We provide a new representation-independent formulation of Occam’s razor theorem, based on Kolmogorov complexity. This new formulation allows us to: (i) Obtain better sample complexity than both length-based [4] and VC-based [3] versions of Occam’s razor theorem, in many applications; and (ii) Achieve a sharper reverse of Occam’s razor theorem than that of [5]. Specifically, we weaken the assum...

Divergence date estimates are central to understand evolutionary processes and depend, in the case of molecular phylogenies, on tests of molecular clocks. Here we propose two non-parametric tests of strict and relaxed molecular clocks built upon a framework that uses the empirical cumulative distribution (ECD) of branch lengths obtained from an ensemble of Bayesian trees and well known non-para...

The concepts of cumulative distribution function and empirical distribution function are investigated for fuzzy random variables. Some limit theorems related to such functions are established. As an application of the obtained results, a method of handling fuzziness upon the usual method of Kolmogorov–Smirnov one-sample test is proposed. We transact the α-level set of imprecise observations in ...

In statistics, two-sample tests are used to determine whether two samples have been drawn from the same population. A widely used test as such is the Kolmogorov-Smirnov two-sample test. There are other distribution-free tests which might be applied in similar occasions. In this article, we describe a two-sample omnibus test introduced by Epps and Singleton, which has – albeit being distribution...