Statistical Computing Model Of Neural Coding

Neural population encoding and analysis of spike train are key problems in the field of neural information processing. With the development of multi-electrodes synchronously recoding technology, theory and methods about multi-spike trains are needed to find patterns and rules in neural information processing in large data sets. First, we introduce homogenous Poisson model for neural firing, including neural response function, instantaneous intensity, possibility function and waiting time. Then inhomogeneous Poisson model and possibility density of ISI (InterSpike-Interval) are introduced. Also, we verified the Fano Factor of inhomogeneous Poisson model. Finally, we present the thinning algorithm which is used to simulate spike train.Second, we reveal Bayesian methods, based on high-order multiple Poisson model, to classify animal’s behavior. We propose spike train transformation methods, give out the estimator for the posterior GAMMA possibility of the Poisson intensity, and propose the measurement of uncertainty of Poisson intensity and MLE of spike train classification. Then, we present the strategy to integrate multi-classification. Our methods are applied to data from U maze and Y maze of mouse experiments which contains about350trails, and the correct rate is up to about97%.Third, we analyze discrete information expressing rate of neural population and the factors affecting the rate. First, we define neural discrete information expressing rate which is the possibility that neural could express the right information to the next level. Then we study how distribution of state on frequency band, length of spike train, spatial setup of state affect the information expressing rate and robustness. Finally, the connection between information expressing rate and Maclaurin’s formula, as well as the optimistic state distribution, is presented.At last, method to detect functional neural cliques is proposed. We first discuss the situation in which direct Person correlation falls and define measurement of correlation of multi-scale dynamic spike train. Then we apply min-cut algorithm to detect neural functional cliques and to sort neurons by their relevance to certain task. Finally, we apply the method to data from U maze experiment of mouse and randomized data, then give out comparative analysis.