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Bifurcations can cause dynamical systems with slowly varying parameters to transition to far-away attractors. The terms ``critical transition'' or ``tipping point'' have been used to describe this situation. Critical transitions have been…

Climate science studies the structure and dynamics of Earth's climate system and seeks to understand how climate changes over time, where the data is usually stored in the format of time series, recording the climate features, geolocation,…

We propose novel methods for change-point testing for nonparametric estimators of expected shortfall and related risk measures in weakly dependent time series. We can detect general multiple structural changes in the tails of marginal…

Change-point detection studies the problem of detecting the changes in the underlying distribution of the data stream as soon as possible after the change happens. Modern large-scale, high-dimensional, and complex streaming data call for…

Hydroclimatic time series analysis focuses on a few feature types (e.g., autocorrelations, trends, extremes), which describe a small portion of the entire information content of the observations. Aiming to exploit a larger part of the…

There is a perception that climate science can only be approached with complex computer simulations. But working climate scientists often use simple models to understand their simulations and make order-of-magnitude estimates. This article…

Time series forecasting has always been a thought-provoking topic in the field of machine learning. Machine learning scientists define a time series as a set of observations recorded over consistent time steps. And, time series forecasting…

The cost of the impacts of climate change have already proven to be larger than previously believed. Understanding the costs and benefits of adapting to the changing climate is necessary to make targeted and appropriate investment…

The continued digitization of societal processes translates into a proliferation of time series data that cover applications such as fraud detection, intrusion detection, and energy management, where anomaly detection is often essential to…

Any experiment with climate models relies on a potentially large set of spatio-temporal boundary conditions. These can represent both the initial state of the system and/or forcings driving the model output throughout the experiment. Whilst…

Changepoints are a very common feature of Big Data that arrive in the form of a data stream. In this paper, we study high-dimensional time series in which, at certain time points, the mean structure changes in a sparse subset of the…

Climate change is the long-term shift in global weather patterns, largely caused by anthropogenic activity of greenhouse gas emissions. Global climate temperatures have unmistakably risen and naturally occurring climate variability alone…

Roy and Bhattacharya (2020) provided Bayesian characterization of infinite series, and their most important application, namely, to the Dirichlet series characterizing the (in)famous Riemann Hypothesis, revealed insights that are not in…

We study the problem of coincidence detection in time series data, where we aim to determine whether the appearance of simultaneous or near-simultaneous events in two time series is indicative of some shared underlying signal or…

The Earth's climate has experienced numerous critical transitions during its history, which have often been accompanied by massive and rapid changes in the biosphere. Such transitions are evidenced in various proxy records covering…

We consider the problem of locating a jump discontinuity (change-point) in a smooth parametric regression model with a bounded covariate. It is assumed that one can sample the covariate at different values and measure the corresponding…

Generative models of complex systems often require post-hoc parameter adjustments to produce useful outputs. For example, energy-based models for protein design are sampled at an artificially low ''temperature'' to generate novel,…

With advances in optical sensor technology, heterogeneous camera systems are increasingly used for high-resolution (HR) video acquisition and analysis. However, motion transfer across multiple cameras poses challenges. To address this, we…

Current research in time-series anomaly detection is using definitions that miss critical aspects of how anomaly detection is commonly used in practice. We list several areas that are of practical relevance and that we believe are either…

Climate sensitivity is defined as the change in global mean equilibrium temperature after a doubling of atmospheric CO2 concentration and provides a simple measure of global warming. An early estimate of climate sensitivity, 1.5-4.5{\deg}C,…