For Γ a countable amenable group consider those actions of Γ as measurepreserving transformations of a standard probability space, written as {Tγ}γ∈Γ acting on (X,F , μ). We say {Tγ}γ∈Γ has completely positive entropy (or simply cpe for short) if for any finite and nontrivial partition P of X the entropy h(T, P ) is not zero. Our goal is to demonstrate what is well known for actions of Z and ev...

We provide a list of functional equations that characterize quantile functions for collections of bounded and measurable functions. Our central axiom is ordinal covariance. When a probability measure is exogeneously given, we characterize quantiles with respect to that measure through monotonicity with respect to stochastic dominance. When none is given, we characterize those functions which ar...

Linear pooling is by the far the most popular method for combining probability forecasts. However, any nontrivial weighted average of two or more distinct, calibrated probability forecasts is necessarily uncalibrated and lacks sharpness. In view of this, linear pooling requires recalibration, even in the ideal case in which the individual forecasts are calibrated. Toward this end, we propose a ...

The simplest Bayesian adaptive randomization scheme is to randomize patients to a treatment with probability equal to the probability p that the treatment is better. We examine three variations on adaptive randomization which are used to compromise between this scheme and equal randomization. The first variation is to apply a power transformation to p to obtain randomization probabilities. The ...

This paper extends previous work in discriminant analysis with von Mises-Fisher distributions (e. g., Morris and Laycock, Biometrika, 1974) to general dimension, allowing computation of misclassification probabilities. The main result is the probability distribution of the cosine transformation of a von Mises-Fisher distribution, that is, the random variable , where , satisfying , is a random d...

The structure of the automorphism group of a simple TAI algebra is studied. In particular, we show that Inn(A) Inn0(A) is isomorphic (as a topological group) to an inverse limit of discrete abelian groups for a unital, simple, AH algebra with bounded dimension growth. Consequently, Inn(A) Inn0(A) is totally disconnected. Another consequence of our results is the following: Suppose A is the tran...

Coined quantum walks may be interpreted as the motion in position space of a quantum particle with a spin degree of freedom; the dynamics are determined by iterating a unitary transformation which is the product of a spin transformation and a translation conditional on the spin state. Coined quantum walks on Z can be treated as special cases of coined quantum walks on R. We study quantum walks ...

There is only one fully supported ergodic invariant probability measure for the adic transformation on the space of infinite paths in the graph that underlies the Eulerian numbers. This result may partially justify a frequent assumption about the equidistribution of random permutations. Résumé. Pour la transformation adique sur l’espace des chemins infinis dans le graphe associé aux nombres Eul...