Modelling for Poisson process intensities over irregular spatial domains

06/08/2021
by   Chunyi Zhao, et al.
0

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, the model construction implies a Bernstein-Dirichlet prior for the Poisson process density, which supports general inference for point process functionals. The key contribution of the methodology is two classes of flexible and computationally efficient models for spatial Poisson process intensities over irregular domains. We address the choice or estimation of the number of beta basis densities, and develop methods for prior specification and posterior simulation for full inference about functionals of the point process. The methodology is illustrated with both synthetic and real data sets.

READ FULL TEXT
POST COMMENT

Comments

There are no comments yet.

Authors

page 14

10/24/2021

Erlang mixture modeling for Poisson process intensities

We develop a prior probability model for temporal Poisson process intens...
09/02/2011

The Stick-Breaking Construction of the Beta Process as a Poisson Process

We show that the stick-breaking construction of the beta process due to ...
06/29/2021

Scaled process priors for Bayesian nonparametric estimation of the unseen genetic variation

There is a growing interest in the estimation of the number of unseen fe...
12/12/2019

Towards Expressive Priors for Bayesian Neural Networks: Poisson Process Radial Basis Function Networks

While Bayesian neural networks have many appealing characteristics, curr...
11/10/2017

Bayesian Gaussian models for interpolating large-dimensional data at misaligned areal units

Areal level spatial data are often large, sparse and may appear with geo...
05/16/2020

BART-based inference for Poisson processes

The effectiveness of Bayesian Additive Regression Trees (BART) has been ...
12/15/2020

Generating from the Strauss Process using stitching

The STrauss process is a point process with unnormalized density with re...
This week in AI

Get the week's most popular data science and artificial intelligence research sent straight to your inbox every Saturday.