Bayesian and Decision Theoretic Tools

核心B：贝叶斯和决策理论工具运动序列的产生本质上受到不确定性的影响：为了快速移动，动物需要根据过去的知识估计下一步要做什么。这样的估计永远不可能是确定的。最近一本很受欢迎的书中的一个生动的例子表明，我们永远无法确定事件的顺序。每天被喂食将近一年的火鸡会在感恩节被宰杀。机器人、经济学、数据挖掘和人类行为模型等许多领域都在采用一种共同的方法来形式化不确定性：贝叶斯决策理论。我们将首先使用这些方法来预测三个实验实验室的行为。我们将继续提取需要由神经系统表示的相关变量（时间尺度，概率），以有效地生成序列。然后将这些变量与测量的神经信号相关联，以询问这些变量是如何表示的。

Core B: Bayesian and decision theoretic tools The production of movement sequences is inherently affected by uncertainty: to move rapidly the animal needs to estimate what to do next given past knowledge. Such estimates can never be certain. A colorful example from a recently popular book shows that we can never be certain about a sequence of events. The turkey that has been fed every day for close to a year gets slaughtered for Thanksgiving. Many communities such as robotics, economics, data mining and models of human behavior are converging on a common approach towards formalizing uncertainty: Bayesian decision theory. We will first use these methods to predict behaviors from each of the three experimental labs. We will continue to extract the relevant variables (timescales, probabilities) that need to be represented by the nervous system to efficiently produce sequences. These variables will then be correlated with measured neural signals to ask how these variables are represented. Moreover, uncertainty is central when analyzing data from neurons. When we are asking how neurons store and recall motor sequences we never directly measure the relevant variables, such as memory, we rather measure spikes or imaging signals that are affected by noise. A central topic for neural data analysis, therefore, is to combine many measurements (say 1000 spikes) into an estimate (of say tuning properties) that has small uncertainty (or narrow error-bars). We will use state of the art Bayesian data analysis techniques to analyze the data resulting from the proposed experiments in the other projects. Specifically we are interested in asking how neurons interact with one another using these Bayesian methods. Lastly, we will use state of the art decoding methods to ask how well various types of information are encoded by the measured signals. This is useful for the experimental projects as it allows asking how much information about a, variable of interest is encoded by neural signals.