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We investigate the predictability of extreme events in time series. The focus of this work is to understand under which circumstances large events are better predictable than smaller events.
Change points in time series are perceived as isolated singularities where two regular trends of a given signal do not match. The detection of such transitions is of fundamental interest for the understanding of the system's internal dynamics.
A wavelet-like model for distributions of objects in natural and man-made terrestrial environments is developed. The model is constructed in a self-similar fashion, with the sizes, amplitudes, and numbers of objects occurring at a constant ratios between parent and offspring objects.
ROOT is an object-oriented C++ framework conceived in the high-energy physics (HEP) community, designed for storing and analyzing petabytes of data in an efficient way. Any instance of a C++ class can be stored into a ROOT file in a machine-independent compressed binary format.
These three lectures provide an introduction to the main concepts of statistical data analysis useful for precision measurements and searches for new signals in High Energy Physics. The frequentist and Bayesian approaches to probability theory are introduced and, for both approaches, inference methods are presented.
These lectures introduce key concepts in probability and statistical inference at a level suitable for graduate students in particle physics. Our goal is to paint as vivid a picture as possible of the concepts covered.
Temporal correlations of time series or event sequences in natural and social phenomena have been characterized by power-law decaying autocorrelation functions with decaying exponent $\gamma$. Such temporal correlations can be understood in terms of power-law distributed interevent times with exponent $\alpha$, and/or...
When data do not conform to the hypothesis of a known sampling-variance, the fitting of a constant to the set of measured values is a long debated problem. Given the data, the fitting would require to find which measurand value is most probable.
A hierarchical approach to the construction of compound distributions for process-induced faults in IC manufacture is proposed. Within this framework, the negative binomial distribution and the compound binomial distribution are treated as level-1 models.
The Feynman-alpha method is a neutron noise technique that is used to estimate the prompt neutron period of fissile assemblies. The method and quantity are of widespread interest including in applications such as nuclear criticality safety, safeguards and nonproliferation, and stockpile stewardship; the prompt neutron...
Statistical distances quantifies the difference between two statistical constructs. In this article, we describe reference values for a distance between samples derived from the Kolmogorov-Smirnov statistic $D_{F,F'}$.
A physical law is represented by the probability distribution of a measured variable. The probability density is described by measured data using an estimator whose kernel is the instrument scattering function.
We make the comparative study of scaling range properties for detrended fluctuation analysis (DFA), detrended moving average analysis (DMA) and recently proposed new technique called modified detrended moving average analysis (MDMA). Basic properties of scaling ranges for these techniques are reviewed.
We present a conclusive answer to Bertrand's paradox, a long standing open issue in the basic physical interpretation of probability. The paradox deals with the existence of mutually inconsistent results when looking for the probability that a chord, drawn at random in a circle, is longer than the side of an inscr...
A code package, BlurRing, is developed as a method to allow for multi-dimensional likelihood visualisation. From the BlurRing visualisation additional information about the likelihood can be extracted.
This paper deals with an estimating of the Fractal Dimension of a hydrometeorology variables like an Air temperature or humidity at a different sites in a landscape (and will be further evaluated from the land use point of view). Three algorithms and methods of an estimation of the Fractal Dimension of a hydrometeorol...
We present a Bayesian approach for the Contamination Source Detection problem in Water Distribution Networks. Given an observation of contaminants in one or more nodes in the network, we try to give probable explanation for it assuming that contamination is a rare event.
Recent approaches to the problem of inferring a continuous probability distribution from a finite set of data have used a scalar field theory for the form of the prior probability distribution. This letter presents a more general form for the prior distribution that has a geometrical interpretation which is useful for...
Modern analysis of high energy physics (HEP) data needs advanced statistical tools to separate signal from background. A C++ package has been implemented to provide such tools for the HEP community.
We propose a method to estimate the probability of new physics discovery in future high energy physics experiments. Physics simulation gives both the average numbers $<N_b>$ of background and $<N_s>$ of signal events.
Practically, for all real measuring devices the result of a measurement is a convolution of an input signal with a hardware function of a unit {\phi}. We call a spline to be {\phi}-interpolating if the convolution of an input signal with a hardware function of a unit {\phi} coincides with the convolution of the spline...
The rapid development of machine learning (ML) methods has fundamentally affected numerous applications ranging from computer vision, biology, and medicine to accounting and text analytics. Until now, it was the availability of large and often labeled data sets that enabled significant breakthroughs.
The Bayesian approach has proved to be a coherent approach to handle ill posed Inverse problems. However, the Bayesian calculations need either an optimization or an integral calculation.
Modular structure is pervasive in many complex networks of interactions observed in natural, social and technological sciences. Its study sheds light on the relation between the structure and function of complex systems.
Power laws are theoretically interesting probability distributions that are also frequently used to describe empirical data. In recent years effective statistical methods for fitting power laws have been developed, but appropriate use of these techniques requires significant programming and statistical insight.
In the context of food quality control, ultrasonics provide proven methods which are able to replace manual controls. The latter are subject to the lack of objectivity of human judgement.
Fluctuating wind energy makes a stable grid operation challenging. Due to the direct contact with atmospheric turbulence, intermittent short-term variations in the wind speed are converted to power fluctuations that cause transient imbalances in the grid.
Evaluated nuclear data uncertainties are often perceived as unrealistic, most often because they are thought to be too small. The impact of this issue in applied nuclear science has been discussed widely in recent years.
Moving from a National Grid Testbed to a Production quality Grid service for the HEP applications requires an effective operations structure and organization, proper user and operations support, flexible and efficient management and monitoring tools. Moreover the middleware releases should be easily deployable using f...
In this paper, we present and analyse two Hopfield-like nonlinear networks, in continuous-time and discrete-time respectively. The proposed network is based on an autonomous linear system with a symmetric weight matrix, which is designed to be unstable, and a nonlinear function stabilizing the whole network thanks to ...
RooStatsCms is an object oriented statistical framework based on the RooFit technology. Its scope is to allow the modelling, statistical analysis and combination of multiple search channels for new phenomena in High Energy Physics.
We report the studies of emission from a novel random amplifying medium that we term a ``Levy Laser'' due to the non-Gaussian statistical nature of its emission over the ensemble of random realizations. It is observed that the amplification is dominated by certain improbable events that are ``larger than rare&...
The local heat transfer coefficient measurement with temperature oscillation induced by periodic thermal perturbation - usually via a Gaussian laser beam, was investigated for the impact of the spikiness (i.e., the standard deviation) elaborated in comparison with the analytical model for dimensional analysis. The sta...
The classical Maximum Entropy (ME) problem consists of determining a probability distribution function (pdf) from a finite set of expectations of known functions. The solution depends on $N+1$ Lagrange multipliers which are determined by solving the set of nonlinear equations formed by the $N$ data constraints and the...
A procedure based on a Mixture Density Model for correcting experimental data for distortions due to finite resolution and limited detector acceptance is presented. Addressing the case that the solution is known to be non-negative, in the approach presented here, the true distribution is estimated by a weighted sum of...
Non-symmetric rectangular correlation matrices occur in many problems in economics. We test the method of extracting statistically meaningful correlations between input and output variables of large dimensionality and build a toy model for artificially included correlations in large random time <a href="http://series....
The various algorithms used to extrapolate particle trajectories from measurements are often very time-consuming with computational complexities which are typically quadratic. In this article, we propose a new algorithm called GEM with a lower complexity and reasonable performance on linear tracks.
Wind energy is becoming a top contributor to the renewable energy mix, which raises potential reliability issues for the grid due to the fluctuating nature of its source. To achieve adequate reserve commitment and to promote market participation, it is necessary to provide models that can capture daily patterns in win...
This thesis describes an analysis developed for the MicroBooNE experiment to investigate an anomalous excess of electron-like events observed in the MiniBooNE detector. The hypothesis investigated here is that the MiniBooNE anomaly represents appearance of electron neutrinos.
We investigate the recently proposed label-propagation algorithm (LPA) for identifying network communities. We reformulate the LPA as an equivalent optimization problem, giving an objective function whose maxima correspond to community solutions.
Modulator testing involved complex biasing conditions, hardware connections and data analysis. Also, any optical signal distortion due to the grating coupler effect could potentially induce additional difficulty in setting the correct bias condition for an accurate measurement of the modulator performance.
Experimenters report an upper limit if the signal they are trying to detect is non-existent or below their experiment's sensitivity. Such experiments may be contaminated with a background too poorly understood to subtract.
Time series of string tension of a simple pendulum has not yet been a interesting motion information, even nowadays using a force tension sensor can be measured easily. A numerical procedure is presented how to obtain motion of pendulum bob from the string tension.
We have studied the effect of annealing temperature on the statistical properties of $WO_3$ surface using atomic force microscopy techniques (AFM). We have applied both level crossing and structure function methods.
WISDoM (Wishart Distributed Matrices) is a new framework for the quantification of deviation of symmetric positive-definite matrices associated to experimental samples, like covariance or correlation matrices, from expected ones governed by the Wishart distribution WISDoM can be applied to tasks of supervised learning,...
We present the modification of natural visibility graph (NVG) algorithm used for the mapping of the time series to the complex networks (graphs). We propose the parametric natural visibility graph (PNVG) algorithm.
By means of an inequality of the information and parametrization of family of distributions of the probabilities, supposing an effective estimation, introduction of the distributions containing time of the first achievement of a level as internal thermodynamic parameter ground.
The measurement of muon energy is critical for many analyses in large Cherenkov detectors, particularly those that involve separating extraterrestrial neutrinos from the atmospheric neutrino background. Muon energy has traditionally been determined by measuring the specific energy loss (dE/dx) along the muon's pat...
Any continuous curve in a higher dimensional space can be considered a trajectory that can be parameterized by a single variable, usually taken as time. It is well known that a continuous curve can have a fractional dimensionality, which can be estimated using already standard algorithms.
Many man-made and natural phenomena, including the intensity of earthquakes, population of cities and size of international wars, are believed to follow power-law distributions. The accurate identification of power-law patterns has significant consequences for correctly understanding and modeling complex systems.
Upcoming HEP experiments, e.g. at the HL-LHC, are expected to increase the volume of generated data by at least one order of magnitude. In order to retain the ability to analyze the influx of data, full exploitation of modern storage hardware and systems, such as low-latency high-bandwidth NVMe devices and distributed...
Linearity is an important and frequently sought property in electronics and instrumentation. Here, we report a method capable of, given a transfer function, identifying the respective most linear region of operation with a fixed width.
The formation of price in a financial market is modelled as a chain of Ising spin with three fundamental figures of trading. We investigate the time behaviour of the model, and we compare the results with the real EURO/USD change rate.
It is well known that projective measurement will not decrease the von Neumann entropy of a quantum state. In this paper, it is shown that projective measurement will not decrease the quantum Tsallis entropy of a quantum state, either.
Although widely used in practice, the behavior and accuracy of the popular module identification technique called modularity maximization is not well understood in practical contexts. Here, we present a broad characterization of its performance in such situations.
We propose an approach to explain fluctuations in time intervals of financial markets data from the view point of the Gini index. We show the explicit form of the Gini index for a Weibull distribution which is a good candidate to describe the first passage time of foreign exchange rate.
We describe a new method of 3D image reconstruction of neutron sources that emit correlated gammas (e.g. Cf-252, Am-Be). This category includes a vast majority of neutron sources important in nuclear threat search, safeguards and non-proliferation.
Understanding chemical mechanisms requires estimating dynamical statistics such as expected hitting times, reaction rates, and committors. Here, we present a general framework for calculating these dynamical quantities by approximating boundary value problems using dynamical operators with a Galerkin expansion.
The entropy density is an intuitive and powerful concept to study the complicated nonlinear processes derived from physical systems. We develop the minimum entropy density method (MEDM) to detect the structure scale of a given time series, which is defined as the scale in which the uncertainty is minimized, hence the ...
Williams and Beer (2010) proposed a nonnegative mutual information decomposition, based on the construction of information gain lattices, which allows separating the information that a set of variables contains about another into components interpretable as the unique information of one variable, or redundant and syner...
We discuss a Bayesian model selection approach to high dimensional data in the deep under sampling regime. The data is based on a representation of the possible discrete states $s$, as defined by the observer, and it consists of $M$ observations of the state.
Unfolding is a well-established tool in particle physics. However, a naive application of the standard regularization techniques to unfold the momentum spectrum of protons ejected in the process of negative muon nuclear capture led to a result exhibiting unphysical artifacts.
Previous studies demonstrated empirically that human mobility exhibits Levy flight behaviour. However, our knowledge of the mechanisms governing this Levy flight behaviour remains limited.
Serial electron diffraction (SerialED) is an emerging technique, which applies the snapshot data-collection mode of serial X-ray crystallography to three-dimensional electron diffraction (3D ED), forgoing the conventional rotation method. Similarly to serial X-ray crystallography, this approach leads to almost complet...
We correct claims about lower bounds on mutual information (MI) between real-valued random variables made in A. Kraskov {\it et al. }, Phys.
We present a method for the nonparametric estimation of the drift function of certain types of stochastic differential equations from the empirical density. It is based on a variational formulation of the Fokker-Planck equation.
The second edition of ISO 19229 expands the guidance in its predecessor in two ways. Firstly, it provides more support and examples describing possible experimental approaches for purity analysis.
We study the effect on the distribution of return periods of rare events of the presence in a time series of finite-term correlations with non-exponential decay. Precisely, we analyze the auto-correlation function and the statistics of the return intervals of extreme values of the resistance fluctuations displayed by ...
The Wasserstein metric is introduced as a probabilistic method to enable quantitative evaluations of LES combustion models. The Wasserstein metric can directly be evaluated from scatter data or statistical results using probabilistic reconstruction against experimental data.
It is shown that for any ensemble, whether classical or quantum, continuous or discrete, there is only one measure of the "volume" of the ensemble that is compatible with several basic geometric postulates. This volume measure is thus a preferred and universal choice for characterising the inherent spread, dis...
In this thesis we investigate high throughput computational methods for processing large quantities of data collected from synchrotrons and their application to spectral analysis of powder diffraction data. We also present the main product of this PhD programme, specifically a software called 'EasyDD' develope...
It has recently been shown that an unbinned distance-based statistic, the energy, can be used to construct an extremely powerful nonparametric multivariate two sample goodness-of-fit test. An extension to this method that makes it possible to perform nonparametric regression using multiple multivariate data sets is pr...
The records statistics in stationary and non-stationary fractal time series is studied extensively. By calculating various concepts in record dynamics, we find some interesting results.
Temporal networks are commonly used to represent systems where connections between elements are active only for restricted periods of time, such as networks of telecommunication, neural signal processing, biochemical reactions and human social interactions. We introduce the framework of temporal motifs to study the me...
This study outlines a numerical methodology aimed at rectifying the neutron scattering cross-sections of fundamental elements across a range of low neutron energies typically employed in general neutron scattering experiments. By using the experimental power law relationship governing the cross-section's dependenc...
The subjects of the paper are the likelihood method (LM) and the expected Fisher information (FI) considered from the point od view of the construction of the physical models which originate in the statistical description of phenomena. The master equation case and structural information principle are derived.
The Visual Physics Analysis (VISPA) project defines a toolbox for accessing software via the web. It is based on latest web technologies and provides a powerful extension mechanism that enables to interface a wide range of applications.
A fractal bears a complex structure that is reflected in a scaling hierarchy, indicating that there are far more small things than large ones. This scaling hierarchy can be effectively derived using head/tail breaks - a clustering and visualization tool for data with a heavy-tailed distribution - and quantified by an ...
Power grids are prone to failure. Time series of reliability measures such as total power loss or energy not supplied can give significant account of the underlying dynamical behavior of these systems, specially when the resulting probability distributions present remarkable features such as an algebraic tail, for exa...
We present a technique for spatiotemporal data analysis called nonlinear Laplacian spectral analysis (NLSA), which generalizes singular spectrum analysis (SSA) to take into account the nonlinear manifold structure of complex data sets. The key principle underlying NLSA is that the functions used to represent temporal ...
We present a top-down approach to calorimeter clustering. An algorithm based on minimal spanning tree theory is described briefly.
Oscillator fluctuations are described as the phase or frequency noise spectrum, or in terms of a wavelet variance as a function of the measurement time. The spectrum is generally approximated by the `power law,' i.e., a Laurent polynomial with integer exponents of the frequency.
With modern data acquisition devices that work fast and very precise, scientists often face the task of dealing with huge amounts of data. These need to be rapidly processed and stored onto a hard disk.
Recent statistical evaluations for High-Energy Physics measurements, in particular those at the Large Hadron Collider, require careful evaluation of many sources of systematic uncertainties at the same time. While the fundamental aspects of the statistical treatment are now consolidated, both using a frequentist or a ...
The extraction of a physical law y=yo(x) from joint experimental data about x and y is treated. The joint, the marginal and the conditional probability density functions (PDF) are expressed by given data over an estimator whose kernel is the instrument scattering function.
The continuous wavelet transform may be enhanced by deconvolution with the wavelet response function. After correcting for the cone-of-influence, the power spectral density of the solar magnetic record as given by the derectified yearly sunspot number is calculated, revealing a spectrum of odd harmonics of the fundame...
I compare and discuss critically several measures of statistical significance in common use in astrophysics and in high energy physics. I also exhibit some relationships among them.
The paper explores the feasibility of using machine learning techniques, in particular neural networks, for classification of the experimental data from the joint $^\text{nat}$C(n,p) and $^\text{nat}$C(n,d) reaction cross section measurement from the neutron time of flight facility n_TOF at CERN. Each relevant $\Delta...
At the center of the ZEUS detector situated on the collider HERA at DESY in Hamburg, a Micro Vertex Detector has been installed in 2000/01. Situated close to the beam line, this subdetector is designed to measure precisely the tracks near the interaction point (the vertex).
We study the susceptible-infected model with power-law waiting time distributions $P(\tau)\sim \tau^{-\alpha}$, as a model of spreading dynamics under heterogeneous human activity patterns. We found that the average number of new infections $n(t)$ at time $t$ decays as a power law in the long time limit, $n(t) \sim t^...
The Hilbert-Huang Transform is a novel, adaptive approach to time series analysis that does not make assumptions about the data form. Its adaptive, local character allows the decomposition of non-stationary signals with hightime-frequency resolution but also renders it susceptible to degradation from noise.
In this work, we explore the use of an iterative Bayesian Monte Carlo (IBM) procedure for nuclear data evaluation within a Talys Evaluated Nuclear data Library (TENDL) framework. In order to identify the model and parameter combinations that reproduce selected experimental data, different physical models implemented w...
Gravitational-wave searches for signals from inspiralling compact binaries have relied on matched filtering banks of waveforms (called template banks) to try to extract the signal waveforms from the detector data. These template banks have been constructed using four main considerations, the region of parameter space ...
The problem of optimal data collection to efficiently learn the model parameters of a graphite nitridation experiment is studied in the context of Bayesian analysis using both synthetic and real experimental data. The paper emphasizes that the optimal design can be obtained as a result of an information theoretic sens...
We present a nonparametric method for estimating the value and several derivatives of an unknown, sufficiently smooth real-valued function of real-valued arguments from a finite sample of points, where both the function arguments and the corresponding values are known only up to measurement errors having some assumed d...
This paper discusses some problems possibly arising when approximating via Monte-Carlo simulations the distributions of goodness-of-fit test statistics based on the empirical distribution function. We argue that failing to re-estimate unknown parameters on each simulated Monte-Carlo sample -- and thus avoiding to empl...
The variances of matched and sidelobe free mismatched filter estimators are given for arbitrary coherent targets in the case of aperiodic transmission. It is shown that mismatched filtering is often better than matched filtering in terms of estimation accuracy.
In this note we present a flexible approach to perform the propagation of track parameters and their derivatives in an inhomogeneous magnetic field, keeping the computational effort small. We discuss also a Kalman filter implementation using this optimized computation of the derivatives.
The usual interpretation of noise is represented by a sum of many independent two-level elementary random signals with a distribution of relaxation times. In this paper it is demonstrated that also the superposition of many similar single-sided two-level signals, with the same relaxation time, produces noise.
The paper addresses general aspects of experimental data analysis, dealing with the separation of ``signal vs. background''. It consists of two parts.

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