Some aestheticians, e.g., Peter Kivy,' are Platonists about pieces of music. They hold that a piece of music is the sound structure indicated by the notation, and that performances are (or, present) tokens of the sound structure, i.e., tokens of a type. Other philosophers, e.g., Jerrold Levinson, deny this; in Kivy's terminology they are anti-Platonists. Levinson holds that the essential charac...

Fisher information has been used to analyze the accuracy of neural population coding. This works well when the Fisher information does not degenerate, but when two stimuli are presented to a population of neurons, a singular structure emerges by their mutual interactions. In this case, the Fisher information matrix degenerates, and the regularity condition ensuring the Cramér-Rao paradigm of st...

X ′Xθ = X ′Y. Here, X ′X is called the “information matrix” of θ and var(θ̂) = σ(X ′X)−1 (provided Rank(X) = t). Let l′θ be an estimable linear parametric function. Then var(l′θ̂) = σ2l′(X ′X)−l. We choose a design d, with design matrix Xd, whose information matrix X ′ dXd is “large” (equivalently, (X ′ dXd) − is “small”) in some sense. Now, suppose we are interested in a component θ1 of θ. We write

We provide a new perspective on Stein’s so-called density approach by introducing a new operator and characterizing class which are valid for a much wider family of probability distributions on the real line. We prove an elementary factorization property of this operator and propose a new Stein identity which we use to derive information inequalities in terms of what we call the generalized Fis...

Any unperturbed and perturbed posterior density can formally be linked by a mixture. Many divergences between the unperturbed and perturbed posterior density global measures of influence of the perturbation are then essentially determined by the Fisher information with respect to the mixing parameter evaluated at the unperturbed density. It is investigated which aspect of change this Fisher inf...

We study Cramér-Rao bounds (CRB’s) for estimation problems on Riemannian manifolds. In (S.T. Smith, Covariance, subspace, and intrinsic Cramér-Rao bounds, IEEE TSP, 53(5):1610–1630, 2005), the author gives intrinsic CRB’s in the form of matrix inequalities relating the covariance of estimators and the Fisher information of estimation problems. We focus on estimation problems whose parameter spa...

We prove that if X1, ..., Xn(n ≥ 2) are selfadjoints in a W ∗-probability space with finite nonmicrostates free Fisher information, then the von Neumann algebra W ∗(X1, ..., Xn) they generate doesn’t have property Γ (especially is not amenable). This is an analog of a well-known result of Voiculescu for microstates free entropy. We also prove factoriality under finite non-microstates entropy.

The problem considered in this letter is to bound the performance of estimators of a deterministic parameter which satisfies given constraints. Specifically, previous work on the constrained Cramér–Rao bound (CRB) is generalized to include singular Fisher information matrices and biased estimators. A necessary and sufficient condition for the existence of a finite CRB is obtained. A closed form...

An important property of Fisher information is that it decreases weakly under transformation of random variables. Kagan and Rao (2003) [A. Kagan, C.R. Rao, Some properties and applications of the efficient Fisher score, J. Statist. Plann. Inference 116 (2003) 343–352] showed that, in the presence of nuisance parameters, Fisher information on the interest parameters decreases similarly. We prove...