1. Dynamic spatial mixture modelling and its application in Bayesian tracking for cell fluorescent microscopic imaging Chunlin Ji & Mike West Department of Statistical Science Duke University Department of Statistical Science, Duke University JSM 2009, Washington, DC Aug. 4, 2009

2. 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

3. 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 )

4. 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)

5.  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

6. 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)

7. 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

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

9. 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=

10. 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

11. Thank You Department of Statistical Science, Duke University