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Using Kalman techniques, it is possible to perform optimal estimation in linear Gaussian state-space models. We address here the case where the noise probability density functions are of unknown functional form. A flexible Bayesian…

Statistics Theory · Mathematics 2009-11-13 François Caron , Manuel Davy , Arnaud Doucet , Emmanuel Duflos , Philippe Vanheeghe

Gaussian processes are widely employed as versatile modelling and predictive tools in spatial statistics, functional data analysis, computer modelling and diverse applications of machine learning. They have been widely studied over…

Statistics Theory · Mathematics 2023-03-28 Didong Li , Wenpin Tang , Sudipto Banerjee

Computing accurate estimates of the Fourier transform of analog signals from discrete data points is important in many fields of science and engineering. The conventional approach of performing the discrete Fourier transform of the data…

Machine Learning · Statistics 2017-12-08 Luca Ambrogioni , Eric Maris

The Cox model is an indispensable tool for time-to-event analysis, particularly in biomedical research. However, medicine is undergoing a profound transformation, generating data at an unprecedented scale, which opens new frontiers to study…

Methodology · Statistics 2023-03-07 Alexander W. Jung , Moritz Gerstung

We present the first fully variational Bayesian inference scheme for continuous Gaussian-process-modulated Poisson processes. Such point processes are used in a variety of domains, including neuroscience, geo-statistics and astronomy, but…

Machine Learning · Statistics 2015-07-29 Chris Lloyd , Tom Gunter , Michael A. Osborne , Stephen J. Roberts

Poisson log-linear models are ubiquitous in many applications, and one of the most popular approaches for parametric count regression. In the Bayesian context, however, there are no sufficient specific computational tools for efficient…

Computation · Statistics 2022-09-02 Laura D'Angelo , Antonio Canale

An algorithm for the unbiased simulation of continuous max-(resp.\ min-)id stochastic processes is developed. The algorithm only requires the simulation of finite Poisson random measures on the space of continuous functions and avoids the…

Probability · Mathematics 2022-10-03 Florian Brück

We propose a new sampling-based approach for approximate inference in filtering problems. Instead of approximating conditional distributions with a finite set of states, as done in particle filters, our approach approximates the…

Machine Learning · Computer Science 2020-03-03 Xuan Su , Wee Sun Lee , Zhen Zhang

In Bayesian nonparametric models, Gaussian processes provide a popular prior choice for regression function estimation. Existing literature on the theoretical investigation of the resulting posterior distribution almost exclusively assume a…

Statistics Theory · Mathematics 2015-03-06 Debdeep Pati , Anirban Bhattacharya , Guang Cheng

We propose a simulation method for multidimensional Hawkes processes based on superposition theory of point processes. This formulation allows us to design efficient simulations for Hawkes processes with differing exponentially decaying…

Machine Learning · Statistics 2018-03-14 Kar Wai Lim , Young Lee , Leif Hanlen , Hongbiao Zhao

Some scenarios require the computation of a predictive distribution of a new value evaluated on an objective function conditioned on previous observations. We are interested on using a model that makes valid assumptions on the objective…

Machine Learning · Computer Science 2021-01-21 Lucia Asencio-Martín , Eduardo C. Garrido-Merchán

Within the past two decades, Gaussian process regression has been increasingly used for modeling dynamical systems due to some beneficial properties such as the bias variance trade-off and the strong connection to Bayesian mathematics. As…

Systems and Control · Electrical Eng. & Systems 2021-02-11 Thomas Beckers

We introduce Gaussian orthogonal latent factor processes for modeling and predicting large correlated data. To handle the computational challenge, we first decompose the likelihood function of the Gaussian random field with a…

Methodology · Statistics 2021-11-30 Mengyang Gu , Hanmo Li

We examine an analytic variational inference scheme for the Gaussian Process State Space Model (GPSSM) - a probabilistic model for system identification and time-series modelling. Our approach performs variational inference over both the…

Machine Learning · Statistics 2018-12-11 Alessandro Davide Ialongo , Mark van der Wilk , Carl Edward Rasmussen

Simulating samples from arbitrary probability distributions is a major research program of statistical computing. Recent work has shown promise in an old idea, that sampling from a discrete distribution can be accomplished by perturbing and…

Computation · Statistics 2016-04-13 Chris J. Maddison

Variational inference techniques based on inducing variables provide an elegant framework for scalable posterior estimation in Gaussian process (GP) models. Besides enabling scalability, one of their main advantages over sparse…

Machine Learning · Statistics 2021-02-24 Simone Rossi , Markus Heinonen , Edwin V. Bonilla , Zheyang Shen , Maurizio Filippone

This paper introduces a new method for performing computational inference on log-Gaussian Cox processes. The likelihood is approximated directly by making novel use of a continuously specified Gaussian random field. We show that for…

Computation · Statistics 2015-11-02 Daniel Simpson , Janine Illian , Finn Lindgren , Sigrunn Sørbye , Håvard Rue

Recently, a novel linear model predictive control algorithm based on a physics-informed Gaussian Process has been introduced, whose realizations strictly follow a system of underlying linear ordinary differential equations with constant…

Optimization and Control · Mathematics 2025-05-01 Adrian Lepp , Jörn Tebbe , Andreas Besginow

A stationary Gaussian process is said to be long-range dependent (resp., anti-persistent) if its spectral density $f(\lambda)$ can be written as $f(\lambda)=|\lambda|^{-2d}g(|\lambda|)$, where $0<d<1/2$ (resp., $-1/2<d<0$), and $g$ is…

Methodology · Statistics 2012-07-24 Judith Rousseau , Nicolas Chopin , Brunero Liseo

Due to their flexibility, Gaussian processes (GPs) have been widely used in nonparametric function estimation. A prior information about the underlying function is often available. For instance, the physical system (computer model output)…

Methodology · Statistics 2017-11-21 Hassan Maatouk