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Over the last few decades, climate scientists have devoted much effort to the development of large numerical models of the atmosphere and the ocean. While there is no question that such models provide important and useful information on…
Fine-grained time series data are crucial for accurate and timely online change detection. While both collective anomalies and change points can coexist in such data, their joint online detection has received limited attention. In this…
A high resolution (0.05 m) water isotopic record ($\delta^{18}\mathrm{O}$) is available from the NorthGRIP ice core. In this study we look into the water isotope diffusion history as estimated by the spectral characteristics of the…
Plasma diagnostics often employ computerized tomography to estimate emissivity profiles from a finite, and often limited, number of line-integrated measurements. Decades of algorithmic refinement have brought considerable improvements, and…
Climate change is a reality of today. Paleoclimatic proxies and climate predictions based on coupled atmosphere-ocean general circulation models provide us with temperature data. Using Detrended Fluctuation Analysis, we are investigating…
We present a novel Bayesian approach to analysing multiple time-series with the aim of detecting abnormal regions. These are regions where the properties of the data change from some normal or baseline behaviour. We allow for the…
Climate changepoint (homogenization) methods abound today, with a myriad of techniques existing in both the climate and statistics literature. Unfortunately, the appropriate changepoint technique to use remains unclear to many. Further…
In audio signal processing, probabilistic time-frequency models have many benefits over their non-probabilistic counterparts. They adapt to the incoming signal, quantify uncertainty, and measure correlation between the signal's amplitude…
Given two sets of functional data having a common underlying mean function but different degrees of distortion in time measurements, we provide a method of estimating the time transformation necessary to align (or `register') them. We prove…
The denoising diffusion probabilistic model has become a mainstream generative model, achieving significant success in various computer vision tasks. Recently, there has been initial exploration of applying diffusion models to time series…
We encounter time series data in many domains such as finance, physics, business, and weather. One of the main tasks of time series analysis, one that helps to take informed decisions under uncertainty, is forecasting. Time series are often…
Sequentially obtained dataset usually exhibits different behavior at different data resolutions/scales. Instead of inferring from data at each scale individually, it is often more informative to interpret the data as an ensemble of time…
We perform Bayesian inference on historical and late Holocene (last 2000 years) rates of sea-level change. The input data to our model are tide-gauge measurements and proxy reconstructions from cores of coastal sediment. These data are…
Tipping points (TPs) in the Earth system have been studied with growing interest and concern in recent years due to the potential risk of anthropogenic forcing causing abrupt, and possibly irreversible, climate transitions. Paleoclimate…
The paper discusses the reconstruction of potentials for quantum systems at finite temperatures from observational data. A nonparametric approach is developed, based on the framework of Bayesian statistics, to solve such inverse problems.…
Context: Several approaches to estimate frequency, phase and amplitude errors in time series analyses were reported in the literature, but they are either time consuming to compute, grossly overestimating the error, or are based on…
Using simulations or experiments performed at some set of temperatures to learn about the physics or chemistry at some other arbitrary temperature is a problem of immense practical and theoretical relevance. Here we develop a framework…
We introduce a method for reconstructing macroscopic models of one-dimensional stochastic processes with long-range correlations from sparsely sampled time series by combining fractional calculus and discrete-time Langevin equations. The…
A specific implementation of Bayesian model averaging has recently been suggested as a method for the calibration of ensemble temperature forecasts. We point out the similarities between this new approach and an earlier method known as…
Extracting meaning from uncertain, noisy data is a fundamental problem across time series analysis, pattern recognition, and language modeling. This survey presents a unified mathematical framework that connects classical estimation theory,…