Asymptotic theory of information-theoretic experimental design
Asymptotic theory of information-theoretic experimental design
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DOI：
10.1162/0899766053723032
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发表时间：
2005-07-01
影响因子：
2.9
通讯作者：
Paninski, L
中科院分区：
文献类型：
--
作者：
Paninski, L
我们讨论了一种以相对有效的方式收集数据的想法。我们的观点是贝叶斯和信息论：在任何给定的试验中，我们希望自适应地选择输入，使得系统的（未知）状态和（随机）输出之间的互信息最大，给定任何先验信息（包括在任何以前的试验中收集的数据）。我们证明了一个定理，量化这种策略的有效性，并给出了一些说明性的例子比较这种自适应技术的性能，更常见的非自适应实验设计。特别是，我们计算的信息最大化策略的渐近效率，并证明了这种方法是在一个定义明确的意义上从来没有更有效的，一般更有效的非自适应策略。例如，我们能够明确计算的渐进相对效率的阶梯方法广泛应用于心理物理学研究，并证明这种效率的依赖形式的心理功能的输出响应。
We discuss an idea for collecting data in a relatively efficient manner. Our point of view is Bayesian and information-theoretic: on any given trial, we want to adaptively choose the input in such a way that the mutual information between the (unknown) state of the system and the (stochastic) output is maximal, given any prior information (including data collected on any previous trials). We prove a theorem that quantifies the effectiveness of this strategy and give a few illustrative examples comparing the performance of this adaptive technique to that of the more usual nonadaptive experimental design. In particular, we calculate the asymptotic efficiency of the information-maximization strategy and demonstrate that this method is in a well-defined sense never less efficient-and is generically more efficient-than the nonadaptive strategy. For example, we are able to explicitly calculate the asymptotic relative efficiency of the staircase method widely employed in psychophysics research and to demonstrate the dependence of this efficiency on the form of the psychometric function underlying the output responses.