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In data science, vector autoregression (VAR) models are popular in modeling multivariate time series in the environmental sciences and other applications. However, these models are computationally complex with the number of parameters…

Rigorous assessment of the uncertainty is crucial to the utility of numerical simulation of Turbulent flow. The Turbulent flows are often stationary and ergodic, after some initial transient time. Therefore, the time averaged of a quantity…

Value at Risk (VaR) and stress testing are two of the most widely used approaches in portfolio risk management to estimate potential market value losses under adverse market moves. VaR quantifies potential loss in value over a specified…

Irreversibility is commonly quantified by entropy production. An external observer can estimate it through measuring an observable that is antisymmetric under time-reversal like a current. We introduce a general framework that, inter alia,…

Computing free energy is a fundamental problem in statistical physics. Recently, two distinct methods have been developed and have demonstrated remarkable success: the tensor-network-based contraction method and the neural-network-based…

This paper concerns sequential computation of risk measures for financial data and asks how, given a risk measurement procedure, we can tell whether the answers it produces are `correct'. We draw the distinction between `external' and…

Expected Shortfall (ES), also known as superquantile or Conditional Value-at-Risk, has been recognized as an important measure in risk analysis and stochastic optimization, and is also finding applications beyond these areas. In finance, it…

Projections of storm surge return levels are a basic requirement for effective management of coastal risks. A common approach to estimate hazards posed by extreme sea levels is to use a statistical model, which may use a time series of a…

Wrong-Way Risk (WWR) is an important component in Funding Valuation Adjustment (FVA) modelling. Yet, the standard assumption is independence between market risks and the counterparty defaults and funding costs. This typical industrial…

High-speed boundary-layer transition is extremely sensitive to the free-stream disturbances which are often uncertain. This uncertainty compromises predictions of models and simulations. To enhance the fidelity of simulations, we directly…

The use of past experiences to accelerate temporal difference (TD) learning of value functions, or experience replay, is a key component in deep reinforcement learning. Prioritization or reweighting of important experiences has shown to…

Sensitivity analysis plays an important role in searching for constitutive parameters (e.g. permeability) subsurface flow simulations. The mathematics behind is to solve a dynamic constrained optimization problem. Traditional methods like…

Reliable value estimation serves as the cornerstone of reinforcement learning (RL) by evaluating long-term returns and guiding policy improvement, significantly influencing the convergence speed and final performance. Existing works improve…

Supervised dimension reduction for time series is challenging as there may be temporal dependence between the response $y$ and the predictors $\boldsymbol x$. Recently a time series version of sliced inverse regression, TSIR, was suggested,…

The vector autoregressive (VAR) model has been used to describe the dependence within and across multiple time series. This is a model for stationary time series which can be extended to allow the presence of a deterministic trend in each…

The methods currently used to determine the scaling exponent of a complex dynamic process described by a time series are based on the numerical evaluation of variance. This means that all of them can be safely applied only to the case where…

We study the temporal dissipation of variance and relative entropy for ergodic Markov Chains in continuous time, and compute explicitly the corresponding dissipation rates. These are identified, as is well known, in the case of the variance…

This paper aims to solve a safe reinforcement learning (RL) problem with risk measure-based constraints. As risk measures, such as conditional value at risk (CVaR), focus on the tail distribution of cost signals, constraining risk measures…

Time series of counts occurring in various applications are often overdispersed, meaning their variance is much larger than the mean. This paper proposes a novel variable selection approach for processing such data. Our approach consists in…

Time series and extreme value analyses are two statistical approaches usually applied to study hydrological data. Classical techniques, such as ARIMA models (in the case of mean flow predictions), and parametric generalised extreme value…