Related papers: Maximum likelihood estimation for Gaussian process…
The first purpose of this article is to obtain a.s. asymptotic properties of the maximum likelihood estimator in the autoregressive process driven by a stationary Gaussian noise. The second purpose is to show the local asymptotic normality…
We introduce constrained Gaussian process (CGP), a Gaussian process model for random functions that allows easy placement of mathematical constrains (e.g., non-negativity, monotonicity, etc) on its sample functions. CGP comes with…
We consider a modification of the covariance function in Gaussian processes to correctly account for known linear constraints. By modelling the target function as a transformation of an underlying function, the constraints are explicitly…
This paper investigates the approximation of Gaussian random variables in Banach spaces, focusing on the high-probability bounds for the approximation of Gaussian random variables using finitely many observations. We derive non-asymptotic…
Graphical models with bi-directed edges (<->) represent marginal independence: the absence of an edge between two vertices indicates that the corresponding variables are marginally independent. In this paper, we consider maximum likelihood…
Gaussian process regression underpins countless academic and industrial applications of machine learning and statistics, with maximum likelihood estimation routinely used to select appropriate parameters for the covariance kernel. However,…
We describe a method to computationally estimate the probability density function of a univariate random variable by applying the maximum entropy principle with some local conditions given by Gaussian functions. The estimation errors and…
Gaussian process emulators of computationally expensive computer codes provide fast statistical approximations to model physical processes. The training of these surrogates depends on the set of design points chosen to run the simulator.…
We consider chance constrained optimization where it is sought to optimize a function while complying with constraints, both of which are affected by uncertainties. The high computational cost of realistic simulations strongly limits the…
The problem of parameter estimation by the continuous time observations of a deterministic signal in white gaussian noise is considered. The asymptotic properties of the maximul likelihood estimator are described in the asymptotics of small…
We consider statistical inference for a class of continuous semimartingale regression models based on high-frequency observations subject to contamination by finite-activity jumps and spike noise. By employing density-power weighting and…
Maximum likelihood estimation has been extensively used in the joint analysis of repeated measurements and survival time. However, there is a lack of theoretical justification of the asymptotic properties for the maximum likelihood…
The Gaussian mixed-effects model driven by a stationary integrated Ornstein-Uhlenbeck process has been used for analyzing longitudinal data having an explicit and simple serial-correlation structure in each individual. However, the…
We derive the precise asymptotic distributional behavior of Gaussian variational approximate estimators of the parameters in a single-predictor Poisson mixed model. These results are the deepest yet obtained concerning the statistical…
We consider the problem of estimating unknown parameters in stochastic differential equations driven by colored noise, which we model as a sequence of Gaussian stationary processes with decreasing correlation time. We aim to infer…
We show that the mean-model parameter is always orthogonal to the error distribution in generalized linear models. Thus, the maximum likelihood estimator of the mean-model parameter will be asymptotically efficient regardless of whether the…
Maximum likelihood estimation is a common method of estimating the parameters of the probability distribution from a given sample. This paper aims to introduce the maximum likelihood estimation in the framework of sublinear expectation. We…
This paper presents an approach for constrained Gaussian Process (GP) regression where we assume that a set of linear transformations of the process are bounded. It is motivated by machine learning applications for high-consequence…
We consider the problem of parameter estimation for a stochastic McKean-Vlasov equation, and the associated system of weakly interacting particles. We study two cases: one in which we observe multiple independent trajectories of the…
Gaussian processes are ubiquitous in machine learning, statistics, and applied mathematics. They provide a flexible modelling framework for approximating functions, whilst simultaneously quantifying uncertainty. However, this is only true…