arXiv subjects

Nils Baillie

Publications and source records attributed to Nils Baillie.

3 recordsLinked to original sources

arXiv2026

Multi-fidelity Monte Carlo estimation of floor response spectra under combined seismic and structural parameter uncertainties

Floor response spectra (FRS) are essential tools for the design of non-structural elements (such as equipment or components). Given the various physical phenomena influencing FRS, high-fidelity (HF) mechanical models of the primary structure may be required to estimate them. Since numerical simulations based on such models are generally computationally expensive, this paper proposes using a multi-fidelity Monte Carlo (MFMC) approach for the efficient estimation of FRS. The method relies on using observations from a fast low-fidelity (LF) model as control variables. If the absolute value of the correlation between LF and HF samples is close to 1, this approach reduces both variance and estimation error compared to a standard Monte Carlo estimate based solely on HF data samples. Through a case study involving the reactor building of the Kashiwazaki-Kariwa nuclear power plant, we demonstrate the suitability of this method for FRS estimation. It effectively reduces variance and estimation error, even when using a LF model as simple as a single-degree-of-freedom system. We also show that the method accounts for modeling uncertainties while maintaining comparable performance. Its ease of use makes it a valuable tool for practitioners.

physics.data-an↗

arXiv2026

Multi-fidelity Gaussian process regression for noisy outputs and non-nested experimental designs: a comparison between the recursive and non-recursive formulations

This paper investigates a recursive formulation of auto-regressive multi-fidelity Gaussian process regression in the challenging setting of noisy and non-nested high- and low-fidelity data. We propose a decoupled optimization strategy based on the expectation-maximization algorithm, which exploits the structure of the recursive model. In particular, we derive closed-form update formulas when the scaling factor is modeled as a parametric linear predictor. This approach is compared with the fully coupled likelihood maximization of the classical non-recursive formulation introduced by Kennedy and O'Hagan. A series of benchmark experiments, covering applications of increasing complexity, highlights the performance of both approaches. The results demonstrate that the proposed recursive strategy significantly reduces training time, especially when large low-fidelity datasets are available, while maintaining competitive predictive accuracy and uncertainty estimation.

stat.AP↗

arXiv2025

Variational inference for approximate objective priors using neural networks

In Bayesian statistics, the choice of the prior can have an important influence on the posterior and the parameter estimation, especially when few data samples are available. To limit the added subjectivity from a priori information, one can use the framework of objective priors, more particularly, we focus on reference priors in this work. However, computing such priors is a difficult task in general. Hence, we consider cases where the reference prior simplifies to the Jeffreys prior. We develop in this paper a flexible algorithm based on variational inference which computes approximations of priors from a set of parametric distributions using neural networks. We also show that our algorithm can retrieve modified Jeffreys priors when constraints are specified in the optimization problem to ensure the solution is proper. We propose a simple method to recover a relevant approximation of the parametric posterior distribution using Markov Chain Monte Carlo (MCMC) methods even if the density function of the parametric prior is not known in general. Numerical experiments on several statistical models of increasing complexity are presented. We show the usefulness of this approach by recovering the target distribution. The performance of the algorithm is evaluated on both prior and posterior distributions, jointly using variational inference and MCMC sampling.

stat.ME↗