Related papers: Insertion and Deletion Tolerance of Point Processe…
We consider the inclusion process on the complete graph with vanishing diffusivity, which leads to condensation of particles in the thermodynamic limit. Describing particle configurations in terms of size-biased and appropriately scaled…
A perturbed lattice is a point process $\Pi=\{x+Y_x:x\in \mathbb{Z}^d\}$ where the lattice points in $\mathbb{Z}^d$ are perturbed by i.i.d.\ random variables $\{Y_x\}_{x\in \mathbb{Z}^d}$. A random point process $\Pi$ is said to be rigid if…
We consider the totally asymmetric exclusion process in discrete time with generalized updating rules. We introduce a control parameter into the interaction between particles. Two particular values of the parameter correspond to known…
We present a new approach to termination analysis of numerical computations in logic programs. Traditional approaches fail to analyse them due to non well-foundedness of the integers. We present a technique that allows to overcome these…
We prove a law of large numbers in terms of complete convergence of independent random variables taking values in increments of monotone functions, with convergence uniform both in the initial and the final time. The result holds also for…
Sparse Gaussian processes and various extensions thereof are enabled through inducing points, that simultaneously bottleneck the predictive capacity and act as the main contributor towards model complexity. However, the number of inducing…
An adapted, right-continuous, non-decreasing, integer-valued process with unit jumps and starting at zero has a minimal predictable intensity if and only if it is a standard Poisson process under an absolutely continuous transformation of…
Many phenomena can be modeled as network dynamics with punctuate interactions. However, most relevant dynamics do not allow for computational tractability. To circumvent this difficulty, the Poisson Hypothesis regime replaces interaction…
We are interested in estimating the location of what we call "smooth change-point" from $n$ independent observations of an inhomogeneous Poisson process. The smooth change-point is a transition of the intensity function of the process from…
We precisely quantify the impact of statistical error in the quality of a numerical approximation to a random matrix eigendecomposition, and under mild conditions, we use this to introduce an optimal numerical tolerance for residual error…
Point processes are an essential tool when we are interested in where in time or space events occur. The basic starting point for point processes is usually the Poisson process. Over the years, Stein's method has been developed with a great…
We offer a natural and extensible measure-theoretic treatment of missingness at random. Within the standard missing data framework, we give a novel characterisation of the observed data as a stopping-set sigma algebra. We demonstrate that…
We study weak convergence of a sequence of point processes to a scale-invariant simple point process. For a deterministic sequence $(z_n)_{n\in\mathbb{N}}$ of positive real numbers increasing to infinity as $n \to \infty$ and a sequence…
We consider a dynamic version of the Neyman contagious point process that can be used for modelling the spacial dynamics of biological populations, including species invasion scenarios. Starting with an arbitrary finite initial…
Real-world data contains various kinds of errors. Before analyzing data, one usually needs to process the raw data. However, traditional data processing based on exactly match often misses lots of valid information. To get high-quality…
A parametric point process model is developed, with modeling based on the assumption that sequential observations often share latent phenomena, while also possessing idiosyncratic effects. An alternating optimization method is proposed to…
We introduce and investigate a new notion of the theory of approximation-the so-called degenerate approximation, i.e. approximation of the function of two (and more) variables (kernel) by means of degenerate function (kernel). We apply…
The paper addresses the tolerance approach to the sensitivity analysis of optimal solutions to the nonlinear optimization problem of the form $$\mbox{$\bigoplus\limits_{y\in S}C(y)\to\min$\quad over\quad $S\in\mathcal{S}$,}$$ where…
We consider the Bernoulli Boolean discrete percolation model on the d-dimensional integer lattice. We study sufficient conditions on the distribution of the radii of balls placed at the points of a Bernoulli point process for the absence of…
A prediction interval covers a future observation from a random process in repeated sampling, and is typically constructed by identifying a pivotal quantity that is also an ancillary statistic. Analogously, a tolerance interval covers a…