The idea that fluctuations can be imparted to a data sequence by passing it through a linear filter has long been familiar to econometricians. It was associated with the discoveries of Slutsky and Yule in the early years of the 20th century. Slutsky (1927, 1937) applied a moving-average filter to random numbers drawn from a public lottery to produce a sequence that had the characteristics of a ...

In now classic work, David Kendall (1966) recognized that the Yule process and Poisson process could be related by a (random) time change. Furthermore, he showed that the Yule population size rescaled by its mean has an almost sure exponentially distributed limit as t → ∞. In this note we introduce a class of coupled delayed continuous time Yule processes parameterized by 0 < α ≤ 1 and find a r...

Approaches to reconstruct phylogenies abound and are widely used in the study of molecular evolution. Partially through extensive simulations, we are beginning to understand the potential pitfalls as well as the advantages of different methods. However, little work has been done on possible biases introduced by the methods if the input data are random and do not carry any phylogenetic signal. A...

Reliable color reproduction can be achieved by establishing, using a model, the correspondence between the spectral reflectance of the printed surface and the amounts of deposited inks. In this paper, we review the main models proposed in the literature, recall how each one is calibrated and compare their prediction accuracy for several print sets. The presented models are the Yule-Nielsen modi...

We investigate some discrete structural properties of evolutionary trees generated under simple null models of speciation, such as the Yule model. These models have been used as priors in Bayesian approaches to phylogenetic analysis, and also to test hypotheses concerning the speciation process. In this paper we describe new results for three properties of trees generated under such models. Fir...

We consider a stochastic process for the generation of species which combines a Yule process with a simple model for hybridization between pairs of co-existent species. We assume that the origin of the process, when there was one species, occurred at an unknown time in the past, and we condition the process on producing n species via the Yule process and a single hybridization event. We prove r...