B. Efron. Defining the curvature of a statistical problem (with applications to second order efficiency). Annals of Statistics, 3(6):1189--1242, 1975. Home/Search Document Not in Database Summary Related Articles Check |
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Using Ancillary Statistics in On-Line Learning Algorithms - Huaiyu Zhu (Correct)
....P on X . If X is of infinite size P forms an infinite dimensional manifold. A statistical model is a finite dimensional submanifold Q P . We shall also consider the space e P of finite measures on X . It is also an infinite dimensional manifold, containing P as a smooth submanifold. See [4, 1, 2, 6, 14, 12]. It has been shown [14, 12] that in general a statistical inference problem can be specified by a prior P (p) on P , the information divergence D ffi (p; q) ffi 2 [0; 1] and the model Q. For a given sample x, there exists a unique ideal estimate, called the ffi estimate, b p 2 e P , given ....
....with tangent l 1 and normal l 2 . The auxiliary point r is unchanged and is represented in the new auxiliary coordinates as 1 and 2 , where 1 = 0. Figure 2: Change of coordinates caused by curvature training is the exponential geometry, a special case of information geometry [4, 1, 2, 6]. Roughly speaking, it is defined by the Fisher information metric, which specifies an inner product on the tangent space, and the exponential affine connection, which specifies that exponential families are to be considered flat submanifolds. Note that as we are considering geometry for the ....
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B. Efron. Defining the curvature of a statistical problem (with applications to second order efficiency) (with discussion). Ann. Statist., 3:1189--1242, 1975.
Bayesian Invariant Measurements of Generalisation for.. - Zhu, Rohwer (1995) (2 citations) (Correct)
....interesting would be direct applications to non Gaussian continuous distributions. For exponential families, which are exactly the distribution families admitting a sufficient statistic of fixed dimension [Dar35, Koo36, Pit36] the procedure would be quite similar. For curved exponential families [Efr75] one of the possible routes of exploration is to assume an exponentially uniform prior on the whole exponential family, and consider the ffi estimates restricted to the curved submanifold [Ama85] It is expected that this will reduce to the results of information geometry for curved exponential ....
B. Efron. Defining the curvature of a statistical problem (with applications to second order efficiency) (with discussion). Ann. Statist., 3:1189--1242, 1975.
Submitted to AUTOMATICA, July 20th, 1999 - The Geometry Of (Correct)
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B. Efron. Defining the curvature of a statistical problem (with applications to second order efficiency). Annals of Statistics, 3(6):1189--1242, 1975.
The Geometry of Active Sensing - Bruyninckx, De Schutter (1999) (Correct)
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B. Efron. Defining the curvature of a statistical problem (with applications to second order efficiency). Annals of Statistics, 3(6):1189--1242, 1975.
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