In these lecture the presenter describes a system of differential equation that is solved for a set of initial condition. The results are used to build a probabilistic model, using the distribution of values and the probability model for state transitions in a dynamic model. The dynamic network is then used to make inference on the system directly with out needing to solve the differential equation.
An interesting side note is that with deterministic differential equation describing a system (in this case a biological system) our observation of the state of the system is noisy and infrequent (once every 30 minutes). Further justifying the probabilistic approach over a deterministic approach.
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