数据分析、统计与概率

In the report the approach to estimation of quality of planned experiments is considered. This approach is based on the analysis of uncertainty, which will take place under the future hypotheses testing about the existence of a new…

Reconstruction of a dynamical system from a time series requires the selection of two parameters, the embedding dimension $d_e$ and the embedding lag $\tau$. Many competing criteria to select these parameters exist, and all are heuristic.…

We discuss the possibility of applying some standard statistical methods (the least square method, the maximum likelihood method, the method of statistical moments for estimation of parameters) to deterministically chaotic low-dimensional…

We study the information metric on instanton moduli spaces in two-dimensional nonlinear sigma models. In the CP^1 model, the information metric on the moduli space of one instanton with the topological charge Q=k which is any positive…

The problem of assigning probability distributions which objectively reflect the prior information available about experiments is one of the major stumbling blocks in the use of Bayesian methods of data analysis. In this paper the method of…

There are recent interests with CsI(Tl) scintillating crystals for Dark Matter experiments. The key merit is the capability to differentiate nuclear recoil (nr) signatures from the background $\beta / \gamma$-events due to ambient…

We develop an effective nonhierarchical data clustering method using an analogy to the dynamic coarse graining of a stochastic system. Analyzing the eigensystem of an interitem transition matrix identifies fuzzy clusters corresponding to…

This report introduces general ideas and some basic methods of the Bayesian probability theory applied to physics measurements. Our aim is to make the reader familiar, through examples rather than rigorous formalism, with concepts such as:…

We show that it is possible to generalize the Ursell-Mayer cluster formalism so that it may cover also the statistics of Internet websites. Our starting point is the introduction of an extra variable that is assumed to take account, as will…

The estimation of signal frequency count in the presence of background noise has had much discussion in the recent physics literature, and Mandelkern [1] brings the central issues to the statistical community, leading in turn to extensive…

The incorporation of systematic uncertainties into confidence interval calculations has been addressed recently in a paper by Conrad et al. (Physical Review D 67 (2003) 012002). In their work, systematic uncertainities in detector…

This paper is devoted to the problem of statistical mechanics raised by the analysis of an issue of sociological interest: the teen birth phenomenon. It is expected that these data are characterized by correlated fluctuations, reflecting…

Most data processing techniques, applied to biomedical and sociological time series, are only valid for random fluctuations that are stationary in time. Unfortunately, these data are often non stationary and the use of techniques of…

We show that the continuous wavelet transform can provide a unique decomposition of a timeseries in to 'signal-like' and 'noise-like' components: From the overall wavelet spectrum two mutually independent skeleton spectra can be extracted,…

We consider nearest neighbor spacing distributions of composite ensembles of levels. These are obtained by combining independently unfolded sequences of levels containing only few levels each. Two problems arise in the spectral analysis of…

We study phase synchronization between atmospheric variables such as daily mean temperature and daily precipitation records. We find significant phase synchronization between records of Oxford and Vienna as well as between the records of…

The lognormal distribution describing, e.g., exponentials of Gaussian random variables is one of the most common statistical distributions in physics. It can exhibit features of broad distributions that imply qualitative departure from the…

In this paper, we consider the problem of blind signal and image separation using a sparse representation of the images in the wavelet domain. We consider the problem in a Bayesian estimation framework using the fact that the distribution…

During the MaxEnt 2002 workshop in Moscow, Idaho, Tony Vignaux asked again a few simple questions about using Maximum Entropy or Bayesian approaches for the famous Dice problems which have been analyzed many times through this workshop and…

The problem of splitting effects by vertex angles is discussed for nonintegrable rational polygonal billiards. A statistical analysis of the decay dynamics in weakly open polygons is given through the orbit survival probability. Two…