180 CHAPTER 6 State Space Modeling space filtering with an estimated dynamic parameter t , p(x t |y 0:t , t ); and state space smoothing with an estimated static parameter , p(x t |y 0:T , ). A third problem is one of prediction, in which we consider p(x t |y 0:T , ) where t > T . This problem arises naturally in the design of algorithms for brain­computer interfaces (Serruya et al., 2002; Taylor et al., 2002; Musallam et al., 2004; Hochberg et al., 2006; Santhanam et al., 2006). 6.3 APPLICATIONS OF THE STATE SPACE PARADIGM IN NEUROSCIENCE DATA ANALYSIS The following sections discuss how the state space paradigm is applied in neuroscientific data analysis. 6.3.1 Neural Spike Train Decoding and Point Process Filter Algorithms The development of multiple electrode arrays allows neuroscientists to record