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，动物需要估计在过去的知识下下一步该做什么。这种估计永远无法确定。最近流行的一本书中有一个生动的例子表明，我们永远无法确定一系列事件。一年来每天都被喂食的火鸡在感恩节被宰杀。许多团体，如机器人，经济学，数据挖掘和人类行为模型，正在汇聚到一个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），以有效地产生序列。然后将这些变量与测量的神经信号相关联，以询问这些变量如何表示。 此外，在分析来自神经元的数据时，不确定性是核心。当我们询问神经元如何存储和回忆运动序列时，我们从不直接测量相关变量，如记忆，而是测量受噪声影响的尖峰或成像信号。因此，神经数据分析的一个中心主题是将联合收割机许多测量（比如1000个尖峰）组合成具有小不确定性（或窄误差条）的估计（比如调谐特性）。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的数据。具体来说，我们感兴趣的是询问神经元如何使用这些贝叶斯方法相互作用。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进行编码的程度。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.