We study a family of coalescent processes that undergo ``simultaneous multiple collisions,'' meaning that many clusters of particles can merge into a single cluster at one time, and many such mergers… Expand

Let Λ be a finite measure on the Borel subsets of [0, 1]. Let Π∞ be the standard Λ-coalescent, which is defined in [4] and also studied in [5]. Then Π∞ is a Markov process whose state space is the… Expand

This work presents an alternative approach to estimating prediction intervals using weight decay to fit the network and shows via a simulation study that this method may be effective in overcoming some of the shortcomings of the other approaches.Expand

For a finite measureon (0,1), the �-coalescent is a coalescent process such that, whenever there are b clusters, each k-tuple of clusters merges into one at rate R 1 0 x k 2 (1 x) b k �(dx). It has… Expand

It is proved that Beta-coalescents can be embedded in continuous stable random trees based on a construction of the Donnelly-Kurtz lookdown process using continuous random trees, which is of independent interest.Expand

Two approximations for the selective sweep of a selective sweep are introduced, one of which is related to Kingman’s paintbox construction, replaces the coin flips by integer-valued random variables and leads to very accurate results.Expand

We determine that the continuous-state branching processes for which the genealogy, suitably time-changed, can be described by an autonomous Markov process are precisely those arising from… Expand