Related papers: Lecture Notes: Temporal Point Processes and the Co…
Event definitions in Complex Event Processing systems are constrained by the expressiveness of each system's language. Some systems allow the definition of instantaneous complex events, while others allow the definition of durative complex…
Second-order statistics play a crucial role in analysing point processes. Previous research has specifically explored locally weighted second-order statistics for point processes, offering diagnostic tests in various spatial domains.…
Causality is a non-obvious concept that is often considered to be related to temporality. In this paper we present a number of past and present approaches to the definition of temporality and causality from philosophical, physical, and…
These are lecture notes for a simple minicourse approaching the satistical properties of a dynamical system by the study of the associated transfer operator (considered on a suitable functions or measures spaces). The following questions…
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.
Point processes often have a natural interpretation with respect to a continuous process. We propose a point process construction that describes arrival time observations in terms of the state of a latent diffusion process. In this…
We propose a new summary statistic for inhomogeneous intensity-reweighted moment stationary spatio-temporal point processes. The statistic is defined through the n-point correlation functions of the point process and it generalises the…
This paper establishes the theoretical foundation for statistical applications of an intriguing new type of spatial point processes called critical point processes. These point processes, residing in Euclidean space, consist of the critical…
We consider the intensity-based approach for the modeling of default times of one or more companies. In this approach the default times are defined as the jump times of a Cox process, which is a Poisson process conditional on the…
We derive joint factorial moment identities for point processes with Papangelou intensities. Our proof simplifies previous approaches to related moment identities and includes the setting of Poisson point processes. Applications are given…
A probabilistic model describes a system in its observational state. In many situations, however, we are interested in the system's response under interventions. The class of structural causal models provides a language that allows us to…
Determinantal point processes are models for regular spatial point patterns, with appealing probabilistic properties. We present their spatio-temporal counterparts and give examples of these models, based on spatio-temporal covariance…
Spatiotemporal point processes (STPPs) are probabilistic models for events occurring in continuous space and time. Real-world event data often exhibit intricate dependencies and heterogeneous dynamics. By incorporating modern deep learning…
Self-exciting spatio-temporal point process models predict the rate of events as a function of space, time, and the previous history of events. These models naturally capture triggering and clustering behavior, and have been widely used in…
Though languages can evolve slowly, they can also react strongly to dramatic world events. By studying the connection between words and events, it is possible to identify which events change our vocabulary and in what way. In this work, we…
We study functional limit theorems for linear type processes with short memory under the assumption that the innovations are dependent identically distributed random variables with infinite variance and in the domain of attraction of stable…
Social goods, such as healthcare, smart city, and information networks, often produce ordered event data in continuous time. The generative processes of these event data can be very complex, requiring flexible models to capture their…
The ability to know in advance the trend of running process instances, with respect to different features, such as the expected completion time, would allow business managers to timely counteract to undesired situations, in order to prevent…
Neural marked temporal point processes have been a valuable addition to the existing toolbox of statistical parametric models for continuous-time event data. These models are useful for sequences where each event is associated with a single…
Temporal Point Processes (TPP) play an important role in predicting or forecasting events. Although these problems have been studied extensively, predicting multiple simultaneously occurring events can be challenging. For instance, more…