Exact simulation of coupled Wright–Fisher diffusions

In this paper an exact rejection algorithm for simulating paths of the coupled Wright–Fisher diffusion is introduced. The coupled Wright–Fisher diffusion is a family of multivariate Wright–Fisher diffusions that have drifts depending on each other through a coupling term and that find applications in the study of networks of interacting genes. The proposed rejection algorithm uses independent neutral Wright–Fisher diffusions as candidate proposals, which are only needed at a finite number of points. Once a candidate is accepted, the remainder of the path can be recovered by sampling from neutral multivariate Wright–Fisher bridges, for which an exact sampling strategy is also provided. Finally, the algorithm’s complexity is derived and its performance demonstrated in a simulation study.

Exact simulation for multivariate Itô diffusions

We provide the first generic exact simulation algorithm for multivariate diffusions. Current exact sampling algorithms for diffusions require the existence of a transformation which can be used to reduce the sampling problem to the case of a constant diffusion matrix and a drift which is the gradient of some function. Such a transformation, called the Lamperti transformation, can be applied in general only in one dimension. So, completely different ideas are required for the exact sampling of generic multivariate diffusions. The development of these ideas is the main contribution of this paper. Our strategy combines techniques borrowed from the theory of rough paths, on the one hand, and multilevel Monte Carlo on the other.

Exact sampling of determinantal point processes without eigendecomposition

Determinantal point processes (DPPs) enable the modeling of repulsion: they provide diverse sets of points. The repulsion is encoded in a kernel K that can be seen, in a discrete setting, as a matrix storing the similarity between points. The main exact algorithm to sample DPPs uses the spectral decomposition of K, a computation that becomes costly when dealing with a high number of points. Here we present an alternative exact algorithm to sample in discrete spaces that avoids the eigenvalues and the eigenvectors computation. The method used here is innovative, and numerical experiments show competitive results with respect to the initial algorithm.

The records of Pagurus trigonocheirus (Stimpson, 1858) (Crustacea: Decapoda: Paguridae) from the continental coasts of the Peter the Great Bay of the Sea of Japan with the list of hermit crab species from the area

The sublittoral hermit crab Pagurus trigonocheirus (Stimpson, 1858) (Crustacea: Decapoda: Paguridae) is recorded from depths of 80–200 m along the continental coastline of the Peter the Great Bay, Sea of Japan. The exact sampling localities as well as photographs of live specimens are presented in the paper. Doubtful records of hermit crabs from the southern Russian coastline of the Sea of Japan are also discussed.