The estimation of the intensity of a Poisson process has been studied extensively and various methodologies have been proposed. In order to use a Poisson process in applications, one key step is to estimate its intensity function from a given sequence of observed events. Recently, Poisson processes have been used to characterize spiking activity in various neural systems. Classical examples include the arrivals of park patrons at an amusement park over a period of time, the goals scored in an association football match, and the clicks on a particular web link in a given time period. In particular, the Poisson process, a common point process, has the most applications. The study of point processes is one of the central topics in stochastic processes and has been widely used to model discrete events in continuous time. Finally, we apply the new framework in a real data set of neural spike trains, and find that the newly estimated intensities provide better classification accuracy than previous methods. The success of the proposed estimation algorithms is illustrated using two simulations.
We then extend the framework to estimating non-negative intensity functions. An asymptotic study shows that the proposed estimation algorithm provides a consistent estimator for the normalized intensity. The estimation of the density relies on a metric which measures the phase difference between two density functions. Then, we decompose the estimation of the intensity by the product of the estimated total intensity and estimated density. Such a property implies that the time warping is only encoded in the normalized intensity, or density, function. We first show that the intensity function is area-preserved with respect to compositional noise. In this paper, we propose an alignment-based framework for positive intensity estimation.
SEQUENTIAL TESTING OF POISSON PROCESS REGISTRATION
The key challenge is that these observations are not “aligned,” and registration procedures are required for successful estimation. Practical observations, however, often contain compositional noise, i.e., a non-linear shift along the time axis, which makes standard methods not directly applicable. Intensity estimation for Poisson processes is a classical problem and has been extensively studied over the past few decades. 2Department of Statistics, Florida State University, Tallahassee, FL, United States.1College of Nursing, Florida State University, Tallahassee, FL, United States.Provably convergent numerical methods and practical near-optimal strategies are described and illustrated on various examples.Glenna Schluck 1, Wei Wu 2 * and Anuj Srivastava 2 This problem is formulated in a Bayesian framework, and its solution is presented. The objective is to determine the correct hypothesis with minimal error probability and as soon as possible after the observation of the process starts.
Provably convergent numerical methods and practical near-optimal strategies are described and illustrated on various examples.ĪB - Suppose that there are finitely many simple hypotheses about the unknown arrival rate and mark distribution of a compound Poisson process, and that exactly one of them is correct. N2 - Suppose that there are finitely many simple hypotheses about the unknown arrival rate and mark distribution of a compound Poisson process, and that exactly one of them is correct. Sezer was supported by the US Army Pantheon Project. The research of Savas Dayanik was supported by the Air Force Office of Scientific Research, under grant AFOSR-FA-0496. The authors thank the anonymous referee for careful reading and suggestions, which improved the presentation of the manuscript. T1 - Sequential multi-hypothesis testing for compound Poisson processes
0 kommentar(er)
