Smoothness Priors Analysis of Time Series

Abstract

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A mixed filter algorithm for cognitive state estimation from simultaneously recorded continuous and binary measures of performance

“…For systems with low-dimensional state and observation models, (5) and (6) can be evaluated numerically (Kitagawa and Gersch 1996). As the dimension of the system increases, numerical computation becomes less feasible.…”

“…Under the Gaussian approximation, the recursion defined by the probability densities in (5) and (6) becomes a recursive filter because it simplifies to computing recursively just the means and variances of these probability densities. In the special case that the state process is a linear Gaussian system and the observation model is a linear Gaussian function of the state process, this recursive computation of the means and variances is the Kalman filter (Fahrmeir and Tutz 2002;Kitagawa and Gersch 1996;Mendel 1995;Roweis and Ghahramani 1999). This would be true if our analysis did not include the binary performance measures.…”

“…State-space modeling is an established framework widely used to study dynamical processes in engineering, computer science and statistics (Fahrmeir and Tutz 2002;Kitagawa and Gersch 1996;Mendel 1995;Roweis and Ghahramani 1999). Applications of this paradigm range from control systems (Kitagawa and Gersch 1996;Mendel 1995), speech recognition (Becchetti and Ricotti 1999), studies of protein structure (White et al 1994), analysis of genetic networks (Harbison et al 2004), studies of neural representations of biological signals (Brown et al 1998;Barbieri et al 2004;Eden et al 2004;Smith and Brown 2003) and analyses of learning (Wirth et al 2003;Smith et al 2004).…”

“…Applications of this paradigm range from control systems (Kitagawa and Gersch 1996;Mendel 1995), speech recognition (Becchetti and Ricotti 1999), studies of protein structure (White et al 1994), analysis of genetic networks (Harbison et al 2004), studies of neural representations of biological signals (Brown et al 1998;Barbieri et al 2004;Eden et al 2004;Smith and Brown 2003) and analyses of learning (Wirth et al 2003;Smith et al 2004). A state-space model consists of two equations: a state equation and an observation equation.…”

“…When the state and observation models are both linear and Gaussian, the well-known Kalman filter gives the optimal estimate of the unobserved states (Mendel 1995). Extensions of this filter to nonlinear system and/or nonlinear observation models have been widely studied using a range of computational strategies (Fahrmeir and Tutz 2002;Kitagawa and Gersch 1996;White et al 1994;Doucet et al 2001). …”