On the Fisher Metric of Conditional Probability Polytopes
نویسندگان
چکیده
منابع مشابه
On the Fisher Metric of Conditional Probability Polytopes
We consider three different approaches to define natural Riemannian metrics on polytopes of stochastic matrices. First, we define a natural class of stochastic maps between these polytopes and give a metric characterization of Chentsov type in terms of invariance with respect to these maps. Second, we consider the Fisher metric defined on arbitrary polytopes through their embeddings as exponent...
متن کاملProbability Density Functions from the Fisher Information Metric
We show a general relation between the spatially disjoint product of probability density functions and the sum of their Fisher information metric tensors. We then utilise this result to give a method for constructing the probability density functions for an arbitrary Riemannian Fisher information metric tensor. We note further that this construction is extremely unconstrained, depending only on...
متن کاملOn the metric dimension of convex polytopes ∗
Metric dimension is a generalization of affine dimension to arbitrary metric spaces (provided a resolving set exists). Let F be a family of connected graphs Gn : F = (Gn)n≥1 depending on n as follows: the order |V (G)| = φ(n) and lim n→∞ φ(n) = ∞ . If there exists a constant C > 0 such that dim(Gn) ≤ C for every n ≥ 1 then we shall say that F has bounded metric dimension. If all graphs in F hav...
متن کاملLowe on Conditional Probability
The concept of conditional probability has been employed for hundreds of years. Thomas Bayes used the expression "the probability that [B] on the supposition that [A]" in the statement of a basic law (1763, p. 378). Frank Ramsey, developing the application of probability to uncertain epistemic attitudes, the "logic of partial belief (1926, p. 166), wrote of your "degree of belief in [B] given [...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Entropy
سال: 2014
ISSN: 1099-4300
DOI: 10.3390/e16063207