数据分析、统计与概率
The discovery of novel experimental techniques often lags behind contemporary theoretical understanding. In particular, it can be difficult to establish appropriate measurement protocols without analytic descriptions of the underlying…
We introduce an RG-inspired coarse-graining for extracting the collective features of data. The key to successful coarse-graining lies in finding appropriate pairs of data sets. We coarse-grain the two closest data in a regular real-space…
$\mathrm{\gamma}$-ray spectroscopy is a quantitative, non-destructive technique that may be utilized for the identification and quantitative isotopic estimation of radionuclides. Traditional methods of isotopic determination have various…
The goal of this paper is to introduce a novel likelihood-based inferential framework for axion haloscopes which is valid under the commonly applied "rescanning" protocol. The proposed method enjoys short data acquisition times and a simple…
A fundamental problem in analysis of complex systems is getting a reliable estimate of entropy of their probability distributions over the state space. This is difficult because unsampled states can contribute substantially to the entropy,…
After collecting data from observations or experiments, the next step is to build an appropriate mathematical or stochastic model to describe the data so that further studies can be done with the help of the models. In this article, the…
We propose a method to account for model error due to unresolved scales in the context of the ensemble transform Kalman filter (ETKF). The approach extends to this class of algorithms the deterministic model error formulation recently…
Different variants of MFDFA technique are applied in order to investigate various (artificial and real-world) time series. Our analysis shows that the calculated singularity spectra are very sensitive to the order of the detrending…
The abundance of observed data in recent years has increased the number of statistical augmentations to complex models across science and engineering. By augmentation we mean coherent statistical methods that incorporate measurements upon…
Principal Geodesic Analysis (PGA) is applied to a climate time series. First, we transform each multidimensional sequence into the path signature. Since the signature lives in a curved space, usual principal component analysis (PCA) is not…
Prediction of the state evolution of complex high-dimensional nonlinear systems is challenging due to the nonlinear sensitivity of the evolution to small inaccuracies in the model. Data Assimilation (DA) techniques improve state estimates…
We present a software tool -- extended Dynamic Causal Modelling for Phase Coupling (eDCM PC) -- that is able to estimate effective connectivity between any kind of oscillating systems, e.g. distant brain regions, using the phase information…
Power spectral density scaling with frequency $f$ as $1/f^\beta$ and $\beta \approx 1$ is widely found in natural and socio-economic systems. Consequently, it has been suggested that such self-similar spectra reflect the universal dynamics…
The paper addresses general aspects of experimental data analysis, dealing with the separation of ``signal vs. background''. It consists of two parts. Part I is a tutorial on statistical event classification, Bayesian inference, and test…
Noise-induced phase transitions are common in various complex systems, from physics to biology. In this article, we investigate the emergence of crucial events in noise-induced phase transition processes and their potential significance for…
Scientists have developed hundreds of techniques to measure the interactions between pairs of processes in complex systems. But these computational methods, from correlation coefficients to causal inference, rely on distinct quantitative…
Recently, there has been significant interest in applying machine learning (ML) techniques to X-ray scattering experiments, which proves to be a valuable tool for enhancing research that involves large or rapidly generated datasets. ML…
Non-stationarity affects the sensitivity of change detection in correlated systems described by sets of measurable variables. We study this by projecting onto different principal components. Non-stationarity is modeled as multiple normal…
The Doomsday argument and anthropic reasoning are two puzzling examples of probabilistic confirmation. In both cases, a lack of knowledge apparently yields surprising conclusions. Since they are formulated within a Bayesian framework, they…
The PandaX dark matter detection project searches for dark matter particles using the technology of dual phase xenon time projection chamber. The low expected rate of the signal events makes the control of backgrounds crucial for the…