The field of nonlinear regression is a long way from reaching a consensus. Once a method decides to explore nonlinear combinations of predictors, a number of questions are raised, such as what nonlinear combinations to permit and how best to search the resulting model space. Genetic Association...

Permutation-valued Markov processes provide a convenient way to describe the genealogical structure of certain population models that allow immigration or mutation. Distinct cycles of the permutation correspond to binary branching trees that describe relationships among members of a particular...

A novel representation of the linear birth process with immigration is analysed. The state space of the process is the collection of permutations of the integers, written in a particular cyclic form. The stochastic structure of the model is particularly simple to describe. The results serve to...

We analyze the role of recurrent mutation on the time to formation or detection of particular genotypes in finite populations. The traditional method of approximating Markov chain models by diffusion processes is used. However, the diffusion approximations that arise in this context are governed...