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确定。最近一本畅销书中的一个五颜六色的例子表明，我们永远无法确定一系列事件。近一年来每天喂食的火鸡在感恩节被宰杀。许多领域，如机器人学、经济学、数据挖掘和人类行为模型，正汇聚在一种将不确定性形式化的共同方法上：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。我们将继续提取相关变量(时间尺度、概率)，这些变量需要由神经系统表示才能有效地产生序列。然后，这些变量将与测量的神经信号相关联，以询问这些变量是如何表示的。 此外，在分析来自神经元的数据时，不确定性是核心问题。当我们询问神经元如何存储和回忆运动序列时，我们从来没有直接测量相关变量，如记忆，而是测量受噪声影响的棘波或成像信号。因此，神经数据分析的一个中心主题是将许多测量(比方说1000个尖峰)组合成具有小不确定性(或窄误差条)的估计(比方说调谐特性)。我们将使用最先进的贝叶斯数据分析技术来分析其他项目中拟议实验产生的数据。具体地说，我们感兴趣的是，神经元是如何使用这些贝叶斯方法相互作用的。最后，我们将使用最先进的解码方法来询问测量信号对各种类型的信息的编码效果如何。这对实验项目很有用，因为它允许询问神经信号编码了多少关于感兴趣变量的信息。

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.