Related papers: Subordinated Wright-Fisher Priors
We propose an effective method to solve the event sequence clustering problems based on a novel Dirichlet mixture model of a special but significant type of point processes --- Hawkes process. In this model, each event sequence belonging to…
We investigate various aspects of the (biallelic) Wright-Fisher diffusion with seed bank in conjunction with and contrast to the two-island model analysed e.g. in Kermany, Zhou and Hickey, 2008, and Nath and Griffiths, 1993, including…
Real-world dynamical systems with retardation effects are described in general not by a single, precisely defined time delay, but by a range of delay times. An exact mapping onto a set of $N+1$ ordinary differential equations exists when…
This paper extends the notion of information processing capacity for non-independent input signals in the context of reservoir computing (RC). The presence of input autocorrelation makes worthwhile the treatment of forecasting and filtering…
We propose a novel hierarchical diffusion planner that embeds task and motion structure directly into the noise model. Unlike standard diffusion-based planners that rely on zero-mean, isotropic Gaussian corruption, we introduce…
Many records in environmental sciences exhibit asymmetric trajectories and there is a need for simple and tractable models which can reproduce such features. In this paper we explore an approach based on applying both a time change and a…
We dedicate this paper to Sir John Kingman on his 70th Birthday. In modern mathematical population genetics the ancestral history of a population of genes back in time is described by John Kingman's coalescent tree. Classical and modern…
Fractional derivatives can be used to model time delays in a diffusion process. When the order of the fractional derivative is distributed over the unit interval, it is useful for modeling a mixture of delay sources. In some special cases…
We prove duality estimates for time-fractional and more general subdiffusion problems. An important example is given by subdiffusive porous medium type equations. Our estimates can be used to prove uniqueness of weak solutions to such…
The time fractional diffusion equation is obtained from the standard diffusion equation by replacing the first-order time derivative with a fractional derivative of order $\beta \in (0,1)$. The fundamental solution for the Cauchy problem is…
Statistical modelling in the presence of data organized in groups is a crucial task in Bayesian statistics. The present paper conceives a mixture model based on a novel family of Bayesian priors designed for multilevel data and obtained by…
We link optimal filtering for hidden Markov models to the notion of duality for Markov processes. We show that when the signal is dual to a process that has two components, one deterministic and one a pure death process, and with respect to…
Self-supervised learning has garnered increasing attention in time series analysis for benefiting various downstream tasks and reducing reliance on labeled data. Despite its effectiveness, existing methods often struggle to comprehensively…
The solution of the continuous time filtering problem can be represented as a ratio of two expectations of certain functionals of the signal process that are parametrized by the observation path. We introduce a new time discretisation of…
Models for human choice prediction in preference learning and psychophysics often consider only binary response data, requiring many samples to accurately learn preferences or perceptual detection thresholds. The response time (RT) to make…
We study discretizations of Hamiltonian systems on the probability density manifold equipped with the $L^2$-Wasserstein metric. Based on discrete optimal transport theory, several Hamiltonian systems on graph (lattice) with different…
In this study, we investigate the performance of two novel first-order optimization algorithms, namely the rescaled-gradient flow (RGF) and the signed-gradient flow (SGF). These algorithms are derived from the forward Euler discretization…
Real data are constrained to finite sampling rates, which calls for a suitable mathematical description of the corrections to the finite-time estimations of the dynamic equations. Often in the literature, lower order discrete time…
We focus on variational inference in dynamical systems where the discrete time transition function (or evolution rule) is modelled by a Gaussian process. The dominant approach so far has been to use a factorised posterior distribution,…
Widely used models in genetics include the Wright-Fisher diffusion and its moment dual, Kingman's coalescent. Each has a multilocus extension but under neither extension is the sampling distribution available in closed-form, and their…