Finish spatial information calculations
Currently, both spatial information (in bits) and sparsity (in percent) exist in nelpy and can easily be computed on a TuningCurve1D object.
However, according to Markus et al. (1994) we should extend our approach as follows:
In order to account for the effects of low firing rates (with fewer spikes there is a tendency toward higher information content) or random bursts of firing, the spike firing time-series was randomly offset in time from the rat location time-series, and the information content was calculated. A distribution of the information content based on 100 such random shifts was obtained and was used to compute a standardized score (Zscore) of information content for that cell. While the distribution is not composed of independent samples, it was nominally normally distributed, and a Z value of 2.29 was chosen as a cut-off for significance (the equivalent of a one-tailed t-test with P = 0.01 under a normal distribution).
Reference: Markus, E. J., Barnes, C. A., McNaughton, B. L., Gladden, V. L., and Skaggs, W. E. (1994). "Spatial information content and reliability of hippocampal CA1 neurons: effects of visual input", Hippocampus, 4(4), 410-421.
Also, we should look at more contemporary sources for the state-of-the-art. @sillyproject ? @jchutrue ?
@sillyproject can we still compare your spatial information to mine that I implemented in nelpy? It would be useful to have verified results. Also, do you think you can implement the second part described above?