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A novel methodology to analyze non-Gaussian probability distribution functions (PDFs) of intermittent turbulent transport in global full-f gyrokinetic simulations is presented. In this work, the Auto-Regressive Integrated Moving Average…

This paper presents a new variable selection approach integrated with Gaussian process (GP) regression. We consider a sparse projection of input variables and a general stationary covariance model that depends on the Euclidean distance…

The purpose of the article is twofold. Firstly, we review some recent results on the maximum likelihood estimation in the regression model of the form $X_t = \theta G(t) + B_t$, where $B$ is a Gaussian process, $G(t)$ is a known function,…

Standard sparse pseudo-input approximations to the Gaussian process (GP) cannot handle complex functions well. Sparse spectrum alternatives attempt to answer this but are known to over-fit. We suggest the use of variational inference for…

Gaussian processes regression is applied to augment experimental data of transfer-path analysis (TPA) by known information about the underlying physical properties of the system under investigation. The approach can be used as an…

We discuss simulation schemes for continuous-time autoregressive moving average (CARMA) processes driven by tempered stable L\'evy noises. CARMA processes are the continuous-time analogue of ARMA processes as well as a generalization of…

This paper introduces a Gegenbauer-based fractional approximation (GBFA) method for high-precision approximation of the left Riemann-Liouville fractional integral (RLFI). By using precomputable fractional-order shifted Gegenbauer…

A new forecasting method based on the concept of the profile predictive the likelihood function is proposed for discrete-valued processes. In particular, generalized autoregressive and moving average (GARMA) models for Poisson distributed…

Transformed Generalized Autoregressive Moving Average (TGARMA) models were recently proposed to deal with non-additivity, non-normality and heteroscedasticity in real time series data. In this paper, a Bayesian approach is proposed for…

We consider high-frequency sampled continuous-time autoregressive moving average (CARMA) models driven by finite-variance zero-mean L\'evy processes. An L^2-consistent estimator for the increments of the driving L\'evy process without order…

Time series in natural sciences, such as hydrology and climatology, and other environmental applications, often consist of continuous observations constrained to the unit interval (0,1). Traditional Gaussian-based models fail to capture…

We reconsider a nonparametric density model based on Gaussian processes. By augmenting the model with latent P\'olya--Gamma random variables and a latent marked Poisson process we obtain a new likelihood which is conjugate to the model's…

Simulating a Gaussian process requires sampling from a high-dimensional Gaussian distribution, which scales cubically with the number of sample locations. Spectral methods address this challenge by exploiting the Fourier representation,…

Folding uncertainty in theoretical models into Bayesian parameter estimation is necessary in order to make reliable inferences. A general means of achieving this is by marginalizing over model uncertainty using a prior distribution…

A time-varying empirical spectral process indexed by classes of functions is defined for locally stationary time series. We derive weak convergence in a function space, and prove a maximal exponential inequality and a…

In this paper, we introduce weighted fractional generalized cumulative past entropy of a nonnegative absolutely continuous random variable with bounded support. Various properties of the proposed weighted fractional measure are studied.…

A novel first-order moving-average model for analyzing time series observed at irregularly spaced intervals is introduced. Two definitions are presented, which are equivalent under Gaussianity. The first one relies on normally distributed…

Generalized autoregressive moving average (GARMA) models are a class of models that was developed for extending the univariate Gaussian ARMA time series model to a flexible observation-driven model for non-Gaussian time series data. This…

A practical approach to evaluate performance of a Gaussian process regression models (GPR) for irregularly sampled sparse time-series is introduced. The approach entails construction of a secondary autoregressive model using the fine scale…

A common task is the determination of system parameters from spectroscopy, where one compares the experimental spectrum with calculated spectra, that depend on the desired parameters. Here we discuss an approach based on a machine learning…