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This book chapter introduces regression approaches and regression adjustment for Approximate Bayesian Computation (ABC). Regression adjustment adjusts parameter values after rejection sampling in order to account for the imperfect match…

Methodology · Statistics 2017-07-06 Michael GB Blum

Using a very cheap Data Assimilation (DA) method, I show an alternative approach to classical DA for numerical climate models which produce a large amount of "big data". The problematic features of state-of-the-art high resolution Regional…

Applications · Statistics 2016-10-12 Bijan Fallah

Approximate Bayesian computation (ABC) is a simulation-based likelihood-free method applicable to both model selection and parameter estimation. ABC parameter estimation requires the ability to forward simulate datasets from a candidate…

Methodology · Statistics 2020-11-10 Louis Raynal , Sixing Chen , Antonietta Mira , Jukka-Pekka Onnela

Approximate Bayesian computation (ABC) is a popular likelihood-free inference method for models with intractable likelihood functions. As ABC methods usually rely on comparing summary statistics of observed and simulated data, the choice of…

Machine Learning · Statistics 2022-06-22 Ayush Bharti , Louis Filstroff , Samuel Kaski

The reconstruction from observations of high-dimensional chaotic dynamics such as geophysical flows is hampered by (i) the partial and noisy observations that can realistically be obtained, (ii) the need to learn from long time series of…

Machine Learning · Statistics 2020-03-31 Marc Bocquet , Julien Brajard , Alberto Carrassi , Laurent Bertino

Data assimilation (DA) integrates observations with model forecasts to produce optimized atmospheric states, whose physical consistency is critical for stable weather forecasting and reliable climate research. Traditional Bayesian DA…

Atmospheric and Oceanic Physics · Physics 2026-03-05 Hang Fan , Lei Bai , Ben Fei , Yi Xiao , Kun Chen , Yubao Liu , Yongquan Qu , Fenghua Ling , Pierre Gentine

Mislabeled, duplicated, or biased data in real-world scenarios can lead to prolonged training and even hinder model convergence. Traditional solutions prioritizing easy or hard samples lack the flexibility to handle such a variety…

Machine Learning · Computer Science 2023-11-08 Zhijie Deng , Peng Cui , Jun Zhu

Bayesian optimisation for real-world problems is often performed interactively with human experts, and integrating their domain knowledge is key to accelerate the optimisation process. We consider a setup where experts provide advice on the…

Machine Learning · Computer Science 2024-10-15 Wenjie Xu , Masaki Adachi , Colin N. Jones , Michael A. Osborne

Statistical analysis of max-stable processes used to model spatial extremes has been limited by the difficulty in calculating the joint likelihood function. This precludes all standard likelihood-based approaches, including Bayesian…

Computation · Statistics 2011-12-14 Robert J. Erhardt , Richard L. Smith

We consider a human-assisted autonomy sensor fusion for dynamic target localization in a Bayesian framework. Autonomous sensor-based tracking systems can suffer from observability and target detection failure. Humans possess valuable…

Robotics · Computer Science 2024-10-08 Min-Won Seo , Solmaz S. Kia

Optimization constrained by high-fidelity computational models has potential for transformative impact. However, such optimization is frequently unattainable in practice due to the complexity and computational intensity of the model. An…

Numerical Analysis · Mathematics 2024-06-04 Joseph Hart , Bart van Bloemen Waanders

Sensitivity forecasts inform the design of experiments and the direction of theoretical efforts. To arrive at representative results, Bayesian forecasts should marginalize their conclusions over uncertain parameters and noise realizations…

Instrumentation and Methods for Astrophysics · Physics 2024-05-24 T. Gessey-Jones , W. J. Handley

Comparing competing mathematical models of complex natural processes is a shared goal among many branches of science. The Bayesian probabilistic framework offers a principled way to perform model comparison and extract useful metrics for…

We research relations between optimal transport theory (OTT) and approximate Bayesian computation (ABC) possibly connected to relevant metrics defined on probability measures. Those of ABC are computational methods based on Bayesian…

Statistics Theory · Mathematics 2021-05-06 Marco Tarsia , Antonietta Mira , Daniele Cassani

Data assimilation algorithms integrate prior information from numerical model simulations with observed data. Ensemble-based filters, regarded as state-of-the-art, are widely employed for large-scale estimation tasks in disciplines such as…

Numerical Analysis · Mathematics 2024-05-24 Iris Rammelmüller , Gottfried Hastermann , Jana de Wiljes

Computational models in fields such as computational neuroscience are often evaluated via stochastic simulation or numerical approximation. Fitting these models implies a difficult optimization problem over complex, possibly noisy parameter…

Machine Learning · Statistics 2017-11-03 Luigi Acerbi , Wei Ji Ma

Scientific knowledge expands by observing the world, hypothesizing some theories about it, and testing them against collected data. When those theories take the form of statistical models, statistical analyses are involved in the process of…

Machine Learning · Statistics 2026-03-11 Arnaud Delaunoy

The nudging data assimilation algorithm is a powerful tool used to forecast phenomena of interest given incomplete and noisy observations. Machine learning is becoming increasingly popular in data assimilation given its ease of computation…

Numerical Analysis · Mathematics 2021-11-24 Harbir Antil , Rainald Löhner , Randy Price

This paper presents a novel centralized, variational data assimilation approach for calibrating transient dynamic models in electrical power systems, focusing on load model parameters. With the increasing importance of inverter-based…

Optimization and Control · Mathematics 2023-11-15 Ahmed Attia , D. Adrian Maldonado , Emil Constantinescu , Mihai Anitescu

The goal of this paper is to explore the basic Approximate Bayesian Computation (ABC) algorithm via the lens of information theory. ABC is a widely used algorithm in cases where the likelihood of the data is hard to work with or…

Methodology · Statistics 2019-08-14 Konstantinos Spiliopoulos