Related papers: Detection of signals by Monte Carlo singular spect…
We present a data-adaptive spectral method - Monte Carlo Singular Spectrum Analysis (MC-SSA) - and its modification to tackle astrophysical problems. Through numerical simulations we show the ability of the MC-SSA in dealing with…
A key step in separating signal from noise in time series by means of singular spectrum analysis (SSA) is grouping. We present a multiple testing method for the grouping step in SSA. As separability criterion, we utilize the weighted…
Appropriate preprocessing is a fundamental prerequisite for analyzing a noisy dataset. The purpose of this paper is to apply a nonparametric preprocessing method, called Singular Spectrum Analysis (SSA), to a variety of datasets which are…
Singular spectrum analysis (SSA), starting from the second half of the XX century, has been a rapidly developing method of time series analysis. Since it can be called principal component analysis for time series, SSA will definitely be a…
Multivariate Singular Spectrum Analysis (MSSA) is a powerful and widely used nonparametric method for multivariate time series, which allows the analysis of complex temporal data from diverse fields such as finance, healthcare, ecology, and…
In the Monte Carlo (MC) method statistical noise is usually present. Statistical noise may become dominant in the calculation of a distribution, usually by iteration, but is less Important in calculating integrals. The subject of the…
Bayesian inference using Markov Chain Monte Carlo (MCMC) on large datasets has developed rapidly in recent years. However, the underlying methods are generally limited to relatively simple settings where the data have specific forms of…
Multivariate singular spectrum analysis (M-SSA), with a varimax rotation of eigenvectors, was recently proposed to provide detailed information about phase synchronization in networks of nonlinear oscillators without any a priori need for…
Singular spectrum analysis (SSA) as a nonparametric tool for decomposition of an observed time series into sum of interpretable components such as trend, oscillations and noise is considered. The separability of these series components by…
We introduce Multivariate Circulant Singular Spectrum Analysis (M-CiSSA) to provide a comprehensive framework to analyze fluctuations, extracting the underlying components of a set of time series, disentangling their sources of variation…
The problem of large scale multiple testing arises in many contexts, including testing for pairwise interaction among large numbers of neurons. With advances in technologies, it has become common to record from hundreds of neurons…
This paper proposes a new method for anomaly detection in time-series data by incorporating the concept of difference subspace into the singular spectrum analysis (SSA). The key idea is to monitor slight temporal variations of the…
We introduce and analyze a variant of multivariate singular spectrum analysis (mSSA), a popular time series method to impute and forecast a multivariate time series. Under a spatio-temporal factor model we introduce, given $N$ time series…
We introduce Contrastive Multivariate Singular Spectrum Analysis, a novel unsupervised method for dimensionality reduction and signal decomposition of time series data. By utilizing an appropriate background dataset, the method transforms a…
The performance of a number of different measures of nonlinearity in a time series is compared numerically. Their power to distinguish noisy chaotic data from linear stochastic surrogates is determined by Monte Carlo simulation for a number…
The Laser Interferometer Space Antenna (LISA) is expected to simultaneously detect many thousands of low frequency gravitational wave signals. This presents a data analysis challenge that is very different to the one encountered in ground…
A Bayesian analysis of the probability of a signal in the presence of background is developed, and criteria are proposed for claiming evidence for, or the discovery of a signal. The method is general and in particular applicable to sparsely…
Statistical signal processing applications usually require the estimation of some parameters of interest given a set of observed data. These estimates are typically obtained either by solving a multi-variate optimization problem, as in the…
We study statistical model checking of continuous-time stochastic hybrid systems. The challenge in applying statistical model checking to these systems is that one cannot simulate such systems exactly. We employ the multilevel Monte Carlo…
Hidden Markov models can describe time series arising in various fields of science, by treating the data as noisy measurements of an arbitrarily complex Markov process. Sequential Monte Carlo (SMC) methods have become standard tools to…