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We propose theoretical methods to infer coupling strength and noise intensity simultaneously through an observation of spike timing in two well-synchronized noisy oscillators. A phase oscillator model is applied to derive formulae relating…
Various hand-crafted features representations of bio-signals rely primarily on the amplitude or power of the signal in specific frequency bands. The phase component is often discarded as it is more sample specific, and thus more sensitive…
We study the time-fractional Ivancevic option pricing model and the coupled nonlinear volatility and option price model via both modulational instability (MI) analysis and direct simulations. For the coupled volatility and option pricing…
The inference of an underlying network topology from local observations of a complex system composed of interacting units is usually attempted by using statistical similarity measures, such as Cross-Correlation (CC) and Mutual Information…
Symbolic Data Analysis works with variables for which each unit or class of units takes a finite set of values/categories, an interval or a distribution (an histogram, for instance). When to each observation corresponds an empirical…
In this survey, we present and compare different approaches to estimate Mutual Information (MI) from data to analyse general dependencies between variables of interest in a system. We demonstrate the performance difference of MI versus…
Utilizing the multi-dimensional (MD) space for constellation shaping has been proven to be an effective approach for achieving shaping gains. Despite there exists a variety of MD modulation formats tailored for specific optical transmission…
There is a well-known problem in Null Hypothesis Significance Testing: many statistically significant results fail to replicate in subsequent experiments. We show that this problem arises because standard `point-form null' significance…
The Curie-Weiss model is used to study phase transitions in statistical mechanics and has been the object of rigorous analysis in mathematical physics. We analyse the problem of reconstructing the probability measure of a multi-group…
Measuring dependence between two events, or equivalently between two binary random variables, amounts to expressing the dependence structure inherent in a $2\times 2$ contingency table in a real number between $-1$ and $1$. Countless such…
Determining the strength of non-linear statistical dependencies between two variables is a crucial matter in many research fields. The established measure for quantifying such relations is the mutual information. However, estimating mutual…
Variability in neural responses is an ubiquitous phenomenon in neurons, usually modeled with stochastic differential equations. In particular, stochastic integrate-and-fire models are widely used to simplify theoretical studies. The…
Independence analysis is an indispensable step before regression analysis to find out essential factors that influence the objects. With many applications in machine Learning, medical Learning and a variety of disciplines, statistical…
Mutual information is a nonlinear measure used in time series analysis in order to measure the linear and non-linear correlations at any lag $\tau$. The aim of this study is to evaluate some of the most commonly used mutual information…
In a range of genomic applications, it is of interest to quantify the evidence that the signal at site~$i$ is active given conditionally independent replicate observations summarized by the sample mean and variance $(\bar Y, s^2)$ at each…
Noncompliance and missing data often occur in randomized trials, which complicate the inference of causal effects. When both noncompliance and missing data are present, previous papers proposed moment and maximum likelihood estimators for…
Measuring conditional dependencies among the variables of a network is of great interest to many disciplines. This paper studies some shortcomings of the existing dependency measures in detecting direct causal influences or their lack of…
The effect of introducing a mass dependent diffusion rate ~ m^{-alpha} in a model of coagulation with single-particle break up is studied both analytically and numerically. The model with alpha=0 is known to undergo a nonequilibrium phase…
Complex systems are often non-stationary, typical indicators are continuously changing statistical properties of time series. In particular, the correlations between different time series fluctuate. Models that describe the multivariate…
Interval jitter and spike resampling methods are used to analyze the time scale on which temporal correlations occur. They allow the computation of jitter corrected cross correlograms and the performance of an associated statistically…