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
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
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 )
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)
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
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)
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
SMC for dynamic (spatial) DP mixtures
Rao-Blackwellized Particle filter
Department of Statistical Science, Duke University
(Escobar & West ,1995)
(Caron et al., 2007)
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=
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
Thank You
Department of Statistical Science, Duke University