Search arXivSearch

arXiv · 2201.01476

RobustCalibration: Robust Calibration of Computer Models in R

Abstract

Two fundamental research tasks in science and engineering are forward predictions and data inversion. This article introduces a recent R package RobustCalibration for Bayesian data inversion and model calibration by experiments and field observations. Mathematical models for forward predictions are often written in computer code, and they can be computationally expensive slow to run. To overcome the computational bottleneck from the simulator, we implemented a statistical emulator from the RobustGaSP package for emulating both scalar-valued or vector-valued computer model outputs. Both posterior sampling and maximum likelihood approach are implemented in the RobustCalibration package for parameter estimation. For imperfect computer models, we implement Gaussian stochastic process and the scaled Gaussian stochastic process for modeling the discrepancy function between the reality and mathematical model. This package is applicable to various types of field observations, such as repeated experiments and multiple sources of measurements. We discuss numerical examples of calibrating mathematical models that have closed-form expressions, and differential equations solved by numerical methods.

Explore related subjects

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Mengyang Gu. 2024-02-19. RobustCalibration: Robust Calibration of Computer Models in R. https://arxiv.org/abs/2201.01476

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

Delayed Acceptance Slice Sampling

Slice sampling is a well-established Markov chain Monte Carlo method for approximate sampling of target distributions which are only known up to a normalizing constant. The method is based on choosing a new state on a slice, i.e., a superlevel set of the given unnormalized target density (with respect to a reference measure). However, slice sampling algorithms usually require per step multiple evaluations of the target density, and thus can become computationally expensive. This is particularly the case for Bayesian inference with costly likelihoods. In this paper, we exploit deterministic approximations of the target density, which are relatively cheap to evaluate, and propose delayed acceptance versions of several common (hybrid) slice samplers. We show ergodicity of the resulting slice sampling methods, discuss the superiority of delayed acceptance (ideal) slice sampling over delayed acceptance Metropolis-Hastings algorithms, and illustrate the benefits of our novel approach in terms of improved computational efficiency in numerical experiments.

stat.CO

Repulsive normalizing flow mixtures for adaptive importance sampling: reliability analysis of complex systems

Accurate rare-event estimation can be computationally expensive. Classical adaptive importance sampling (IS) schemes often rely on restrictive proposal families and can struggle under multiple failure modes. We propose FAMIS, a flow-based multiple importance sampling (MIS) framework that learns a nonuniform mixture of normalizing flow proposals for rare event estimation. The method does not require presampled failure data or prior knowledge of the number, location, or geometry of the failure modes. Instead, it adaptively learns the mixture through sequential evaluations of the limit state function. To guide training toward the failure domain, FAMIS uses a smooth rare-event surrogate and a tempered target sequence. A defensive exploration mixture improves early-stage coverage, a Rao Blackwellized update adapts the mixture weights, and a Jensen-Shannon repulsion term promotes separation and diversity among the base components. The final failure probability is computed with a deterministic-mixture MIS estimator. Numerical experiments demonstrate that FAMIS accurately approximates quasi-optimal IS densities with fewer training samples and model evaluations, providing stable variance reduction across complex reliability problems.

stat.CO

Scentree: a framework for generating scenario trees for multistage stochastic programming

We present scentree, an open-source Python package for constructing a scenario fan and a scenario tree for multistage stochastic programming from historical data. It combines machine learning and multivariate time series models to obtain a scenario fan that captures inter-stage dependencies in the stochastic processes. This scenario fan is subsequently transformed into a scenario tree suitable for multistage stochastic optimization, providing a flexible and extensible framework for uncertainty modeling. A key contribution is the automation of the complete workflow, including model selection, parameter estimation, scenario fan generation, and scenario tree construction. Scentree does not rely on assumptions about the underlying data distribution, reducing the statistical expertise required to produce a scenario tree. Furthermore, it is agnostic to the specific multistage stochastic problem to be solved.

stat.CO