Bayesian hypothesis testing and experimental design for two-photon imaging data
Fig 3
Application of a warping function to model input features.
Data: ROI from a retinal bipolar cell filled with OGB-1 via sharp electrode injection. Model: RBF kernel, 300 inducing inputs, 20 iterations per fit, best of 3 fits per model. a: “Full-field chirp” stimulus (top). Autocorrelation functions corresponding to Gaussian curves fit to the empirical autocorrelation function over a 500 ms window (middle). Length scale parameter of the Gaussian distribution fitted to the autocorrelation functions. b: Cumulative sum of the inverse lengthscale over time. If the signal were stationary, the lengthscale would be constant, corresponding to the dashed line. This cumulative sum maps time onto a warped time dimension. c: Full field chirp stimulus with observations of the activity of one ROI labelled with OGB-1. d: The same stimulus and observations after a warping operation has been applied. e: GP fitted to the original data. f: GP fitted to the warped data. The function has been projected back onto un-warped time. Note the increased uncertainty in regions where the stimulus is changing rapidly and the variations in the smoothness of the inferred signal over time.