Related papers: A Tutorial on Bayesian Data Assimilation
This introduction to Bayesian statistics presents the main concepts as well as the principal reasons advocated in favour of a Bayesian modelling. We cover the various approaches to prior determination as well as the basis asymptotic…
This paper is a step-by-step tutorial for fitting a mixture distribution to data. It merely assumes the reader has the background of calculus and linear algebra. Other required background is briefly reviewed before explaining the main…
We present a Bayesian data fusion method to approximate a posterior distribution from an ensemble of particle estimates that only have access to subsets of the data. Our approach relies on approximate probabilistic inference of model…
Machine learning algorithms frequently require careful tuning of model hyperparameters, regularization terms, and optimization parameters. Unfortunately, this tuning is often a "black art" that requires expert experience, unwritten rules of…
Global data association is an essential prerequisite for robot operation in environments seen at different times or by different robots. Repetitive or symmetric data creates significant challenges for existing methods, which typically rely…
Physics increasingly uses Bayesian techniques for systematic data analysis and model-to-data comparison. This paper describes how these methods can be implemented to answer questions of relevance to teaching laboratories. It demonstrates…
In this paper the problem of learning appropriate bias for an environment of related tasks is examined from a Bayesian perspective. The environment of related tasks is shown to be naturally modelled by the concept of an {\em objective}…
Machines, not humans, are the world's dominant knowledge accumulators but humans remain the dominant decision makers. Interpreting and disseminating the knowledge accumulated by machines requires expertise, time, and is prone to failure.…
AI and data-driven models have large potential for data assimilation applications by creating fast and accurate forecasts. Their tendency to produce spurious inaccurate, nonphysical results -- hallucination -- however, raises a serious…
The Bayesian approach to data analysis provides a powerful way to handle uncertainty in all observations, model parameters, and model structure using probability theory. Probabilistic programming languages make it easier to specify and fit…
Bayesian quadrature is a probabilistic, model-based approach to numerical integration, the estimation of intractable integrals, or expectations. Although Bayesian quadrature was popularised already in the 1980s, no systematic and…
We propose practical extensions to Bayesian optimization for solving dynamic problems. We model dynamic objective functions using spatiotemporal Gaussian process priors which capture all the instances of the functions over time. Our…
Data assimilation combines information from physical observations and numerical simulation results to obtain better estimates of the state and parameters of a physical system. A wide class of physical systems of interest have solutions that…
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…
Data assimilation (DA) is a fundamental computational technique that integrates numerical simulation models and observation data on the basis of Bayesian statistics. Originally developed for meteorology, especially weather forecasting, DA…
This paper describes methods for comparative evaluation of the interpretability of models of high dimensional time series data inferred by unsupervised machine learning algorithms. The time series data used in this investigation were logs…
A general challenge in statistics is prediction in the presence of multiple candidate models or learning algorithms. Model aggregation tries to combine all predictive distributions from individual models, which is more stable and flexible…
A wide range of machine learning algorithms iteratively add data to the training sample. Examples include semi-supervised learning, active learning, multi-armed bandits, and Bayesian optimization. We embed this kind of data addition into…
Bayesian networks are a versatile and powerful tool to model complex phenomena and the interplay of their components in a probabilistically principled way. Moving beyond the comparatively simple case of completely observed, static data,…
Optimal design facilitates intelligent data collection. In this paper, we introduce a fully Bayesian design approach for spatial processes with complex covariance structures, like those typically exhibited in natural ecosystems. Coordinate…