Sequential updating via dynamic hierarchical models: A Bayesian approach to longitudinal data analysis

Most statistical analysis, theory and practice, is concerned with static models; models with a proposed set of parameters whose values are fixed across observational units. Static models implicitly assume that the quantified relationships remain the same across the design space of the data. While this is reasonable under many circumstances this can be a dangerous assumption when dealing with sequentially ordered data. The mere passage of time always brings fresh considerations and the interrelationships among parameters, or subsets of parameters, may need to be continually revised. ^ When data are gathered sequentially dynamic interim monitoring may be useful as new subject-specific parameters are introduced with each new observational unit. Sequential imputation via dynamic hierarchical models is an efficient strategy for handling missing data and analyzing longitudinal studies. Dynamic conditional independence models offers a flexible framework that exploits the Bayesian updating scheme for capturing the evolution of both the population and individual effects over time. While static models often describe aggregate information well they often do not reflect conflicts in the information at the individual level. Dynamic models prove advantageous over static models in capturing both individual and aggregate trends. Computations for such models can be carried out via the Gibbs sampler. An application using a small sample repeated measures normally distributed growth curve data is presented. ^

Cellular dynamic simulator: an event driven molecular simulation environment for cellular physiology.

In this paper, we present the Cellular Dynamic Simulator (CDS) for simulating diffusion and chemical reactions within crowded molecular environments. CDS is based on a novel event driven algorithm specifically designed for precise calculation of the timing of collisions, reactions and other events for each individual molecule in the environment. Generic mesh based compartments allow the creation / importation of very simple or detailed cellular structures that exist in a 3D environment. Multiple levels of compartments and static obstacles can be used to create a dense environment to mimic cellular boundaries and the intracellular space. The CDS algorithm takes into account volume exclusion and molecular crowding that may impact signaling cascades in small sub-cellular compartments such as dendritic spines. With the CDS, we can simulate simple enzyme reactions; aggregation, channel transport, as well as highly complicated chemical reaction networks of both freely diffusing and membrane bound multi-protein complexes. Components of the CDS are generally defined such that the simulator can be applied to a wide range of environments in terms of scale and level of detail. Through an initialization GUI, a simple simulation environment can be created and populated within minutes yet is powerful enough to design complex 3D cellular architecture. The initialization tool allows visual confirmation of the environment construction prior to execution by the simulator. This paper describes the CDS algorithm, design implementation, and provides an overview of the types of features available and the utility of those features are highlighted in demonstrations.