论文标题
两位观察员的合作假设检验不对称信息
Cooperative Hypothesis Testing by Two Observers with Asymmetric Information
论文作者
论文摘要
我们考虑了两个观察者的二元假设检验问题。有两个可能的自然状态（或假设）。两个观察者收集的观察结果与自然的真实状态统计有关。观察者未知收集的观察结果和自然的真实状态的联合分布的知识。观察者需要解决两个问题：（i）已知自然状态：找到收集的局部信息的分布； （ii）真正的自然状态是未知的：通过解决第一个问题发现的分布，协作估算了相同的估计。我们提出了四种算法，每个算法都有两个阶段解决两个问题，重点是观察者和结果模式之间的信息交换。我们证明了算法的不同属性，包括以下内容：由于解决第一个问题而构建的概率空间取决于观察者的信息模式； （ii）解决第二个问题时，算法误差概率的衰减率取决于观察者之间的信息交换。我们提出了一个数字示例，证明了四种算法。
We consider the binary hypothesis testing problem with two observers. There are two possible states of nature (or hypotheses). Observations collected by the two observers are statistically related to the true state of nature. The knowledge of joint distribution of the observations collected and the true state of nature is unknown to the observers. There are two problems to be solved by the observers: (i) true state of nature is known: find the distribution of the local information collected; (ii) true state of nature is unknown: collaboratively estimate the same using the distributions found by solving the first problem. We present four algorithms, each having two phases where the two problems are solved, with emphasis on the information exchange between the observers and resulting patterns. We prove different properties of the algorithms including the following: the probability spaces constructed as a consequence of solving the first problem are dependent on the information patterns at the observers; (ii) the rate of decay of probability of error of algorithms while solving the second problem is dependent on the information exchange between the observers. We present a numerical example demonstrating the four algorithms.
