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A Novel Bayesian Change-point Algorithm for Genome-wide Analysis of Diverse ChIPseq Data Types
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Nonparametric Bayesian Segmentation of a Multivariate Inhomogeneous Space-Time Poisson Process.

Mingtao Ding1, Lihan He, David Dunson

  • 1Department of Electrical & Computer Engineering, Duke University, Durham, NC mingtao.ding@ece.duke.edu.

Bayesian Analysis
|June 7, 2013
PubMed
Summary

This study introduces a new Bayesian model for analyzing spatial point patterns that change over time. The model effectively segments data into contiguous regions, improving the understanding of dynamic spatial processes.

Keywords:
Bayesian hierarchical modelGaussian processinhomogeneous Poisson processlogistic stick breaking processspatial segmentationtemporal dynamics

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Area of Science:

  • Spatial Statistics
  • Bayesian Inference
  • Point Process Modeling

Background:

  • Analyzing time-evolving spatial data is challenging.
  • Existing methods may struggle with complex spatial structures and temporal dynamics.
  • Understanding dynamic spatial patterns is crucial in fields like criminology and ecology.

Purpose of the Study:

  • To propose a nonparametric Bayesian model for segmenting time-evolving multivariate spatial point process data.
  • To develop a model that favors spatially contiguous segments and infers the number of segments from data.
  • To incorporate temporal dynamics using autoregressive or Gaussian process models.

Main Methods:

  • Utilized a logistic stick-breaking process (LSBP) for piecewise-constant spatial Poisson intensities.
  • Modeled temporal dynamics with exponential correlation via autoregressive or Gaussian process models.
  • Compared Markov chain Monte Carlo (MCMC) sampling with variational Bayesian analysis for inference.

Main Results:

  • The proposed LSBP model successfully encourages spatially contiguous segments.
  • The model infers the number of segments adaptively from the data.
  • Both MCMC and variational Bayesian methods were applied, with the latter offering computational efficiency.

Conclusions:

  • The developed Bayesian model provides a flexible framework for segmenting dynamic spatial point process data.
  • The model's ability to favor contiguous regions and adapt segment numbers enhances spatial analysis.
  • The study demonstrates the model's utility with both simulated data and real-world crime event data.