Related papers: Palm distributions of superposed point processes f…
This note aims at presenting several new theoretical results for the compound Poisson point process, which follows the work of Zhang \emph{et al.} [Insurance~Math.~Econom.~59(2014), 325-336]. The first part provides a new characterization…
Many models for point process data are defined through a thinning procedure where locations of a base process (often Poisson) are either kept (observed) or discarded (thinned). In this paper, we go back to the fundamentals of the…
We present a machine learning model for the analysis of randomly generated discrete signals, modeled as the points of an inhomogeneous, compound Poisson point process. Like the wavelet scattering transform introduced by Mallat, our…
In this chapter we review some examples, methods, and recent results involving comparison of clustering properties of point processes. Our approach is founded on some basic observations allowing us to consider void probabilities and moment…
The increased availability of massive data sets provides a unique opportunity to discover subtle patterns in their distributions, but also imposes overwhelming computational challenges. To fully utilize the information contained in big…
We consider Palm distributions arising in a Markov process with time homogeneous transitions which is jointly stationary with multiple point processes. Motivated by a BAR approach studied in the recent paper Braverman, Dai and Miyazawa…
The robust detection of statistical dependencies between the components of a complex system is a key step in gaining a network-based understanding of the system. Because of their simplicity and low computation cost, pairwise statistics are…
In this paper we study the volatility and its probability distribution function for the cumulative production based on the experience curve hypothesis. This work presents a generalization of the study of volatility in [1], which addressed…
The particle-in-cell numerical method of plasma physics balances a trade-off between computational cost and intrinsic noise. Inference on data produced by these simulations generally consists of binning the data to recover the particle…
We introduce and study a unified Bayesian framework for extended feature allocations which flexibly captures interactions -- such as repulsion or attraction -- among features and their associated weights. We provide a complete Bayesian…
We use point processes theory to describe the asymptotic distribution of all upper order statistics for observations collected at renewal times. As a corollary, we obtain limiting theorems for corresponding extremal processes.
Diffusions are a successful technique to sample from high-dimensional distributions. The target distribution can be either explicitly given or learnt from a collection of samples. They implement a diffusion process whose endpoint is a…
In many contexts such as queuing theory, spatial statistics, geostatistics and meteorology, data are observed at irregular spatial positions. One model of this situation involves considering the observation points as generated by a Poisson…
Consider a locally finite Dawson-Watanabe superprocess $\xi=(\xi_t)$ in $\mathsf{R}^d$ with $d\geq2$. Our main results include some recursive formulas for the moment measures of $\xi$, with connections to the uniform Brownian tree, a…
The Mellin transform is usually applied in probability theory to the product of independent random variables. In recent times the machinery of the Mellin transform has been adopted to describe the L\'evy stable distributions, and more…
Simulating samples from arbitrary probability distributions is a major research program of statistical computing. Recent work has shown promise in an old idea, that sampling from a discrete distribution can be accomplished by perturbing and…
The diffraction of various random subsets of the integer lattice $\mathbb{Z}^{d}$, such as the coin tossing and related systems, are well understood. Here, we go one important step beyond and consider random point sets in $\mathbb{R}^{d}$.…
In [Schuhmacher, Electron. J. Probab. 10 (2005), 165--201] estimates of the Barbour-Brown distance d_2 between the distribution of a thinned point process and the distribution of a Poisson process were derived by combining discretization…
Statistical NLP systems are frequently evaluated and compared on the basis of their performances on a single split of training and test data. Results obtained using a single split are, however, subject to sampling noise. In this paper we…
Although the study of weak convergence of superpositions of point processes to the Poisson process dates back to the work of Grigelionis in 1963, it was only recently that Schuhmacher [Stochastic Process. Appl. 115 (2005) 1819--1837]…