One Kind Of Models For Stochastic Encoding And Bayesian Decoding Of Neuronal Populations

It is theoretically significant to study the encoding and decoding mechanism of neuronal population for revealing how the brain deals with information, discriminates stimulus and cognizes the world. The random response of neurons to stimulus is called the encoding of neuronal populations, and decoding is to estimate the stimulus with the information from the responses of neuronal populations. This process shows a great complexity as the encoding and decoding of neuronal populations is influenced by many factors and disturbances. From what has been discussed above, it is necessary to do some further research.In the first chapter we briefly describe the research background and some preliminary knowledge about the encoding and decoding of neuronal populations. In the second chapter we mainly discuss the encoding and decoding models of neuronal populations for two-dimension stimulus. To realize encoding the response of neurons we suppose that the firing rates follow Poisson distribution, and the related tuning functions are multidimensional Gaussian distributions. Decoding means statistical inference by Bayesian method. Through the Bayesian decoding we can get the mean and variance of the posterior distribution about the two-dimension stimulus. In addition, we also discuss the encoding and decoding of the multi-sensory neurons about the two-dimension stimulus. Finally, by numerical simulations we verify that the integrated estimate of the stimulus from multi-sensory neurons is superior to that from the single sensory neurons. In the third chapter, considering prior information we first give a deciding function to determine whether the aim appears, and then calculate the probability density function of firing rates for the neuronal population. Based on these we derive the expression of the deciding function. Finally, we verify the correctness of the theoretical model by using numerical simulations. In the fourth chapter we consider the firing rates with random amplitude during the process of encoding, and we assume that there exist correlations between firing rates. For the first time we put forward a model in which the correlation coefficients depend on the random amplitude. In this new model we study the Fisher information of the neuronal population, and estimate the value of stimulus by maximum likelihood method. We then show by numerical simulations that the neuronal population can identify different stimulus.