Related papers: Prediction of Spatial Point Processes: Regularized…

Existing inferential methods for small area data involve a trade-off between maintaining area-level frequentist coverage rates and improving inferential precision via the incorporation of indirect information. In this article, we propose a…

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…

A temporal point process is a mathematical model for a time series of discrete events, which covers various applications. Recently, recurrent neural network (RNN) based models have been developed for point processes and have been found…

Many algorithms in computer vision and robotics make strong assumptions about uncertainty, and rely on the validity of these assumptions to produce accurate and consistent state estimates. In practice, dynamic environments may degrade…

We propose a new class of parameterizations for spatio-temporal point processes which leverage Neural ODEs as a computational method and enable flexible, high-fidelity models of discrete events that are localized in continuous time and…

In a wide range of applications, the stochastic properties of the observed time series change over time. The changes often occur gradually rather than abruptly: the prop- erties are (approximately) constant for some time and then slowly…

Intensity estimation is a common problem in statistical analysis of spatial point pattern data. This paper proposes a nonparametric Bayesian method for estimating the spatial point process intensity based on mixture of finite mixture (MFM)…

We consider a network of sensors deployed to sense a spatio-temporal field and estimate a parameter of interest. We are interested in the case where the temporal process sensed by each sensor can be modeled as a state-space process that is…

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…

Sequences of labeled events observed at irregular intervals in continuous time are ubiquitous across various fields. Temporal Point Processes (TPPs) provide a mathematical framework for modeling these sequences, enabling inferences such as…

Probabilistic programming has emerged as a powerful paradigm in statistics, applied science, and machine learning: by decoupling modelling from inference, it promises to allow modellers to directly reason about the processes generating…

We introduce a sharpness functional for probabilistic models that quantifies sharpness as an intrinsic property of the probability distribution. The measure is derived based on a rank-based concentration principle that tracks upward…

We develop nonparametric Bayesian modelling approaches for Poisson processes, using weighted combinations of structured beta densities to represent the point process intensity function. For a regular spatial domain, such as the unit square,…

Probabilistic and set-based methods are two approaches for model invalidation, parameter and state estimation. Both classes of methods use different types of data, i.e. deterministic or probabilistic data, which allow different statements…

We can, and should, do statistical inference on simulation models by adjusting the parameters in the simulation so that the values of {\em randomly chosen} functions of the simulation output match the values of those same functions…

Assume that several competing methods are available to estimate a parameter in a given statistical model. The aim of estimator averaging is to provide a new estimator, built as a linear combination of the initial estimators, that achieves…

Predicting the response at an unobserved location is a fundamental problem in spatial statistics. Given the difficulty in modeling spatial dependence, especially in non-stationary cases, model-based prediction intervals are at risk of…

We consider the inference problem for parameters in stochastic differential equation models from discrete time observations (e.g. experimental or simulation data). Specifically, we study the case where one does not have access to…

We give a finite-sample analysis of predictive inference procedures after model selection in regression with random design. The analysis is focused on a statistically challenging scenario where the number of potentially important…

This paper proposes a new methodology to perform Bayesian inference for a class of multidimensional Cox processes in which the intensity function is piecewise constant. Poisson processes with piecewise constant intensity functions are…