Statistical analysis of neural data : Continuous - space models ( First 2 / 3 )

1 Autoregressive models and Kalman filter models are Gaussian Markov and hidden Markov models, respectively 3 1.1 Example: voltage smoothing and interpolation; inferring biophysical parameters 5 1.2 We may perform inference in the Kalman model either via the forward-backwards recursion or by direct optimization methods . . . . . . . . . . . . . . . . . . . 9 1.3 The Kalman model is only identifiable up to linear transformations of the state variable . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 1.4 Examples: intermittent, noisy, filtered, nonlinearly transformed voltage observations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 1.5 Example: spike sorting given nonstationary data using a mixture-of-Kalmanfilters model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21