Intensity Estimation for Poisson Process with Compositional Noise

09/23/2019
by   Glenna Schluck, et al.
0

Intensity estimation for Poisson processes is a classical problem and has been extensively studied over the past few decades. Practical observations, however, often contain compositional noise, i.e. a nonlinear shift along the time axis, which makes standard methods not directly applicable. The key challenge is that these observations are not "aligned", and registration procedures are required for successful estimation. In this paper, we propose an alignment-based framework for positive intensity estimation. We first show that the intensity function is area-preserved with respect to compositional noise. Such a property implies that the time warping is only encoded in the normalized intensity, or density, function. Then, we decompose the estimation of the intensity by the product of the estimated total intensity and estimated density. The estimation of the density relies on a metric which measures the phase difference between two density functions. An asymptotic study shows that the proposed estimation algorithm provides a consistent estimator for the normalized intensity. We then extend the framework to estimating non-negative intensity functions. The success of the proposed estimation algorithms is illustrated using two simulations. 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.

READ FULL TEXT

page 1

page 2

page 3

page 4

research
10/24/2021

Erlang mixture modeling for Poisson process intensities

We develop a prior probability model for temporal Poisson process intens...
research
08/10/2021

First Order Locally Orderless Registration

First Order Locally Orderless Registration (FLOR) is a scale-space frame...
research
11/28/2018

Local polynomial estimation of the intensity of a doubly stochastic Poisson process with bandwidth selection procedure

We consider a doubly stochastic Poisson process with stochastic intensit...
research
10/09/2020

Uniform Deconvolution for Poisson Point Processes

We focus on the estimation of the intensity of a Poisson process in the ...
research
07/12/2020

Estimating Stochastic Poisson Intensities Using Deep Latent Models

We present methodology for estimating the stochastic intensity of a doub...
research
06/17/2018

Poisson Source Localization on the Plane. Cusp Case

This work is devoted to the problem of estimation of the localization of...
research
04/18/2016

Most Likely Separation of Intensity and Warping Effects in Image Registration

This paper introduces a class of mixed-effects models for joint modeling...

Please sign up or login with your details

Forgot password? Click here to reset