标题： 对编辑的回信 显示英文标题

标题： Response to the Letter to the Editor

摘要： 这篇论文引起了全球媒体（包括电视和报纸）的关注。 此外，我们收到了信件、电子邮件和电话。 我们最喜欢的一条是语音留言，询问我们是否可以回拨澳大利亚的电话，在那时我们会知道真正刺杀肯尼迪的人是谁。 我们欢迎回应Fiorentino先生给编辑的信的机会。 Fiorentino先生声称我们的“基于三颗或更多独立子弹的前提下关于第二个射手可能性的陈述是明显错误的”。 作为回应，我们想简单地引用杰拉德·波斯纳的著作《案情已明》第327页的内容，这是一本最著名的支持单一凶手理论的作品：“如果康纳利被另一颗子弹击中，那么必须是由第二个射手发射的，因为沃伦委员会自己的重建显示奥尔沃德不可能在1.4秒内操作枪栓并再次射击。” Fiorentino先生还声称“第二个致命缺陷是使用了一个基于贝叶斯定理的相当简单的公式”。 设$E$表示证据，$T$表示只有两颗子弹（因此只有一个射手）的理论。 我们使用贝叶斯定理从$P(E|T)$和先验概率$P(T)$假设性地计算出$P(T|E)$。 为了使$P(T|E)$比$P(\bar{T}|E)$更有可能十倍，先验概率的比值[i.e.,$P(T) / P(\bar{T})$]必须大于15。 因此，我们再次得出结论，这严重质疑了古恩博士的结论，即证据支持仅两颗子弹。 令人遗憾的是，这远不是概率在公众关注的案件中被误解和/或误用的第一次。 一个著名的英国例子是克拉克案。 详情请参见诺布尔斯和施夫(2005)。 最后，我们欢迎并鼓励科学界的成员提供对数据的替代分析。 显示英文摘要

摘要： This paper has attracted interest around the world from the media (both TV and newspapers). In addition, we have received letters, emails and telephone calls. One of our favorites was a voicemail message asking us to return a call to Australia at which point we would learn who really killed JFK. We welcome the opportunity to respond to the letter to the editor from Mr. Fiorentino. Mr. Fiorentino claims that our ``statement relating to the likelihood of a second assassin based on the premise of three or more separate bullets is demonstrably false.'' In response we would like to simply quote from page 327 of Gerald Posner's book Case Closed, one of the most well known works supporting the single assassin theory: ``If Connally was hit by another bullet, it had to be fired from a second shooter, since the Warren Commission's own reconstructions showed that Oswald could not have operated the bolt and refired in 1.4 seconds.'' Mr. Fiorentino also claims that the ``second fatal flaw is the use of a rather uncomplicated formula based on Bayes Theorem.'' Let $E$ denote the evidence and $T$ denote the theory that there were just two bullets (and hence a single shooter). We used Bayes Theorem to hypothetically calculate $P(T|E)$ from $P(E|T)$ and the prior probability $P(T)$. In order to make $P(T|E)$ ten times more likely than $P(\bar{T}|E)$, the ratio of the prior probabilities [i.e., $P(T) / P(\bar{T})$] would have to be greater than 15. Thus, we again conclude that this casts serious doubt on Dr. Guinn's conclusion that the evidence supported just two bullets. Sadly, this is far from the first time that probability has been misunderstood and/or misapplied in a case of public interest. A notable British example is the Clark case. See Nobles and Schiff (2005) for details. Finally, we welcome and, in fact, encourage members of the scientific community to provide alternative analyses of the data.