Related papers: Filtering coupled Wright-Fisher diffusions
We consider systems of particles hopping stochastically on $d$-dimensional lattices with space-dependent probabilities. We map the master equation onto an evolution equation in a Fock space where the dynamics are given by a quantum…
The purpose of this Note is twofold: First, we introduce the general formalism of evolutionary genetics dynamics involving fitnesses, under both the deterministic and stochastic setups, and chiefly in discrete-time. In the process, we…
Spatial profiling technologies in biology, such as imaging mass cytometry (IMC) and spatial transcriptomics (ST), generate high-dimensional, multi-channel data with strong spatial alignment and complex inter-channel relationships.…
In this paper, a general model of wireless channels is established based on the physics of wave propagation. Then the problems of inverse scattering and channel prediction are formulated as nonlinear filtering problems. The solutions to the…
Probabilistic models help us encode latent structures that both model the data and are ideally also useful for specific downstream tasks. Among these, mixture models and their time-series counterparts, hidden Markov models, identify…
The Wright-Fisher model is the most popular population model for describing the behaviour of evolutionary systems with a finite population size. Approximations to the model have commonly been used for the analysis of time-resolved genome…
In the present paper new insights into the study of the Non-central Dirichlet distribution are provided. This latter is the analogue of the Dirichlet distribution obtained by replacing the Chi-Squared random variables involved in its…
The Ricker model was introduced in the context of managing fishing stocks. It is a discrete non-linear iterative model given by $N(t+1)=rN(t)\exp(-N(t))$ where $N(t)$ is the population at time $t$. The model treated in this paper includes a…
One-dimensional Fisher-Wright diffusion process on the interval $(0,1)$ with mutations is considered. This is a widely known model in population genetics. The goal of the paper is an exponential recurrence of the process, which also implies…
By approximating posterior distributions with weighted samples, particle filters (PFs) provide an efficient mechanism for solving non-linear sequential state estimation problems. While the effectiveness of particle filters has been…
The famous Fisher-KPP reaction-diffusion model combines linear diffusion with the typical KPP reaction term, and appears in a number of relevant applications in biology and chemistry. It is remarkable as a mathematical model since it…
In this paper, we introduce a mixture of skew-t factor analyzers as well as a family of mixture models based thereon. The mixture of skew-t distributions model that we use arises as a limiting case of the mixture of generalized hyperbolic…
This paper is concerned with exploring the microscopic basis for the discrete versions of the standard replicator equation and the adjusted replicator equation. To this end, we introduce frequency-dependent selection -- as a result of…
This paper develops information geometric representations for nonlinear filters in continuous time. The posterior distribution associated with an abstract nonlinear filtering problem is shown to satisfy a stochastic differential equation on…
The goal of this paper is to develop a theory of graphon-valued stochastic processes, and to construct and analyse a natural class of such processes arising from population genetics. We consider finite populations where individuals change…
When analyzing data from multiple sources, it is often convenient to strike a careful balance between two goals: capturing the heterogeneity of the samples and sharing information across them. We introduce a novel framework to model a…
A one species time-delay reaction-diffusion system defined on a complex networks is studied. Travelling waves are predicted to occur as follows a symmetry breaking instability of an homogenous stationary stable solution, subject to an…
The paper proposes a latent variable model for binary data coming from an unobserved heterogeneous population. The heterogeneity is taken into account by replacing the traditional assumption of Gaussian distributed factors by a finite…
Probabilistic forecasting of irregularly sampled multivariate time series with missing values is an important problem in many fields, including health care, astronomy, and climate. State-of-the-art methods for the task estimate only…
Previous studies showed that hydro-climate processes are stochastic and complex systems, and it is difficult to discover the hidden patterns in the all non-stationary data and thoroughly understand the hydro-climate relationships. For the…