In many scientific fields, advances in data collection and numerical simulation have resulted in large amounts of data for processing; however, relevant and efficient computational tools appropriate to analyze the data for further prediction and decision-making are still in their infancy. To tackle these challenges, the scientific research community has developed and used probabilistic tools in at least two different ways: first, stochastic methods to model and quantify these uncertainties in applications where there is underlying uncertainty; second, in applications that may be inherently deterministic but randomness is used as an algorithmic tool to drastically reduce computational costs while retaining the high accuracy of classic approaches.
Stochastic and randomized algorithms have already made a tremendous impact in areas such as numerical linear algebra (where matrix sketching and randomized approaches are used for efficient matrix approximations), Bayesian inverse problems... (more)