Inferring oscillatory modulation in neural spike trains
Fig 3
Interaction of spike history and latent state.
Two inhomogeneous, history dependent spike trains, with first spike train A) generated with stochastic oscillational modulation at 10Hz and OCV at 0.18, and spiking at 40Hz, and the second spike train F) without modulation, spiking at 60Hz. Gibbs samples from 4 (3) separate LOST for first (second) spike train in B-E (G-I). In B-E and G-I, we show the 3 representative sampled quantities, frequency and modulus of the slowest root and the amplitude of the inferred latent state on the left, and the ISI distribution and spike history term on the right. The ground truth, sampled mean and 5-95% intervals of the sampled spike history term plotted in black, red and cyan, respectively. The differences between the different LOST runs is in how spike history knots were chosen, or if a fixed spike history function was used. For the first spike train A, B uses the standard knot choices, C uses a constant history set to 0 and D, a fixed spike history set to a time-compressed ground-truth history. For the second spike train, G uses the standard knot choice, H the ground truth and I the standard knots moved farther out in time. For the first spike train, misspecification of the history may lead to a false inference of a flat latent state, a latent state with high uncertainty in its parameters or the correct latent state. For the second spike train, a misspecified history can lead to a latent state with significant amplitude but with uncertain parameters, making the inference inconclusive.