視覺的預測對動物的生存至關重要，它可以克服訊號從神經節細胞傳輸到大腦的時間延遲。研究指出預測作用主要發生在視網膜，其中包含對於動作的預測與時間上的預測。在我們的研究中，全域的刺激包括規則的與隨機的刺激模式被用來測試牛蛙視網膜的預測作用，並且以互信息(time-lag mutual information; TLMI)的分析方法來確認細胞的輸出是否能預測隨機的刺激。為了進一步了解視網膜是如何預測多樣化的刺激，我們採用群延遲(group delay)的概念，其可以描述一個信號在不同頻率域的延遲，而負群延遲則能導致訊號的預測。從一個延時回饋(delayed-feedback)模型，我們可以得到負群延遲的結果（因此又稱Negative group delay模型；NGD模型），而在群延遲的解析解裡，只有在低於\SI{1}{\hertz}時出現負值，因此，實驗結果顯示，低通濾波後的的隨機刺激在截止頻率更低時有更好的預測效果，此結果也得到了合理的解釋。另外，在互信息出現的雙峰與多峰的結果可以用以NGD模型為基礎的視網膜迴路重現，藉由理解這些模型，我們可以給予視網膜的預測作用在生理上更佳的解釋。

Prediction of vision is crucial for animals to survive. It can overcome the neuron delay during the transmission from retina ganglion cells to the brain. Studies show that prediction mainly occurs in retinae, including motion prediction and temporal prediction. In our work, whole field stimuli with regular and stochastic pattern are applied to confirm the temporal prediction in bullfrog retinae. The result of stochastic stimuli are analyzed by time-lag mutual information (TLMI) to determine the prediction in a cell. To better realize how retinae predict various stimuli, group delay ($\delta(\omega)$), which describes the signal delay as a function of frequency, is used. Negative group delay (NGD) leads to prediction. It can be demonstrated by a delayed feedback model (named negative group delay model, or NGD model). The analytic analysis of group delay shows that NGD of the model exists at low frequency domain ($f<\SI{1}{\hertz}$). This offers a reasonable explanation to the experiment result that low-pass stochastic stimuli can elicit larger prediction under low enough cut-off frequency ($f_c$). Also, the double or multiple peaks in TLMI can be reproduced by the circuit model which are based on the NGD model: NGD retinal circuit and the one with additional feedforward pathway, NGDFF retinal circuit. By understanding these models, we can give better physiological explanations of the anticipatory dynamics in a retina.

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