Related papers: First Steps Towards an Imprecise Poisson Process
The convergence of a sequence of point processes with dependent points, defined by a symmetric function of iid high-dimensional random vectors, to a Poisson random measure is proved. This also implies the convergence of the joint…
We consider stochastic processes arising from dynamical systems simply by evaluating an observable function along the orbits of the system and study marked point processes associated to extremal observations of such time series…
Optimization of a random processes by restart is a subject of active theoretical research in statistical physics and has long found practical application in computer science. Meanwhile, one of the key issues remains largely unsolved: when…
Changing time of simple continuous-time Markov counting processes by independent unit-rate Poisson processes results in Markov counting processes for which we provide closed-form transition rates via composition of trajectories and with…
The telegraph process models a random motion with finite velocity and it is usually proposed as an alternative to diffusion models. The process describes the position of a particle moving on the real line, alternatively with constant…
Sparse sequences of neural spikes are posited to underlie aspects of working memory, motor production, and learning. Discovering these sequences in an unsupervised manner is a longstanding problem in statistical neuroscience. Promising…
A common approach to modelling extreme values is to consider the excesses above a high threshold as realisations of a non-homogeneous Poisson process. While this method offers the advantage of modelling using threshold-invariant extreme…
Historical processes manifest remarkable diversity. Nevertheless, scholars have long attempted to identify patterns and categorize historical actors and influences with some success. A stochastic process framework provides a structured…
We consider forecasting the latent rate profiles of a time series of inhomogeneous Poisson processes. The work is motivated by operations management of queueing systems, in particular, telephone call centers, where accurate forecasting of…
To model recurrent interaction events in continuous time, an extension of the stochastic block model is proposed where every individual belongs to a latent group and interactions between two individuals follow a conditional inhomogeneous…
We consider the problem of parameter estimation by observations of inhomogeneous Poisson process. It is well-known that if the regularity conditions are fulfilled then the maximum likelihood and Bayesian estimators are consistent,…
We consider the nonparametric estimation of the intensity function of a Poisson point process in a circular model from indirect observations $N_1,\ldots,N_n$. These observations emerge from hidden point process realizations with the target…
For a class of excitatory spiking neuron models with delayed feedback fed with a Poisson stochastic process, it is proven that the stream of output interspike intervals cannot be presented as a Markov process of any order. Keywords: spiking…
A Neural Process (NP) estimates a stochastic process implicitly defined with neural networks given a stream of data, rather than pre-specifying priors already known, such as Gaussian processes. An ideal NP would learn everything from data…
Stochastic processes on topological vector spaces over non-Archimedean fields and with transition measures having values in non-Archimedean fields are defined and investigated. For this the non-Archimedean analog of the Kolmogorov theorem…
The compound Poisson process and the Dirichlet process are the pillar structures of Renewal theory and Bayesian nonparametric theory, respectively. Both processes have many useful extensions to fulfill the practitioners needs to model the…
In this paper, we revisit the original ideas of Stein and propose an estimator of the intensity parameter of a homogeneous Poisson point process defined in $\R^d$ and observed in a bounded window. The procedure is based on a new general…
A non-homogeneous Poisson cluster model is studied, motivated by insurance applications. The Poisson center process which expresses arrival times of claims, triggers off cluster member processes which correspond to number or amount of…
Parameter identification problems are formulated in a probabilistic language, where the randomness reflects the uncertainty about the knowledge of the true values. This setting allows conceptually easily to incorporate new information, e.g.…
In this paper the generalization of the Poisson distribution is derived for the case when each consecutive event changes event rate. A simple formula for the probability of observing of a given number of events for the selected period of…