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Suppose a process yields independent observations whose distributions belong to a family parameterized by \theta\in\Theta. When the process is in control, the observations are i.i.d. with a known parameter value \theta_0. When the process…
Time series forecasting plays an increasingly important role in modern business decisions. In today's data-rich environment, people often aim to choose the optimal forecasting model for their data. However, identifying the optimal model…
Steady-state models which have been learned from historical operational data may be unfit for model-based optimization unless correlations in the training data which are introduced by control are accounted for. Using recent results from…
In this paper, we present a comprehensive analysis of extreme temperature patterns using emerging statistical machine learning techniques. Our research focuses on exploring and comparing the effectiveness of various statistical models for…
We present statistical methods for big data arising from online analytical processing, where large amounts of data arrive in streams and require fast analysis without storage/access to the historical data. In particular, we develop…
Inverse problems use physical measurements along with a computational model to estimate the parameters or state of a system of interest. Errors in measurements and uncertainties in the computational model lead to inaccurate estimates. This…
Improving the representation of precipitation in Earth system models (ESMs) is critical for assessing the impacts of climate change and especially of extreme events like floods and droughts. In existing ESMs, precipitation is not resolved…
The class of autoregressive (AR) processes is extensively used to model temporal dependence in observed time series. Such models are easily available and routinely fitted using freely available statistical software like R. A potential…
Diffusion models have emerged as powerful generative tools with applications in computer vision and scientific machine learning (SciML), where they have been used to solve large-scale probabilistic inverse problems. Traditionally, these…
Operations research (OR) approaches have been increasingly applied to model the resilience of a system to surprise events. In order to model a surprise event, one must have an understanding of its characteristics, which then become…
We propose a novel method for modeling data by using structural models based on economic theory as regularizers for statistical models. We show that even if a structural model is misspecified, as long as it is informative about the…
Stochastic processes offer a flexible mathematical formalism to model and reason about systems. Most analysis tools, however, start from the premises that models are fully specified, so that any parameters controlling the system's dynamics…
Climate models exhibit an approximately invariant surface warming pattern in typical end-of-century projections. This observation has been used extensively in climate impact assessments for fast calculations of local temperature anomalies,…
Post-processing typically takes the outputs of a Numerical Weather Prediction (NWP) model and applies linear statistical techniques to produce improve localized forecasts, by including additional observations, or determining systematic…
Seasonal climate variations affect electricity demand, which in turn affects month-to-month electricity planning and operations. Electricity system planning at the monthly timescale can be improved by adapting climate forecasts to estimate…
The ultimate goal of regression analysis is to obtain information about the conditional distribution of a response given a set of explanatory variables. This goal is, however, seldom achieved because most established regression models only…
We investigate model assessment and selection in a changing environment, by synthesizing datasets from both the current time period and historical epochs. To tackle unknown and potentially arbitrary temporal distribution shift, we develop…
We consider the scenario where the parameters of a probabilistic model are expected to vary over time. We construct a novel prior distribution that promotes sparsity and adapts the strength of correlation between parameters at successive…
Representing and quantifying uncertainty in physical parameterisations is a central challenge in weather and climate modelling, and approaches are often developed separately for different timescales. Here, we introduce a unified framework…
Climate change affects occurrences of floods and droughts worldwide. However, predicting climate impacts over individual watersheds is difficult, primarily because accurate hydrological forecasts require models that are calibrated to past…