Related papers: Self-excited Threshold Poisson Autoregression
Probabilistic approaches for handling count-valued time sequences have attracted amounts of research attentions because their ability to infer explainable latent structures and to estimate uncertainties, and thus are especially suitable for…
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…
Although the specification of bivariate probability models using a collection of assumed conditional distributions is not a novel concept, it has received considerable attention in the last decade. In this study, a bivariate…
We present methodology for estimating the stochastic intensity of a doubly stochastic Poisson process. Statistical and theoretical analyses of traffic traces show that these processes are appropriate models of high intensity traffic…
We derive strong mixing conditions for many existing discrete-valued time series models that include exogenous covariates in the dynamic. Our main contribution is to study how a mixing condition on the covariate process transfers to a…
The Peaks Over Threshold (POT) method is the most popular statistical method for the analysis of univariate extremes. Even though there is a rich applied literature on Bayesian inference for the POT, the asymptotic theory for such proposals…
We review the methods of constructing confidence intervals that account for a priori information about one-sided constraints on the parameter being estimated. We show that the so-called method of sensitivity limit yields a correct solution…
We consider the non-parametric Poisson regression problem where the integer valued response $Y$ is the realization of a Poisson random variable with parameter $\lambda(X)$. The aim is to estimate the functional parameter $\lambda$ from…
Real-world data often exhibits sequential dependence, across diverse domains such as human behavior, medicine, finance, and climate modeling. Probabilistic methods capture the inherent uncertainty associated with prediction in these…
We consider the asymptotic behavior of posterior distributions and Bayes estimators based on observations which are required to be neither independent nor identically distributed. We give general results on the rate of convergence of the…
Count data appears in various disciplines. In this work, a new method to analyze time series count data has been proposed. The method assumes exponentially decaying covariance structure, a special class of the Mat\'ern covariance function,…
We obtain the posterior distribution of a random process conditioned on observing the empirical frequencies of a finite sample path. We find under a rather broad assumption on the "dependence structure" of the process, {\em c.f.}…
Neural computations arising from myriads of interactions between spiking neurons can be modeled as network dynamics with punctuate interactions. However, most relevant dynamics do not allow for computational tractability. To circumvent this…
This study defines a multivariate Self--Exciting Threshold Autoregressive with eXogenous input (MSETARX) models and present an estimation procedure for the parameters. The conditions for stationarity of the nonlinear MSETARX models is…
We consider event-driven clinical trials, where the analysis is performed once a pre-determined number of clinical events has been reached. For example, these events could be progression in oncology or a stroke in cardiovascular trials. At…
We develop a new statistical model to analyse time-varying ranking data. The model can be used with a large number of ranked items, accommodates exogenous time-varying covariates and partial rankings, and is estimated via the maximum…
In this paper, we propose a novel robust stochastic optimization approach with a distinctive consideration for rare events, in which divergence measures are used to bound the event-wise ambiguity sets. This is done by using the Poisson…
Economic and financial models -- such as vector autoregressions, local projections, and multivariate volatility models -- feature complex dynamic interactions and spillovers across many time series. These models can be integrated into a…
We study online change point detection for multivariate inhomogeneous Poisson point process time series. This setting arises commonly in applications such as earthquake seismology, climate monitoring, and epidemic surveillance, yet remains…
The dynamics of opinion is a complex and interesting process, especially for the systems with large number individuals. It is usually hard to describe the evolutionary features of these systems. In this paper, we study the self excitation…