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The effect of additive white noise on a model for bursting behavior in large aspect-ratio binary fluid convection is considered. Such bursts are present in systems with nearly square symmetry and are the result of heteroclinic cycles…
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…
Uncertainty is the only certainty there is. Modeling data uncertainty is essential for regression, especially in unconstrained settings. Traditionally the direct regression formulation is considered and the uncertainty is modeled by…
Order patterns apply well to many fields, because of minimal stationarity assumptions. Here we fix the methodology of patterns of length 3 by introducing an orthogonal system of four pattern contrasts. These contrasts are statistically…
We assume a spatial blind source separation model in which the observed multivariate spatial data is a linear mixture of latent spatially uncorrelated Gaussian random fields containing a number of pure white noise components. We propose a…
Diffusion models for image generation function by progressively adding noise to an image set and training a model to separate out the signal from the noise. The noise profile used by these models is white noise -- that is, noise based on…
This brief article gives an overview of quantum mechanics as a {\em quantum probability theory}. It begins with a review of the basic operator-algebraic elements that connect probability theory with quantum probability theory. Then quantum…
Structure-agnostic causal inference studies how well one can estimate a treatment effect given black-box machine learning estimates of nuisance functions (like the impact of confounders on treatment and outcomes). Here, we find that the…
This paper proposes a novel model inference procedure to identify system matrix from a single noisy trajectory over a finite-time interval. The proposed inference procedure comprises an observation data processor, a redundant data processor…
Ensemble learning is characterized by flexibility, high precision, and refined structure. As a critical component within computational finance, option pricing with machine learning requires both high predictive accuracy and reduced…
Fractional Gaussian noise (fGn) is a self-similar stochastic process used to model anti-persistent or persistent dependency structures in observed time series. Properties of the autocovariance function of fGn are characterised by the Hurst…
We consider an ensemble of Ornstein-Uhlenbeck processes featuring a population of relaxation times and a population of noise amplitudes that characterize the heterogeneity of the ensemble. We show that the centre-of-mass like variable…
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…
Financial correlation matrices measure the unsystematic correlations between stocks. Such information is important for risk management. The correlation matrices are known to be ``noise dressed''. We develop a new and alternative method to…
Dynamical systems driven by a general L\'evy stable noise are considered. The inertia is included and the noise, represented by a generalised Ornstein-Uhlenbeck process, has a finite relaxation time. A general linear problem (the additive…
Contamination of covariates by measurement error is a classical problem in multivariate regression, where it is well known that failing to account for this contamination can result in substantial bias in the parameter estimators. The nature…
Stochastic resonance is a phenomenon where a noise of appropriate intensity enhances the input signal strength. In this work, by employing the recently developed convex optimization methods in the context of dynamical systems and stochastic…
Ordinal Patterns are a time-series data analysis tool used as a preliminary step to construct the Permutation Entropy which itself allows the same characterization of dynamics as chaotic or regular as more theoretical constructs such as the…
We develop a computational procedure to estimate the covariance hyperparameters for semiparametric Gaussian process regression models with additive noise. Namely, the presented method can be used to efficiently estimate the variance of the…
In 2002, in a seminal article, Christoph Bandt and Bernd Pompe proposed a new methodology for the analysis of complex time series, now known as Ordinal Analysis. The ordinal methodology is based on the computation of symbols (known as…