Related papers: Stochastic modelling of Gaussian processes by impr…
A general formalism is developed to construct a Markov chain model that converges to a one-dimensional map in the infinite population limit. Stochastic fluctuations are therefore internal to the system and not externally specified. For…
Consider estimation of the regression function based on a model with equidistant design and measurement errors generated from a fractional Gaussian noise process. In previous literature, this model has been heuristically linked to an…
In the pathwise stochastic calculus framework, the paper deals with the general study of equations driven by an additive Gaussian noise, with a drift function having an infinite limit at point zero. An ergodic theorem and the convergence of…
A stochastic theory for the toppling activity in sandpile models is developed, based on a simple mean-field assumption about the toppling process. The theory describes the process as an anti-persistent Gaussian walk, where the diffusion…
We obtain a representation theorem for Banach space valued Gaussian random variables as integrals against a white noise. As a corollary we obtain necessary and sufficient conditions for the existence of a white noise representation for a…
Bayesian nonparametric regression under a rescaled Gaussian process prior offers smoothness-adaptive function estimation with near minimax-optimal error rates. Hierarchical extensions of this approach, equipped with stochastic variable…
One of the pivotal tasks in scientific machine learning is to represent underlying dynamical systems from time series data. Many methods for such dynamics learning explicitly require the derivatives of state data, which are not directly…
In this paper, we introduce the notion of Gaussian processes indexed by probability density functions for extending the Mat\'ern family of covariance functions. We use some tools from information geometry to improve the efficiency and the…
We investigate the frequentist guarantees of the variational sparse Gaussian process regression model. In the theoretical analysis, we focus on the variational approach with spectral features as inducing variables. We derive guarantees and…
Gaussian processes models are widely adopted for nonparameteric/semi-parametric modeling. Identifiability issues occur when the mean model contains polynomials with unknown coefficients. Though resulting prediction is unaffected, this leads…
Stochastic calculus with respect to fractional Brownian motion (fBm) has attracted a lot of interest in recent years, motivated in particular by applications in finance and Internet traffic modeling. Multifractional Brownian motion (mBm) is…
A new class of fractional-order stochastic evolution equations of the form $(\partial_t + A)^\gamma X(t) = \dot{W}^Q(t)$, $t\in[0,T]$, $\gamma \in (0,\infty)$, is introduced, where $-A$ generates a $C_0$-semigroup on a separable Hilbert…
Gaussian process regression is widely applied in computational science and engineering for surrogate modeling owning to its kernel-based and probabilistic nature. In this work, we propose a Bayesian approach that integrates the variability…
We extend our recently introduced stochastic nonlocal traffic flow model to more general random perturbations, including Markovian noise derived from a discretized Jacobi-type stochastic differential equation. Invoking a deterministic…
In this paper, we present a new statistical approach to the problem of incorporating experimental observations into a mathematical model described by linear partial differential equations (PDEs) to improve the prediction of the state of a…
Motivated by constraints on the dark energy equation of state from supernova-data, we propose a formalism for the Bayesian inference of functions: Starting at a functional variant of the Kullback-Leibler divergence we construct a functional…
In this work we review the application of the theory of Gaussian processes to the modeling of noise in pulsar-timing data analysis, and we derive various useful and optimized representations for the likelihood expressions that are needed in…
The computational cost for inference and prediction of statistical models based on Gaussian processes with Mat\'ern covariance functions scales cubicly with the number of observations, limiting their applicability to large data sets. The…
Gaussian process classification (GPC) provides a flexible and powerful statistical framework describing joint distributions over function space. Conventional GPCs however suffer from (i) poor scalability for big data due to the full kernel…
The declining response rates in probability surveys along with the widespread availability of unstructured data has led to growing research into non-probability samples. Existing robust approaches are not well-developed for non-Gaussian…