数据分析、统计与概率

Noise induced jumping between meta-stable states in a potential depends on the structure of the noise. For an $\alpha$-stable noise, jumping triggered by single extreme events contributes to the transition probability. This is also called…

A suggestion is made for improving the Feldman Cousins method of estimating signal counts in the presence of background. The method concentrates on finding essential information about the signal and ignoring extraneous information about…

An exact formula for the distribution of lifetimes in coherent-noise models and related models is derived. For certain stress distributions, this formula can be analytically evaluated and yields simple closed expressions. For those types of…

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 <Nb> of background and <Ns> of signal events. We find that the proper…

Pulsars are the most stable natural frequency standards. They can be applied to a number of principal problems of modern astronomy and time-keeping metrology. The full exploration of pulsar properties requires obtaining unbiased estimates…

Fourier spectral estimates and, to a lesser extent, the autocorrelation function are the primary tools to detect periodicities in experimental data in the physical and biological sciences. We propose a new method which is more reliable than…

A parametric method similar to autoregressive spectral estimators is proposed to determine the probability density function (pdf) of a random set. The method proceeds by maximizing the likelihood of the pdf, yielding estimates that perform…

We approach the theoretical problem of compressing a signal dominated by Gaussian noise. We present expressions for the compression ratio which can be reached, under the light of Shannon's noiseless coding theorem, for a linearly quantized…

A formula of Doetsch ({\em Math. Zeitschr.} {\bf 42}, 263 (1937)) is generalized and used to numerically invert the one-sided Laplace transform ${\hat C}(\beta)$. The necessary input is only the values of ${\hat C}(\beta)$ on the positive…

It is well known that the output of a Neural Network trained to disentangle between two classes has a probabilistic interpretation in terms of the a-posteriori Bayesian probability, provided that a unary representation is taken for the…

A generalization of the coherent-noise models [M. E. J. Newman and K. Sneppen, Phys. Rev. E{\bf54}, 6226 (1996)] is presented where the agents in the model are subjected to a multitude of stresses, generated in a hierarchy of different…

A method to approximate continuous multi-dimensional probability density functions (PDFs) using their projections and correlations is described. The method is particularly useful for event classification when estimates of systematic…

The decay pattern of aftershocks in the so-called 'coherent-noise' models [M. E. J. Newman and K. Sneppen, Phys. Rev. E54, 6226 (1996)] is studied in detail. Analytical and numerical results show that the probability to find a large event…

Conventional statistics begins with a model, and assigns a likelihood of obtaining any particular set of data. The opposite approach, beginning with the data and assigning a likelihood to any particular model, is explored here for the case…

Predictions of missing links of incomplete networks like protein-protein interaction networks or very likely but not yet existent links in evolutionary networks like friendship networks in web society can be considered as a guideline for…

Missing link prediction of networks is of both theoretical interest and practical significance in modern science. In this paper, we empirically investigate a simple framework of link prediction on the basis of node similarity. We compare…

We discuss the conditions under which Scan Statistics can be fruitfully implemented to signal a departure from the underlying probability model that describes the experimental data. It is shown that local perturbations (``bumps'' or…

By studying the statistics of recurrence intervals, $\tau$, between volatilities of Internet traffic rate changes exceeding a certain threshold $q$, we find that the probability distribution functions, $P_{q}(\tau)$, for both byte and…

This paper presents a detailed characterization of the trajectory of a single housefly with free range of a square cage. The trajectory of the fly was recorded and transformed into a time series, which was fully analyzed using an…

We derive the bias, variance, covariance, and mean square error of the standard lag windowed correlogram estimator both with and without sample mean removal for complex white noise with an arbitrary mean. We find that the arbitrary mean…