Name: 貝氏推理的威力！| BBC Ideas (The power of Bayesian reasoning | BBC Ideas)
Uploaded: 2026-01-22T18:21:13.000Z
Duration: 4 min 56 s

情態副詞

every time you change your mind based on new information, like rethinking a decision after hearing a friend's advice, you're using something called Bayesian reasoning.

每次你根據新資訊改變想法，像是聽了朋友的建議後重新考慮一個決定，你其實就在使用一種叫做貝氏推理的東西。

基礎被動語態

Bayesian reasoning was first articulated by the Reverend Thomas Bayes, a clergyman from Tunbridge Wells in southern England, way back in the 18th century.

貝氏推理最早是由湯瑪斯·貝氏牧師提出的，他是一位來自英格蘭南部頓布里奇威爾斯的教士，早在18世紀就提出了。

In fact, his theory wasn't published until two years after he had died.

事實上，他的理論在他去世兩年後才出版。

But his work has gone on to profoundly shape science, medicine, and artificial intelligence.

但他的工作對科學、醫學和人工智慧產生了深遠的影響。

It even helped crack the Nazis Enigma code during World War II.

它甚至在第二次世界大戰期間幫助破解了納粹的恩尼格瑪密碼。

So what is Bayesian reasoning, and how can it help us understand the world?

那麼，貝氏推理是什麼？它又如何幫助我們理解這個世界呢？

湯瑪斯·貝氏提出了兩個重要的概念。

First, that our beliefs can be expressed as probabilities, and

第一，我們的信念可以用機率來表達，而且

second, how our beliefs should be revised when we obtain more information.

第二，當我們獲得更多資訊時，我們的信念應該如何修正。

Essentially, he produced a theory for learning from experience.

基本上，他提出了一個從經驗中學習的理論。

Bayesian analysis can be used in any situation where each new item of information changes our beliefs.

貝氏分析可以用在任何情況，只要有新的資訊出現，就會改變我們的信念。

Alan Turing and his team at Bletchley park used Bayesian ideas to learn about the settings of Enigma machines in World War II, changing their opinion as new patterns were found.

在第二次世界大戰期間，艾倫·圖靈和他在布萊切利園的團隊利用貝氏想法來瞭解恩尼格瑪機器的設定，隨著新模式的出現而改變他們的看法。

The spam filter on your email account will use Bayesian analysis to change its probability that your email message is spam as each new suspicious feature is detected.

你電子郵件帳戶裡的垃圾郵件過濾器會使用貝氏分析，隨著偵測到每個新的可疑特徵，來改變郵件是垃圾郵件的機率。

Take breast cancer Screening in the UK, mammograms are rather accurate, detecting about 90% of cancers, and

以英國的乳房癌篩檢為例，乳房攝影相當準確，大約能偵測到 90% 的癌症，而且

97% of women without cancer correctly get a negative test result.

97% 沒有罹患癌症的女性會正確得到陰性檢測結果。

Let's consider what we would expect to happen to 100 women being tested.

讓我們來看看我們預期對 100 位接受檢測的女性會發生什麼事。

Based on past experience of the rate of breast cancer among women getting mammograms, we would expect one out of the hundred to have cancer, and

根據過去女性接受乳房攝影時罹患乳癌的經驗比率，我們預期這 100 位女性中，有 1 位會罹患癌症，而

that case is almost certain to be picked up on the mammogram.

那種情況幾乎一定會在乳房攝影中被偵測到。

Of the remaining 99 without cancer, we would expect three women to get a false positive result.

在剩下的 99 位沒有罹患癌症的女性中，我們預期會有三位得到偽陽性結果。

So in total, we expect one plus three equals four positive tests.

所以總共，我們預期會有 1 加 3 等於 4 個陽性檢測結果。

From this perspective, looking only at the women who get a positive result, perhaps the test does not seem so accurate.

從這個角度來看，只看那些得到陽性結果的女性，也許這個檢測看起來沒那麼準確。

Around three out of four or 75% of the women recalled don't have cancer.

大約有四分之三，也就是 75% 被再次通知的女性沒有罹患癌症。

Further tests should rapidly identify these three false positives.

進一步的檢查應該能快速找出這三位偽陽性。

This is an example of using Bayesian analysis.

這就是一個使用貝氏分析的例子。

Since we are taking into account the base rate for the condition, our prior probability that a random woman being tested has breast cancer is 1%.

因為我們考慮了情況的基礎比率，我們隨機一位接受檢測的女性罹患乳癌的先驗機率是 1%。

And after getting a positive test result, this is updated to what is called a posterior probability, which is 1 out of 4 or 25% of course, further investigations will eventually change the probabilities of those who are recalled either to 0% or less, fortunately 100%.

而在得到陽性檢測結果後，這會更新成所謂的後驗機率，也就是 4 分之 1，當然是 25%，進一步的調查最終會將被再次通知者的機率改變為 0% 或，幸運的是 100%。

The use of Bayesian analysis in medical testing is now standard.

貝氏分析在醫學檢測上現在已經是標準做法了。

However, more controversial is the use of Bayesian methods in science, so called Bayesian inference.

不過，在科學上使用貝氏方法，也就是所謂的貝氏推論，就比較有爭議了。

The traditional view of science is that it is a completely objective activity, that data is analyzed without preconceptions and the results speak for the the Bayesian perspective is somewhat different.

科學的傳統觀點認為，科學是一項完全客觀的活動，數據分析時沒有預設立場，結果會自己說話，但貝氏觀點卻有點不一樣。

It acknowledges that there are always judgments underlying every analysis and that we don't start from a blank slate.

它承認在每次分析背後總是有一些判斷，而且我們並非從一張白紙開始。

Each set of data adds to our existing knowledge rather than standing entirely on its own.

每一組數據都會增加我們現有的知識，而不是完全獨立存在。

For example, clinical trials of new drugs are not designed in complete ignorance.

例如，新藥的臨床試驗並非在完全無知的狀態下設計的。

There is always some historical evidence available about the potential effectiveness of the new therapy, and

總會有一些關於新療法潛在療效的歷史證據，

expert judgments can be elicited and used to prioritize investigations and produce efficient designs.

並且可以徵詢專家意見，用來優先安排調查和設計出有效率的方案。

And it's even thought that we have Bayesian brains.

甚至有人認為我們的大腦就是貝氏的。

We don't start from scratch to interpret our sensations for each second that passes.

我們並不是從零開始，來解讀每一秒過去的感覺。

Instead, we always have prior expectations of what we might experience next, and

所以，我們總是對接下來可能會遇到的情況抱有先驗的預期，

then new observations update our beliefs accordingly.

然後新的觀察會據此更新我們的信念。

Fundamentally, Bayesian ideas reflect what it means to be human.

基本上，貝氏的想法反映了身而為人的意義。

我們活在一個充滿不確定性的世界，但是

we always have prior expectations of what might happen next, and

我們總是對接下來可能會發生的事情抱有先驗的預期，

we revise that uncertainty as we learn from experience, all based on the ideas of a rather obscure 18th century cleric from Tunbridge Wells.

然後隨著我們從經驗中學習，我們會修正這種不確定性，這一切都基於一位來自頓布里奇威爾斯的 18 世紀不起眼神職人員的想法。

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貝氏推理的威力！| BBC Ideas (The power of Bayesian reasoning | BBC Ideas)

perspective

articulate

vital

prioritize