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Complex computer codes or models can often be run in a hierarchy of different levels of complexity ranging from the very basic to the sophisticated. The top levels in this hierarchy are typically expensive to run, which limits the number of…

We introduce statistical techniques required to handle complex computer models with potential applications to astronomy. Computer experiments play a critical role in almost all fields of scientific research and engineering. These computer…

Despite a large corpus of recent work on scaling up Gaussian processes, a stubborn trade-off between computational speed, prediction and uncertainty quantification accuracy, and customizability persists. This is because the vast majority of…

This paper explores Vecchia likelihood approximation for modeling physical phenomena sensed by mobile and fixed low-cost sensors in urban environments. A three-level hierarchical model is proposed to simultaneously accounts for the physical…

Over the last two decades, the science has come a long way from relying on only physical experiments and observations to experimentation using computer simulators. This chapter focusses on the modelling and analysis of data arising from…

The growing field of large-scale time domain astronomy requires methods for probabilistic data analysis that are computationally tractable, even with large datasets. Gaussian Processes are a popular class of models used for this purpose…

Multivariate Gaussian processes (GPs) offer a powerful probabilistic framework to represent complex interdependent phenomena. They pose, however, significant computational challenges in high-dimensional settings, which frequently arise in…

Variational autoencoders employ an amortized inference model to approximate the posterior of latent variables. However, such amortized variational inference faces two challenges: (1) the limited posterior expressiveness of fully-factorized…

Approximation algorithms are widely used in many engineering problems. To obtain a data set for approximation a factorial design of experiments is often used. In such case the size of the data set can be very large. Therefore, one of the…

Gaussian processes (GPs) are a Bayesian machine learning approach widely used to construct surrogate models for the uncertainty quantification of computer simulation codes in industrial applications. It provides both a mean predictor and an…

We present methods for emulating the matter power spectrum by combining information from cosmological $N$-body simulations at different resolutions. An emulator allows estimation of simulation output by interpolating across the parameter…

We introduce new Gaussian Process (GP) high-order approximations to linear operations that are frequently used in various numerical methods. Our method employs the kernel-based GP regression modeling, a non-parametric Bayesian approach to…

The scientific understanding of real-world processes has dramatically improved over the years through computer simulations. Such simulators represent complex mathematical models that are implemented as computer codes which are often…

Optimization of expensive computer models with the help of Gaussian process emulators in now commonplace. However, when several (competing) objectives are considered, choosing an appropriate sampling strategy remains an open question. We…

Gaussian random field is a ubiquitous model for spatial phenomena in diverse scientific disciplines. Its approximation is often crucial for computational feasibility in simulation, inference, and uncertainty quantification. The…

Simulation models are widely used in practice to facilitate decision-making in a complex, dynamic and stochastic environment. But they are computationally expensive to execute and optimize, due to lack of analytical tractability. Simulation…

Gaussian Processes (GPs) are powerful kernelized methods for non-parameteric regression used in many applications. However, their use is limited to a few thousand of training samples due to their cubic time complexity. In order to scale GPs…

Sparse variational approximations allow for principled and scalable inference in Gaussian Process (GP) models. In settings where several GPs are part of the generative model, theses GPs are a posteriori coupled. For many applications such…

Sequential Monte Carlo is a family of algorithms for sampling from a sequence of distributions. Some of these algorithms, such as particle filters, are widely used in the physics and signal processing researches. More recent developments…

DPPs were introduced by Macchi as a model in quantum optics the 1970s. Since then, they have been widely used as models and subsampling tools in statistics and computer science. Most applications require sampling from a DPP, and given their…