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