State-Space Model with One Binary, Two Continuous, and a Spiking-Type Observation

Spiking-type observations are occasionally recorded in experiments. For instance, neural spiking activity may be recorded from a macaque monkey engaged in a learning experiment or an EKG signal may be recorded from a human subject in an experiment. In such instances, we can model the spiking-type variable using a conditional intensity function (CIF). The CIF is similar to the rate parameter in a Poisson distribution but is more general. With spiking-type observations, we usually assume that our state variable \(x_{k}\) affects the rate of spiking through the CIF.