Related papers: Statistical modeling for adaptive trait evolution …
We extend our study of a simple model of biological coevolution to its statistical properties. Staring with a complete description in terms of a master equation, we provide its relation to the deterministic evolution equations used in…
Single-spin quantum sensors, for example based on nitrogen-vacancy centres in diamond, provide nanoscale mapping of magnetic fields. In applications where the magnetic field may be changing rapidly, total sensing time is crucial and must be…
This paper first strictly proved that the growth of the second moment of a large class of Gaussian processes is not greater than power function and the covariance matrix is strictly positive definite. Under these two conditions, the maximum…
Practical Bayesian learning often requires (1) online inference, (2) dynamic models, and (3) ensembling over multiple different models. Recent advances have shown how to use random feature approximations to achieve scalable, online…
We provide an asymptotic analysis of a nonlinear integro-differential equation describing the evolutionary dynamics of a population which reproduces sexually and which is subject to selection and competition. The sexual reproduction is…
Variational quantum circuits have arisen as an important method in quantum computing. A crucial step of it is parameter optimization, which is typically tackled through gradient-descent techniques. We advantageously explore instead the use…
The Bayesian additive regression trees (BART) model is an ensemble method extensively and successfully used in regression tasks due to its consistently strong predictive performance and its ability to quantify uncertainty. BART combines…
This paper contributes to the human-machine interface community in two ways: as a critique of the closed-loop AC (augmented cognition) approach, and as a way to introduce concepts from complex systems and systems physiology into the field.…
Posterior sampling by Monte Carlo methods provides a more comprehensive solution approach to inverse problems than computing point estimates such as the maximum posterior using optimization methods, at the expense of usually requiring many…
Information theoretic active learning has been widely studied for probabilistic models. For simple regression an optimal myopic policy is easily tractable. However, for other tasks and with more complex models, such as classification with…
The goal of these lectures is to review some mathematical aspects of random tree models used in evolutionary biology to model gene trees or species trees. We start with stochastic models of tree shapes (finite trees without edge lengths),…
Felsenstein's classical model for Gaussian distributions on a phylogenetic tree is shown to be a toric variety in the space of concentration matrices. We present an exact semialgebraic characterization of this model, and we demonstrate how…
Brown-Resnick processes are max-stable processes that are associated to Gaussian processes. Their simulation is often based on the corresponding spectral representation which is not unique. We study to what extent simulation accuracy and…
The problem of estimating the parameters of a linear regression model $Z(s,t)=m_1g_1(s,t)+ \cdots + m_pg_p(s,t)+U(s,t)$ based on observations of $Z$ on a spatial domain $G$ of special shape is considered, where the driving process $U$ is a…
In this paper, we investigate the optimal strong convergence rate of numerical approximations for the Cox--Ingersoll--Ross model driven by fractional Brownian motion with Hurst parameter $H\in(1/2,1)$. To deal with the difficulties caused…
The research presented in this article concerns the stroboscopic approach to quantum tomography, which is an area of science where quantum Physics and linear algebra overlap. In this article we introduce the algebraic structure of the…
We develop a Gaussian process framework for learning interaction kernels in multi-species interacting particle systems from trajectory data. Such systems provide a canonical setting for multiscale modeling, where simple microscopic…
Gaussian process regression in its most simplified form assumes normal homoscedastic noise and utilizes analytically tractable mean and covariance functions of predictive posterior distribution using Gaussian conditioning. Its…
In this paper we consider two continuous-mass population models as analogues of logistic branching random walks, one is supported on a finite trait space and the other one is supported on an infinite trait space. For the first model with…
Bayesian learning using Gaussian processes provides a foundational framework for making decisions in a manner that balances what is known with what could be learned by gathering data. In this dissertation, we develop techniques for…