Statistical System To Raise The Odds
提高解決問題機率的統計法
By F. D. Flam

A Long Island fisherman might have died in the Atlantic Ocean after falling off his boat one day last year if not for a once obscure field known as Bayesian statistics – a set of mathematical rules for using new data to continuously update beliefs or knowledge.
紐約長島的一名漁民去年某日在大西洋落海。若不是因為曾經鮮為人知的貝葉斯（貝氏）統計學，他可能已經喪命。這套數學法則可以藉由運用新數據不斷更新看法或知識。

The method was invented in the 18th century by an English minister named Thomas Bayes – by some accounts to calculate the probability of God’s existence. Now, Bayesian statistics has grown vastly more useful because of computing power that didn’t exist even 20 years ago. It is proving especially useful in approaching complex problems, including the search to find the fisherman, John Aldridge.
這種方法18世紀由英國基督教傳教士貝葉斯發明，有人說是為了計算上帝存在的機率。如今，貝氏統計法因為20年前還不存在的運算能力而用途大增，經證實特別適合解決複雜的問題，包括搜救落海的漁民歐德里吉。

Bayesian statistics is rippling through everything from physics to cancer research, ecology to psychology. And lately, those who adhere to the Bayesian way have been thrust into an intense debate over how scientists turn data into knowledge and predictions.
貝氏統計法已經實際運用在許多領域，包括物理學、癌症研究、生態學與心理學。最近，奉行此法者就科學家該如何將數據化為知識與預測，展開了熱烈討論。

Concern has been growing that some fields are not doing a very good job at this sort of analysis. In 2012, for example, a team at the biotech company Amgen announced that it had analyzed 53 cancer studies and found it could not replicate 47 of them. Similar follow-up analyses have cast doubt on so many findings in fields such as neuroscience and social science that researchers talk about a “replication crisis.”
有人擔心，某些領域此類分析做得不好。例如，美國安進生技公司研究團隊2012年表示，分析53項癌症研究後發現，其中有47項無法複製。類似後續分析使人對神經科學、社會科學等領域的許多發現起疑。研究人員稱之為「複製危機」。

Some are optimistic that Bayesian methods can improve the reliability of research by allowing scientists to crosscheck work done with the more traditional or “classical” approach, known as frequentist statistics.
部分人士樂觀認為，貝氏統計法使科學家得以反覆比對以較傳統或「古典」的頻率統計法獲得的研究成果，進而提高其可靠性。

The essence of the frequentist technique is to apply probability to data. If you suspect your friend has a weighted coin, for example, and you observe that it came up heads nine times out of 10, a frequentist would calculate the probability of getting such a result with an unweighted coin. The answer (about 1 percent) is not a direct measure of the probability that the coin is weighted; it’s a measure of how improbable the nine-in-10 result is.
頻率統計法的本質是把或然率運用於數據。例如，如果你懷疑你的朋友持有一枚加重的硬幣，而且看到它拋出10次有9次是人頭在上，相信頻率統計法的人會以一枚未加重的硬幣計算得出這種結果的機率。答案（約1%）不是直接估計硬幣加重的或然率，而是估算9次人頭在上不會出現的或然率。

By contrast, Bayesian calculations go straight for the probability of the hypothesis, factoring in not just the data from the coin-toss experiment but any other relevant information – including whether you have previously seen your friend use a weighted coin.
相較之下，貝氏統計法直接估算這種假設的或然率，考慮的因素不只是來自拋硬幣實驗的數據，還有其他相關資訊，包括你是否看到過你的朋友使用加重硬幣。

Frequentist statistics became the standard of the 20th century by promising objectivity. In the 2003 statistics primer “Dicing With Death,” Stephen Senn traces the technique’s roots to 18th-century England, when a physician named John Arbuthnot calculate the ratio of male to female births. Arbuthnot gathered records from 1629 to 1710 and found that in London, a few more boys were recorded every year. The odds that such an 82-year run could occur simply by chance were one in trillions.
頻率統計法因為使人對客觀性產生信心而成為20世紀的標準。盧森堡「方法論及統計學能力中心」主任塞恩在他2003年出版的入門書「與死亡丟骰子」中，把這種方法的起源追溯到18世紀的英國。當時內科醫師艾爾巴斯納計算男性與女性出生的比率。他蒐集1629至1710年之間的紀錄後發現，在倫敦，每年出生的男性略多於女性。如此結果在82年間湊巧發生的機率是幾兆分之一。

Later in the 1700s, the astronomer Daniel Bernoulli used a similar technique to investigate the curious geometry of the solar system, in which planets orbit the sun in a flat, pancake-shaped plane. If the orbital angles were purely random the solar system would look more like a sphere than a pancake. But Bernoulli calculated that all the planets orbited within seven degrees of the plane, known as the ecliptic. Bernoulli’s calculations put the odds at about one in 13 million. This number is called a p-value, the probability that an observed phenomenon or one more extreme could have occurred by chance. Results are considered “statistically significant” if the p-value is less than 5 percent.
1700年代稍後，荷蘭天文學家貝爾努里以類似技術研究令人好奇的太陽系幾何學。在太陽系，行星沿著薄煎餅狀的軌道環繞太陽運行。如果軌道的角度純粹出於隨機，太陽系看來會比較像一個球體而不是煎餅。然而貝爾努里估算，全部的行星在名為黃道的平面7度內環繞太陽運行。根據他的計算，機率大約1300萬分之一。這個數字又稱p值，指的是一個觀察到或一個更極端現象隨機出現的機率。如果p值低於5%，結果會被視為「具統計意義」。

But there is a danger in this tradition, said Andrew Gelman of Columbia University in New York. Even if scientists did the calculations correctly accepting everything with a p-value of 5 percent means that one in 20 “statistically significant” results are random noise. The proportion of wrong results published in journals is probably higher, Dr. Gelman said, because such findings are often counterintuitive.
然而紐約哥倫比亞大學教授傑爾曼表示，這種傳統有危險。即使科學家計算正確，接受p值5%的任何事物意味，20項「有統計意義」結果當中的一項是隨機噪音。傑爾曼指出，透過學術期刊發表的錯誤結果可能比例更高，因為這種結果往往違反直覺。

The Bayesian approach lends itself well to problems like searches, which involve a single incident and many different kinds of relevant data, said Lawrence Stone of Metron, a consulting firm in Virginia that works with the United States Coast Guard.
維吉尼亞州的Metron科學顧問公司長期與美國海岸防衛隊合作，該公司的史東表示，貝氏統計法有助於解決搜尋之類的問題，這些問題則涉及單一的意外事故及許多不同種類的相關資訊。

At first, all the Coast Guard knew about the fisherman lost at sea was that he fell off his boat between 9 p.m. and 6 a.m. Searchers added new information to their calculations – on prevailing currents, places the search helicopters had already flown and other clues. The system continued to narrow down the search area. A searcher in a helicopter finally spotted a man clinging to buoys. He had been in the water for 12 hours; he was hypothermic but alive.
海岸防衛隊所掌握有關歐德里吉的初步訊息是，他在晚間9點與清晨6點之間落海。搜救人員為他們的估計添加相關資訊，包括主要的海流方向、搜救直升機已經飛越的海面及其他線索。這套系統持續縮小搜尋範圍。一架直升機上的一名搜救人員終於看到一名男子在海面上緊緊抓住幾個浮筒。他落海已經12個小時。他已經失溫，但還活著。

Even in the jaded 21st century, it was considered something of a miracle.
即使在見怪不怪的21世紀，這還是被視為一次奇蹟。

原文參照：
http://www.nytimes.com/2014/09/30/science/the-odds-continually-updated.html

2014-10-14聯合報/G5版/UNITEDDAILYNEWS 陳世欽譯 原文參見紐時週報十版左