20.500.12556/DiRROS-30697 Sparse simulation of autoregressive Gaussian processes This study proposes a novel and improved numerical approximation of the simulation of Gaussian process autoregressive models. As a Bayesian nonparametric regression method, Gaussian process models offer the unique advantage of providing closed-form uncertainty quantification. When Gaussian process models are used for autoregressive models, the validation procedure requires the model’s simulation or multi-step-ahead prediction. However, simulating dynamical Gaussian process models is complex due to the intractable propagation of uncertain inputs through the nonlinear model. Numerical approximation, namely Monte Carlo simulation, is one of the most frequent options for simulating dynamical models based on Gaussian processes. The computational burden of Monte Carlo simulation algorithms increases cubically with data size, representing a challenge. This paper introduces a unified simulation framework invariant to sparse and variational approximations to obtain a static sample from the pseudo-point posterior. Furthermore, we propose an innovative method for simulating Gaussian process dynamical models. A single parameter is proposed to regulate the trade-off between computational complexity and algorithmic accuracy. This innovation demonstrates the potential to replace the conditionally independent Monte Carlo method with no additional computational burden, thereby enhancing estimates of latent responses. The proposed simulation method is demonstrated using two synthetic examples and a realistic case study. Gaussian process models autoregressive models Monte Carlo simulation dynamical systems uncertainty quantification modeli Gaussovih procesov avtoregresijski modeli simulacija Monte Carlo dinamični sistemi kvantifikacija negotovosti true false true MDPI Švica Angleški jezik Slovenski jezik © 2026 by the authors. Neznano 2026-07-01 10:44:39 2026-07-01 10:44:40 2026-07-02 03:59:40 0000-00-00 00:00:00 2026 0 0 Nasl. z nasl. zaslona; Opis vira z dne 30. 6. 2026; str. 1-34 iss. 12, [article no.] 2111 Vol. 14 Jun. 2026 0000-00-00 Zaloznikova Objavljeno NiDoloceno 2026-05-04 2026-06-11 2026-06-13 519.2 2227-7390 10.3390/math14122111 283059203 https://www.mdpi.com/2227-7390/14/12/2111 1 1a041514-7529-11f1-b0d9-001a4af901a5 https://dirros.openscience.si/Dokument.php?lang=slv&id=46825 RAZ_Krivec_Tadej_2026.pdf RAZ_Krivec_Tadej_2026.pdf 1 535B564E31B1E4FF2226E7C7FBBA906E e21b68bba9e03df2eebb586a76303c82e7ab90fd8ca38b937629226ab0101cc6 54707363-7529-11f1-b0d9-001a4af901a5 https://dirros.openscience.si/Dokument.php?lang=slv&id=46827 Institut Jožef Stefan 0 0 0