Chunlin Ji & Mike West Department of Statistical Science Duke University
description
Transcript of Chunlin Ji & Mike West Department of Statistical Science Duke University
![Page 1: Chunlin Ji & Mike West Department of Statistical Science Duke University](https://reader036.fdocuments.us/reader036/viewer/2022062520/568160cc550346895dd000f4/html5/thumbnails/1.jpg)
Dynamic spatial mixture modelling and its application in Bayesian tracking for cell fluorescent microscopic imaging
Chunlin Ji & Mike WestDepartment of Statistical
ScienceDuke University
Department of Statistical Science, Duke University
JSM 2009, Washington, DCAug. 4, 2009
![Page 2: Chunlin Ji & Mike West Department of Statistical Science Duke University](https://reader036.fdocuments.us/reader036/viewer/2022062520/568160cc550346895dd000f4/html5/thumbnails/2.jpg)
Dynamic spatial point processes
Department of Statistical Science, Duke University
Multiple extended targets tracking.
Dynamic spatial inhomogeneous point processes
Single-level cell fluorescence microscopic image. (Wang et al. 2009)
Exploratory questions: -Characterizing Intensity dynamic
-Quantify drifts in intensity
![Page 3: Chunlin Ji & Mike West Department of Statistical Science Duke University](https://reader036.fdocuments.us/reader036/viewer/2022062520/568160cc550346895dd000f4/html5/thumbnails/3.jpg)
Spatial Poisson point process
Department of Statistical Science, Duke University
Point process over S Intensity function
Density
Realized locations
Likelihood
Flexible nonparametric model for characterizing spatial heterogeneity in
Dirichlet process mixture for density function(Kottas & Sanso 07; Ji et al 09 )
![Page 4: Chunlin Ji & Mike West Department of Statistical Science Duke University](https://reader036.fdocuments.us/reader036/viewer/2022062520/568160cc550346895dd000f4/html5/thumbnails/4.jpg)
Dynamic spatial DP mixture DP Mixture at each time point
Time evolution of mixture model parameters induces dynamic model for time-varying intensity function
Department of Statistical Science, Duke University
Dynamic spatial point process
Intensity function
Parameters of DPMs
Dependent DP mixture with Generalized Polya Urn (Caron et al., 2007)
![Page 5: Chunlin Ji & Mike West Department of Statistical Science Duke University](https://reader036.fdocuments.us/reader036/viewer/2022062520/568160cc550346895dd000f4/html5/thumbnails/5.jpg)
System equation
-- Observation equation
Initial information
Dynamic spatial mixture modelling
Department of Statistical Science, Duke University
--Likelihood of spatial Poisson point process
--Dependent Dirichlet process
--Dirichlet process prior
![Page 6: Chunlin Ji & Mike West Department of Statistical Science Duke University](https://reader036.fdocuments.us/reader036/viewer/2022062520/568160cc550346895dd000f4/html5/thumbnails/6.jpg)
Time propagation models Generalized Polya Urn (GPU) scheme for random
partition
Time propagation models for cluster means
Time propagation models for covariances
Department of Statistical Science, Duke University
--physically attractive dynamic model
--discount factor-based stochastic model(Carvalho & West, 2008)
(Caron et al. 2007)
![Page 7: Chunlin Ji & Mike West Department of Statistical Science Duke University](https://reader036.fdocuments.us/reader036/viewer/2022062520/568160cc550346895dd000f4/html5/thumbnails/7.jpg)
SMC for Dirichlet process mixtures Previous work
SMC for nonparametric Bayesian models(Liu, 1996; MacEachern, et al. 1999)
Particle filter for mixtures(Fearnhead, 2004; Fearnhead & Meligkotsidou, 2007)
Particle learning for mixtures(Carvalho, et al., 2009)
Key point Marginalization of ; propagated and updated only for
SMC for dependent DP mixtures
SMC for time-varying DP mixtures (Caron et al., 2007)
--no marginalization, very low effective sample size (ESS)
Department of Statistical Science, Duke University
![Page 8: Chunlin Ji & Mike West Department of Statistical Science Duke University](https://reader036.fdocuments.us/reader036/viewer/2022062520/568160cc550346895dd000f4/html5/thumbnails/8.jpg)
SMC for dynamic (spatial) DP mixtures
Rao-Blackwellized Particle filter
Department of Statistical Science, Duke University
(Escobar & West ,1995)
(Caron et al., 2007)
![Page 9: Chunlin Ji & Mike West Department of Statistical Science Duke University](https://reader036.fdocuments.us/reader036/viewer/2022062520/568160cc550346895dd000f4/html5/thumbnails/9.jpg)
Simulation study for synthetic data
Department of Statistical Science, Duke University
a) Synthetic multi-target tracking scenario
b) Estimation of the intensity of the spatial point processes--image plots
c) Estimation of the intensity function--3D mesh plots
ESS=
![Page 10: Chunlin Ji & Mike West Department of Statistical Science Duke University](https://reader036.fdocuments.us/reader036/viewer/2022062520/568160cc550346895dd000f4/html5/thumbnails/10.jpg)
Human cell fluorescence microscopic image
Simulation study of cell fluorescence images
Department of Statistical Science, Duke University
Movie of estimated intensity based on the SMC output-DP mixtures.
Spatial point pattern generated by image segmentation
![Page 11: Chunlin Ji & Mike West Department of Statistical Science Duke University](https://reader036.fdocuments.us/reader036/viewer/2022062520/568160cc550346895dd000f4/html5/thumbnails/11.jpg)
Thank You
Department of Statistical Science, Duke University