance, Tarantola, 2004 ). In the special case when these two matrices are diagonal and isotropic, and, and, in this case, the equations of inverse theory reduce to the equations above, with .
Read more about this topic: Tikhonov Regularization
Famous quotes containing the words relation to, relation and/or formulation:
“There is the falsely mystical view of art that assumes a kind of supernatural inspiration, a possession by universal forces unrelated to questions of power and privilege or the artist’s relation to bread and blood. In this view, the channel of art can only become clogged and misdirected by the artist’s concern with merely temporary and local disturbances. The song is higher than the struggle.”
—Adrienne Rich (b. 1929)
“There is undoubtedly something religious about it: everyone believes that they are special, that they are chosen, that they have a special relation with fate. Here is the test: you turn over card after card to see in which way that is true. If you can defy the odds, you may be saved. And when you are cleaned out, the last penny gone, you are enlightened at last, free perhaps, exhilarated like an ascetic by the falling away of the material world.”
—Andrei Codrescu (b. 1947)
“You do not mean by mystery what a Catholic does. You mean an interesting uncertainty: the uncertainty ceasing interest ceases also.... But a Catholic by mystery means an incomprehensible certainty: without certainty, without formulation there is no interest;... the clearer the formulation the greater the interest.”
—Gerard Manley Hopkins (1844–1889)