The holiday season requires a close eye on the weather. Modern people do this, not by looking at the sky, but by consulting a smartphone. Yahoo, the most popular weather app, tells you the probability of rain, hour by hour.

在假日季，人们需要密切关注天气。现代人关注天气的方式不再是观察天象，而是求助于智能手机。雅虎(Yahoo)出的天气应用最受用户欢迎，该应用会告诉你每个小时的下雨概率。

But you don’t want to know the probability that it will rain. It either will rain or it won’t and you want to know which of these outcomes will occur. And you can never know whether such a prediction was accurate. Both rain and no rain are consistent with the claim that the probability that it would rain was 10 per cent.

但人们想知道的并不是下雨的概率。只有下雨和不下雨这两种可能性，人们想知道的是结果到底会是哪一种。人们永远无从判断这样的预测是否准确。不管是下雨还是不下雨，都符合下雨概率为10%的预测。

The British meteorological office gives some help in interpretation. It suggests that if the probability of rain was 10 per cent you might be willing to hang your sheets out to dry, but not a shirt needed for an important dinner. While this may be useful advice, however, it is not an explanation of the meaning of the statement that the probability of rain is 10 per cent.

英国气象局(Meteorological Office)为我们解读这种预测提供了一些帮助。该局建议，如果下雨概率为10%，那么你可能愿意把床单（而不是参加一场重要晚宴要穿的衬衫）晾到外面。虽然这可能是条有用的建议，但这并未解释“下雨概率为10%”这种说法的含义。

The analysis of probability originates in games of chance, in which the rules are sufficiently simple and well-defined that the game can be repeated in more or less identical form over and over again. If you toss a fair coin repeatedly, it will come up heads about 50 per cent of the time. If you can be bothered, you can verify that fact empirically. Perhaps more strikingly, the theory of probability tells you that if you repeatedly toss that coin 50 times you will get 23 or more heads about 67 per cent of the time, and you can verify that prediction empirically too.

概率分析起源于碰运气的游戏，这种游戏的规则非常简单明确，因此能够以大体相同的方式反复重玩。如果你反复扔一个正常的硬币，正面朝上的概率大约是50%。如果不怕麻烦的话，你可以通过实验去证实这一点。可能更令人吃惊的是，概率论告诉你，如果你扔50次硬币，那么有大约67%的概率，正面朝上的次数为23次或23次以上。这一点也可以通过实验来证实。

It is a stretch, but perhaps not a very long stretch, to extend this analysis of frequency to single events, and to say that the probability that England will win the toss in the fifth Ashes cricket test against Australia is 50 per cent. And that the probability the home side will win the toss at least 23 times in a decade of five-test match series is 67 per cent. Tosses to start sporting contests are repeated at similar events, and theory and experience validate the probabilistic approach.

如果将这种频率分析应用于单独的事件中，预测英格兰在“灰烬杯”(Ashes)板球赛第五场测试赛中掷硬币时掷赢澳大利亚的概率是50%，那确实牵强，但或许只是略微牵强。主场一方在10年的系列比赛（每场系列比赛举行5次测试赛）中至少掷赢23次的概率为67%。体育赛事通过掷硬币开赛的情形在类似的场合重复出现，理论和经验也证实了概率方法的正确性。

Perhaps one could stretch the approach further and apply it to the probability of rain. The Met Office might form a view of tomorrow’s weather. Records might show that it rains on 10 per cent of similar days. The difficulty is defining exactly what is meant by “a similar day”.

或许我们还可以将这种方法的应用范围进一步扩大，将其应用于推测下雨概率。英国气象局可能需要对未来一天的天气做出预测。纪录可能显示，在情况类似的其他日子里，下雨的天数占10%。而困难在于，如何准确定义“情况类似的其他日子”。

“A typical April day in England” is a rather loose concept.

“英国典型的四月天”是一个非常宽泛的概念。

However, this is not, in fact, what weather forecasters do. Their analysis is based on elaborate computer models and they tweak the assumptions of these models to generate many different predictions. What they mean when they say the probability of rain is 10 per cent is that rain occurs in 10 per cent of these simulations. The validity of that prediction depends on two rather implausible assumptions; that the model correctly describes the physical world, and that the range of assumptions made by the modellers properly reflects the full range of possible assumptions.

然而，这实际上并不是天气预报员采取的方法。他们的分析是基于复杂的计算机模型。通过微调这些模型的假设，他们得出了很多不同的预测。当他们说下雨概率为10%时，意思就是在这些模拟中有10%的情况会下雨。这种预测的可靠性取决于两个似乎不大合理的假设，即：模型正确地反映了现实世界，且分析人员的假设范围恰当地涵盖了所有可能出现的假设。

Despite these difficulties – and popular derision comparable to that experienced by economic forecasters – weather forecasters do rather well. Certainly short-term weather forecasts are better than medium-term economic forecasts. These weather forecasting models are constantly calibrated and adjusted in light of the wealth of data that the weather provides hour by hour, and the physical system that governs the weather is relatively constant, even if our understanding of it is limited.

尽管存在这些困难，遭受的公众嘲讽也与经济领域的预测者不相上下，但天气预报员做得相当不错。毫无疑问，短期的天气预报比中长期的经济预测更准确。天气预报模型会根据来自每小时天气状况的大量数据不断校准和调整，而控制天气的物理系统则相对固定，即使我们对它的理解有限。

In contrast, severe recessions, property bubbles and bank failures are relatively infrequent, and calibration by economists has come to mean tweaking models to better explain the past rather than revising them to better predict the future – a particularly dangerous methodology when there are many reasons to think that the underlying structure of the economy is in a state of constant flux.

与此形成对照的是，由于严重的衰退、房地产泡沫、银行破产相对罕见，经济学家的校准意味着将模型修正得能更好地解释过去，而不是更好地预测未来。考虑到我们有很多理由认为经济的基础结构始终处于不稳定状态，这种方法特别危险。

The further one moves from mechanisms that are well understood and events that are frequently repeated, the less appropriate is the use of probabilistic language. What does it mean to say: “I am 90 per cent certain that the extinction of the dinosaurs was caused by an object hitting the earth at Yucatán?” Not, I think, that on 90 per cent of occasions on which the dinosaurs were wiped out, the cause was an asteroid landing in what is now Mexico. There is a difference – often elided – between a probability and a degree of confidence in a forecast. It is one reason why we are better at avoiding drizzle than financial crises.

我们越不理解一种事件的发生机制、这种事件重复的频率越低，使用概率语言来描述这种事件就越不合适。“我90%肯定，恐龙灭绝是由于一个物体撞击了地球上的尤卡坦（Yucatán，位于现在的墨西哥）这个地方。”这句话是什么意思呢？我认为，这句话并不是说，在恐龙灭绝的所有情况中，有90%的情况都是由于一个小行星撞击了现在的墨西哥所在地。概率与预测结果的肯定程度是有区别的，这种区别往往被忽略。我们之所以更擅于躲避小雨（而不是金融危机），原因之一就在这里。