TEDGlobal 2005
Peter Donnelly: How juries are fooled by statistics
Peter Donnelly：被統計愚弄的陪審團
Filmed:
Readability: 3.6
1,279,860 views
牛津數學家Peter Donnelly揭露一般大眾在解讀統計資訊時所會犯的錯誤，這些錯誤在罪犯的審判上，會造成致命的影響。
Peter Donnelly - Mathematician; statistician
Peter Donnelly is an expert in probability theory who applies statistical methods to genetic data -- spurring advances in disease treatment and insight on our evolution. He's also an expert on DNA analysis, and an advocate for sensible statistical analysis in the courtroom. Full bio
Peter Donnelly is an expert in probability theory who applies statistical methods to genetic data -- spurring advances in disease treatment and insight on our evolution. He's also an expert on DNA analysis, and an advocate for sensible statistical analysis in the courtroom. Full bio
Double-click the English transcript below to play the video.
00:25
As other speakers have said, it's a rather daunting experience --
0
0
2000
我像其他講者一樣，覺得在各位面前演講，
00:27
a particularly daunting experience -- to be speaking in front of this audience.
1
2000
3000
是一件很令人害怕的事。
00:30
But unlike the other speakers, I'm not going to tell you about
2
5000
3000
但我不像其他演講者，我不會講述有關宇宙的奧妙，
00:33
the mysteries of the universe, or the wonders of evolution,
3
8000
2000
或是講述演化的神奇之處，
00:35
or the really clever, innovative ways people are attacking
4
10000
4000
我也不會講述那些人們用來對抗世上不公不義
00:39
the major inequalities in our world.
5
14000
2000
所採行的創新招術，
00:41
Or even the challenges of nation-states in the modern global economy.
6
16000
5000
甚至那些現代國家所需要面對的全球經濟問題，
00:46
My brief, as you've just heard, is to tell you about statistics --
7
21000
4000
我會講的就是剛才主持人所提到的：統計學，
00:50
and, to be more precise, to tell you some exciting things about statistics.
8
25000
3000
正確地說，我會告訴各位統計學有趣之處，
00:53
And that's --
9
28000
1000
那就是...
00:54
(Laughter)
10
29000
1000
(笑聲)
00:55
-- that's rather more challenging
11
30000
2000
這項挑戰可不亞於在我之前
00:57
than all the speakers before me and all the ones coming after me.
12
32000
2000
或在我之後出現的講者啊！
00:59
(Laughter)
13
34000
1000
(笑聲)
01:01
One of my senior colleagues told me, when I was a youngster in this profession,
14
36000
5000
有一位前輩在我剛加入這一行時很驕傲地告訴我，
01:06
rather proudly, that statisticians were people who liked figures
15
41000
4000
他說，統計學家是一群很喜歡數字的人，
01:10
but didn't have the personality skills to become accountants.
16
45000
3000
但卻不具備得以使他們成為會計師的人際關係技巧。
01:13
(Laughter)
17
48000
2000
(笑聲)
01:15
And there's another in-joke among statisticians, and that's,
18
50000
3000
還有另一個關於統計學家的笑話：
01:18
"How do you tell the introverted statistician from the extroverted statistician?"
19
53000
3000
「要怎麼分辨一個統計學家的個性是內向還是外向？」
01:21
To which the answer is,
20
56000
2000
答案是：
01:23
"The extroverted statistician's the one who looks at the other person's shoes."
21
58000
5000
「外向的統計學家會盯著別人的鞋子看。」
01:28
(Laughter)
22
63000
3000
(笑聲)
01:31
But I want to tell you something useful -- and here it is, so concentrate now.
23
66000
5000
我要告訴各位一些有用的資訊，所以請專心一點。
01:36
This evening, there's a reception in the University's Museum of Natural History.
24
71000
3000
今晚，在學校的自然歷史博物館裡有一場招待會，
01:39
And it's a wonderful setting, as I hope you'll find,
25
74000
2000
我希望各位覺得辦得還不錯，
01:41
and a great icon to the best of the Victorian tradition.
26
76000
5000
主題是維多利亞時期的優良傳統。
01:46
It's very unlikely -- in this special setting, and this collection of people --
27
81000
5000
在這場盛會裡，聚集了很多人，
01:51
but you might just find yourself talking to someone you'd rather wish that you weren't.
28
86000
3000
但你有可能會和一個你根本不想說話的人對談，
01:54
So here's what you do.
29
89000
2000
我給各位一點建議，
01:56
When they say to you, "What do you do?" -- you say, "I'm a statistician."
30
91000
4000
當他們問說：「你做哪一行？」，你就回答：「我是個統計學家。」
02:00
(Laughter)
31
95000
1000
(笑聲)
02:01
Well, except they've been pre-warned now, and they'll know you're making it up.
32
96000
4000
除非先前就有人告訴他們這個小伎倆，否則他們不會知道你在說謊。
02:05
And then one of two things will happen.
33
100000
2000
接下來就有二種可能，
02:07
They'll either discover their long-lost cousin in the other corner of the room
34
102000
2000
他們要不是會突然發現久未聯絡的表兄弟
02:09
and run over and talk to them.
35
104000
2000
出現在大廳另一頭而趕去找他說話，
02:11
Or they'll suddenly become parched and/or hungry -- and often both --
36
106000
3000
要不就會突然覺得很渴或很餓，或是又渴又餓，
02:14
and sprint off for a drink and some food.
37
109000
2000
不得不趕緊去找些東西來吃吃或喝喝。
02:16
And you'll be left in peace to talk to the person you really want to talk to.
38
111000
4000
這時你就獲得自由了，你可以找你想要說話的人聊天了。
02:20
It's one of the challenges in our profession to try and explain what we do.
39
115000
3000
做我們這一行的人，有時很難向別人解釋我們在做什麼，
02:23
We're not top on people's lists for dinner party guests and conversations and so on.
40
118000
5000
我們也不是別人晚宴賓客或是聊天的首選名單，
02:28
And it's something I've never really found a good way of doing.
41
123000
2000
甚至我自己也覺得很難説明我的工作内容。
02:30
But my wife -- who was then my girlfriend --
42
125000
3000
但我的太太，那時還是我的女友，
02:33
managed it much better than I've ever been able to.
43
128000
3000
倒是説明得比我還清楚。
02:36
Many years ago, when we first started going out, she was working for the BBC in Britain,
44
131000
3000
多年以前，當我們開始約會時，她那時在英國的BBC(英國廣播公司)工作，
02:39
and I was, at that stage, working in America.
45
134000
2000
而我那時則在美國工作，
02:41
I was coming back to visit her.
46
136000
2000
有一次我要回來英國跟她見面。
02:43
She told this to one of her colleagues, who said, "Well, what does your boyfriend do?"
47
138000
6000
她和一個同事有了這樣的對話，對方問：「你男朋友是做什麼的？」
02:49
Sarah thought quite hard about the things I'd explained --
48
144000
2000
於是莎拉把我之前對她解釋的工作內容
02:51
and she concentrated, in those days, on listening.
49
146000
4000
再仔細地想了一遍，她在那時候都還很認真地聽我說話。
02:55
(Laughter)
50
150000
2000
(笑聲)
02:58
Don't tell her I said that.
51
153000
2000
不要告訴她我說過這件事。
03:00
And she was thinking about the work I did developing mathematical models
52
155000
4000
接著她想到我那時正在為解開演化與現代基因之謎
03:04
for understanding evolution and modern genetics.
53
159000
3000
建立一些數學模型，
03:07
So when her colleague said, "What does he do?"
54
162000
3000
所以當她的同事問道：「他是做什麼的？」
03:10
She paused and said, "He models things."
55
165000
4000
她停了好一會兒才說：「他是做模型的。」
03:14
(Laughter)
56
169000
1000
(笑聲)
03:15
Well, her colleague suddenly got much more interested than I had any right to expect
57
170000
4000
哇！她的同事突然對我所做的事感到高度興趣，
03:19
and went on and said, "What does he model?"
58
174000
3000
接著問：「他做什麼模型？」
03:22
Well, Sarah thought a little bit more about my work and said, "Genes."
59
177000
3000
莎拉想了一會兒，說：「基因。」
03:25
(Laughter)
60
180000
4000
(笑聲)
03:29
"He models genes."
61
184000
2000
「他為基因建立模型。」
03:31
That is my first love, and that's what I'll tell you a little bit about.
62
186000
4000
莎拉是我的初戀，只能說到這裡了。
03:35
What I want to do more generally is to get you thinking about
63
190000
4000
接下來，我想讓各位想想，我們所處的世界
03:39
the place of uncertainty and randomness and chance in our world,
64
194000
3000
是不是充滿了不確定性、各種隨機因素與機會？
03:42
and how we react to that, and how well we do or don't think about it.
65
197000
5000
我們的反應又是如何，有或沒有意識到這件事呢？
03:47
So you've had a pretty easy time up till now --
66
202000
2000
剛剛那幾分鐘各位都聽得很輕鬆，
03:49
a few laughs, and all that kind of thing -- in the talks to date.
67
204000
2000
有笑話還有一些別的事情，
03:51
You've got to think, and I'm going to ask you some questions.
68
206000
3000
但各位得動動腦，我要問各位幾個問題。
03:54
So here's the scene for the first question I'm going to ask you.
69
209000
2000
在我問各位第一個問題之前，
03:56
Can you imagine tossing a coin successively?
70
211000
3000
我要先請各位想像一下連續投擲幾次銅板的畫面。
03:59
And for some reason -- which shall remain rather vague --
71
214000
3000
基於一些我們還無法解釋的因素，
04:02
we're interested in a particular pattern.
72
217000
2000
統計學家對於銅板正反面出現的次序很感興趣，
04:04
Here's one -- a head, followed by a tail, followed by a tail.
73
219000
3000
例如：先是人頭、再來字、再來一次字。
04:07
So suppose we toss a coin repeatedly.
74
222000
3000
假設我們不斷重覆投擲一個銅板，
04:10
Then the pattern, head-tail-tail, that we've suddenly become fixated with happens here.
75
225000
5000
那麼「人頭、字、字」這個順序就是我們關注的重點，
04:15
And you can count: one, two, three, four, five, six, seven, eight, nine, 10 --
76
230000
4000
接下來你數：1, 2, 3, 4, 5, 6, 7, 8, 9, 10...
04:19
it happens after the 10th toss.
77
234000
2000
在第10次投擲時才出現。
04:21
So you might think there are more interesting things to do, but humor me for the moment.
78
236000
3000
你一定在想這有什麼好玩的？但還是先遷就我一下。
04:24
Imagine this half of the audience each get out coins, and they toss them
79
239000
4000
想像一下，這一半的聽眾都拿到一個銅板，開始投擲，
04:28
until they first see the pattern head-tail-tail.
80
243000
3000
要一直投到看到「人頭、字、字」這個順序為止。
04:31
The first time they do it, maybe it happens after the 10th toss, as here.
81
246000
2000
第一輪，或許就像我剛才說的，到第十次才看到，
04:33
The second time, maybe it's after the fourth toss.
82
248000
2000
到了第二輪，或許在第四次會看到，
04:35
The next time, after the 15th toss.
83
250000
2000
第三輪，或許在第15次才看到。
04:37
So you do that lots and lots of times, and you average those numbers.
84
252000
3000
就這樣一直重覆做下去，然後把所有數字平均，
04:40
That's what I want this side to think about.
85
255000
3000
這是我要這一半聽眾去想的事情。
04:43
The other half of the audience doesn't like head-tail-tail --
86
258000
2000
另外這一半的聽眾，我就不要你們做「人頭、字、字」了，
04:45
they think, for deep cultural reasons, that's boring --
87
260000
3000
基於深厚的文化因素，你們一定覺得，那種順序太無聊了，
04:48
and they're much more interested in a different pattern -- head-tail-head.
88
263000
3000
我們想要有趣一點的順序：「人頭、字、人頭」
04:51
So, on this side, you get out your coins, and you toss and toss and toss.
89
266000
3000
所以，這邊的聽眾，你們拿起了銅板，投了再投
04:54
And you count the number of times until the pattern head-tail-head appears
90
269000
3000
把第一次出現「人頭、字、人頭」這個順序的次數記錄下來，
04:57
and you average them. OK?
91
272000
3000
再算出平均數，好嗎？
05:00
So on this side, you've got a number --
92
275000
2000
這一半的聽眾，你們有一個平均數，
05:02
you've done it lots of times, so you get it accurately --
93
277000
2000
你們投過很多次，所以一定很準確，
05:04
which is the average number of tosses until head-tail-tail.
94
279000
3000
一定可以得出一個第一次出現「人頭、字、字」的平均數。
05:07
On this side, you've got a number -- the average number of tosses until head-tail-head.
95
282000
4000
而這一半聽眾，你們也有一個關於「人頭、字、人頭」的平均數。
05:11
So here's a deep mathematical fact --
96
286000
2000
因此我們可以得出一個深奧的數學理論：
05:13
if you've got two numbers, one of three things must be true.
97
288000
3000
若你有二個數字，一定會有以下三種情形的其中之一，
05:16
Either they're the same, or this one's bigger than this one,
98
291000
3000
要不他們二個相等，要不就是這個數大於另一個數，
05:19
or this one's bigger than that one.
99
294000
1000
要不就是另一個數大於這個數。
05:20
So what's going on here?
100
295000
3000
你們覺得會是哪一種情形？
05:23
So you've all got to think about this, and you've all got to vote --
101
298000
2000
大家得好好想一想，然後我要你們投票，
05:25
and we're not moving on.
102
300000
1000
現在就想一想。
05:26
And I don't want to end up in the two-minute silence
103
301000
2000
我可不想讓接下來的二分鐘冷場，
05:28
to give you more time to think about it, until everyone's expressed a view. OK.
104
303000
4000
所以我要你們都好好想一想，每個人都得表達出自己的意見。
05:32
So what you want to do is compare the average number of tosses until we first see
105
307000
4000
我要你們比較一下，第一次出現「人頭、字、人頭」的平均投擲數，
05:36
head-tail-head with the average number of tosses until we first see head-tail-tail.
106
311000
4000
和第一次出現「人頭、字、字」的平均投擲數孰大孰小。
05:41
Who thinks that A is true --
107
316000
2000
認為A是正確的請舉手？
05:43
that, on average, it'll take longer to see head-tail-head than head-tail-tail?
108
318000
4000
也就是說，平均下來要花較多時間才會看到「人頭、字、人頭」這種順序？
05:47
Who thinks that B is true -- that on average, they're the same?
109
322000
3000
認為B是正確的請舉手？就是二者平均數相等？
05:51
Who thinks that C is true -- that, on average, it'll take less time
110
326000
2000
認為C是正確的請舉手？也就是說，平均下來，
05:53
to see head-tail-head than head-tail-tail?
111
328000
3000
要花較多時間才會看到「人頭、字、字」這種順序？
05:57
OK, who hasn't voted yet? Because that's really naughty -- I said you had to.
112
332000
3000
還有誰沒投票？你們真的很不乖哦！我說過你們都得投票啊！
06:00
(Laughter)
113
335000
1000
(笑聲)
06:02
OK. So most people think B is true.
114
337000
3000
好，大部分的人都認為B是正確的，
06:05
And you might be relieved to know even rather distinguished mathematicians think that.
115
340000
3000
如果你們知道最傑出的數學家也會這麼想，應該就會釋懷了吧！
06:08
It's not. A is true here.
116
343000
4000
事實上不是，A才是正確的，
06:12
It takes longer, on average.
117
347000
2000
平均來說會花比較多時間才會看到「人頭、字、人頭」這種順序。
06:14
In fact, the average number of tosses till head-tail-head is 10
118
349000
2000
「人頭、字、人頭」的平均投擲次數是10次，
06:16
and the average number of tosses until head-tail-tail is eight.
119
351000
5000
而「人頭、字、字」的平均投擲次數則是8次。
06:21
How could that be?
120
356000
2000
怎麼會這樣？
06:24
Anything different about the two patterns?
121
359000
3000
這二種順序有什麼不同？
06:30
There is. Head-tail-head overlaps itself.
122
365000
5000
的確有所不同，「人頭、字、人頭」的頭尾是重覆的，
06:35
If you went head-tail-head-tail-head, you can cunningly get two occurrences
123
370000
4000
所以如果你投出「人頭、字、人頭、字、人頭」，
06:39
of the pattern in only five tosses.
124
374000
3000
在這五次投擲裡你就會看到二次這種順序，
06:42
You can't do that with head-tail-tail.
125
377000
2000
「人頭、字、字」就沒有這種重覆性，
06:44
That turns out to be important.
126
379000
2000
這是很重要的一點，
06:46
There are two ways of thinking about this.
127
381000
2000
我們可以從二方面來思考這件事。
06:48
I'll give you one of them.
128
383000
2000
我們來看看其中一個面向，
06:50
So imagine -- let's suppose we're doing it.
129
385000
2000
先想像一下我們在投擲銅板，
06:52
On this side -- remember, you're excited about head-tail-tail;
130
387000
2000
記住，這一邊是支持「人頭、字、字」的，
06:54
you're excited about head-tail-head.
131
389000
2000
這一邊是支持「人頭、字、人頭」的。
06:56
We start tossing a coin, and we get a head --
132
391000
3000
我們來開始投吧！我們得到一個人頭，
06:59
and you start sitting on the edge of your seat
133
394000
1000
你緊張得坐不住了吧？
07:00
because something great and wonderful, or awesome, might be about to happen.
134
395000
5000
因為有件很神奇的事情就要發生了！
07:05
The next toss is a tail -- you get really excited.
135
400000
2000
接下來投出一個字，你真的很興奮，
07:07
The champagne's on ice just next to you; you've got the glasses chilled to celebrate.
136
402000
4000
似乎看到冰桶裡的香檳就在你身邊，只要拿起杯子就可以慶祝了！
07:11
You're waiting with bated breath for the final toss.
137
406000
2000
你現在不敢大口呼吸，
07:13
And if it comes down a head, that's great.
138
408000
2000
如果最後出現一個人頭，那就太棒了！
07:15
You're done, and you celebrate.
139
410000
2000
你成功了！你可以慶祝了！
07:17
If it's a tail -- well, rather disappointedly, you put the glasses away
140
412000
2000
但如果是字，嗯，你會很失望，只好把杯子放回去，
07:19
and put the champagne back.
141
414000
2000
把香檳退掉，
07:21
And you keep tossing, to wait for the next head, to get excited.
142
416000
3000
然後繼續投擲，等待下一個人頭出現。
07:25
On this side, there's a different experience.
143
420000
2000
而這一邊，則是完全不同的際遇，
07:27
It's the same for the first two parts of the sequence.
144
422000
3000
頭二次投擲的結果都一樣，
07:30
You're a little bit excited with the first head --
145
425000
2000
你對出現第一個人頭很興奮，
07:32
you get rather more excited with the next tail.
146
427000
2000
接下來出現一個字讓你更加興奮，
07:34
Then you toss the coin.
147
429000
2000
最後，你再投一次，
07:36
If it's a tail, you crack open the champagne.
148
431000
3000
如果是字，你就開香檳慶祝，
07:39
If it's a head you're disappointed,
149
434000
2000
如果是人頭，你就會很失望，
07:41
but you're still a third of the way to your pattern again.
150
436000
3000
但你至少不用再等下一個人頭，因為你已經投出下一輪的第一個人頭了。
07:44
And that's an informal way of presenting it -- that's why there's a difference.
151
439000
4000
這不是正規的解釋方法，但這確實是他們之間的差異所在。
07:48
Another way of thinking about it --
152
443000
2000
現在我用另一個思考面向來解釋，
07:50
if we tossed a coin eight million times,
153
445000
2000
如果我們投擲八百萬次，
07:52
then we'd expect a million head-tail-heads
154
447000
2000
「人頭、字、人頭」應該會出現一百萬次，
07:54
and a million head-tail-tails -- but the head-tail-heads could occur in clumps.
155
449000
7000
「人頭、字、字」也應該會出現一百萬次，但是「人頭、字、人頭」卻會成群地出現。
08:01
So if you want to put a million things down amongst eight million positions
156
456000
2000
如果你要把一百萬件東西分散放在八百萬件東西裡面，
08:03
and you can have some of them overlapping, the clumps will be further apart.
157
458000
5000
而某些東西是可以重疊的話，群集間的距離會更遠，
08:08
It's another way of getting the intuition.
158
463000
2000
這就是另一種思考方式。
08:10
What's the point I want to make?
159
465000
2000
我到底想要說什麼？
08:12
It's a very, very simple example, an easily stated question in probability,
160
467000
4000
這是一個非常淺顯易懂的例子，很容易說明的機率問題，
08:16
which every -- you're in good company -- everybody gets wrong.
161
471000
3000
每一個人都會在這問題上犯錯，你們也不例外。
08:19
This is my little diversion into my real passion, which is genetics.
162
474000
4000
這是我的另一個嗜好，基因。
08:23
There's a connection between head-tail-heads and head-tail-tails in genetics,
163
478000
3000
「人頭、字、人頭」或「人頭、字、字」
08:26
and it's the following.
164
481000
3000
和基因有某種關聯，
08:29
When you toss a coin, you get a sequence of heads and tails.
165
484000
3000
當你投擲一個銅板，你會丟出一連串的人頭或字，
08:32
When you look at DNA, there's a sequence of not two things -- heads and tails --
166
487000
3000
而我們來看看DNA，它的組成就不是人頭或字，
08:35
but four letters -- As, Gs, Cs and Ts.
167
490000
3000
而是這四個字母：A, G, C, T。
08:38
And there are little chemical scissors, called restriction enzymes
168
493000
3000
有一種像是剪刀的化學成份，叫做限制酶，
08:41
which cut DNA whenever they see particular patterns.
169
496000
2000
會在他們看到某種特定順序組合出現時，將DNA切斷，
08:43
And they're an enormously useful tool in modern molecular biology.
170
498000
4000
這是現代分子生物學裡的一項強大工具。
08:48
And instead of asking the question, "How long until I see a head-tail-head?" --
171
503000
3000
除了問說：「多久才會看到一個人頭、字、人頭呢？」
08:51
you can ask, "How big will the chunks be when I use a restriction enzyme
172
506000
3000
你還可以問：「若限制酶在看到G-A-A-G出現時就切斷DNA，
08:54
which cuts whenever it sees G-A-A-G, for example?
173
509000
4000
那麼G-A-A-G出現前的那一段DNA
08:58
How long will those chunks be?"
174
513000
2000
會有多長呢？」
09:00
That's a rather trivial connection between probability and genetics.
175
515000
5000
這是機率與基因間淺顯的關聯性，
09:05
There's a much deeper connection, which I don't have time to go into
176
520000
3000
但他們之間還存在著很深的關係，今天我沒有足夠的時間可以說明，
09:08
and that is that modern genetics is a really exciting area of science.
177
523000
3000
但那卻是現代基因學最令人著迷之處，
09:11
And we'll hear some talks later in the conference specifically about that.
178
526000
4000
待會兒還會有其他講者就這個主題再詳細說明。
09:15
But it turns out that unlocking the secrets in the information generated by modern
179
530000
4000
我們發現，若要公開現代實驗科技產生的資訊的祕密，
09:19
experimental technologies, a key part of that has to do with fairly sophisticated --
180
534000
5000
就不得不提到一個很複雜的關鍵因素，
09:24
you'll be relieved to know that I do something useful in my day job,
181
539000
3000
各位會很高興知道我的工作還是有些用途的，
09:27
rather more sophisticated than the head-tail-head story --
182
542000
2000
這可比丟銅板複雜多了，
09:29
but quite sophisticated computer modelings and mathematical modelings
183
544000
4000
牽涉到複雜的電腦模型、數學模型
09:33
and modern statistical techniques.
184
548000
2000
和現代的統計技巧。
09:35
And I will give you two little snippets -- two examples --
185
550000
3000
我會給各位二個提示，也就是二個例子，
09:38
of projects we're involved in in my group in Oxford,
186
553000
3000
那是我在牛津的小組所參與的專案，
09:41
both of which I think are rather exciting.
187
556000
2000
這二個專案都很有趣。
09:43
You know about the Human Genome Project.
188
558000
2000
各位都知道人體基因元計畫，
09:45
That was a project which aimed to read one copy of the human genome.
189
560000
4000
這個專案的目標是要訂出人體的基因序列，
09:51
The natural thing to do after you've done that --
190
566000
2000
而接下來很自然就產生另一個專案，
09:53
and that's what this project, the International HapMap Project,
191
568000
2000
叫做國際單體型測繪計畫，
09:55
which is a collaboration between labs in five or six different countries.
192
570000
5000
由五、六個不同國家的實驗室共同合作執行。
10:00
Think of the Human Genome Project as learning what we've got in common,
193
575000
4000
人體基因計畫旨在瞭解人類基因的共通性，
10:04
and the HapMap Project is trying to understand
194
579000
2000
而國際單體型測繪計畫就是要去瞭解
10:06
where there are differences between different people.
195
581000
2000
不同人之間的基因有何相異之處。
10:08
Why do we care about that?
196
583000
2000
為什麼我們要知道這些？
10:10
Well, there are lots of reasons.
197
585000
2000
嗯，有許多原因，
10:12
The most pressing one is that we want to understand how some differences
198
587000
4000
最主要的原因是我們想要瞭解，為何基因的不同
10:16
make some people susceptible to one disease -- type-2 diabetes, for example --
199
591000
4000
會使某些人容易得某種疾病，例如第二型糖尿病，
10:20
and other differences make people more susceptible to heart disease,
200
595000
5000
而另一種基因的差異則會讓人容易產生心臟病，
10:25
or stroke, or autism and so on.
201
600000
2000
或是中風、自閉症等疾病。
10:27
That's one big project.
202
602000
2000
這是一項大型專案，
10:29
There's a second big project,
203
604000
2000
還有另一項大型專案，
10:31
recently funded by the Wellcome Trust in this country,
204
606000
2000
是由英國的衛爾康基金會出資運作，
10:33
involving very large studies --
205
608000
2000
要進行非常大規模的研究，
10:35
thousands of individuals, with each of eight different diseases,
206
610000
3000
針對數千人進行調查，主要研究八種不同的疾病，
10:38
common diseases like type-1 and type-2 diabetes, and coronary heart disease,
207
613000
4000
像是第一型與第二型糖尿病、冠狀動脈心臟病、
10:42
bipolar disease and so on -- to try and understand the genetics.
208
617000
4000
躁鬱症等，要研究病患的基因序列，
10:46
To try and understand what it is about genetic differences that causes the diseases.
209
621000
3000
試圖找出病患的基因有何不同之處。
10:49
Why do we want to do that?
210
624000
2000
為什麼要做這個研究？
10:51
Because we understand very little about most human diseases.
211
626000
3000
因為我們對於大部分的疾病都瞭解不多，
10:54
We don't know what causes them.
212
629000
2000
我們不知道人們是怎麼染病的，
10:56
And if we can get in at the bottom and understand the genetics,
213
631000
2000
但如果我們能知道最基本的基因差異，
10:58
we'll have a window on the way the disease works,
214
633000
3000
我們或許可一窺疾病運作之祕密，
11:01
and a whole new way about thinking about disease therapies
215
636000
2000
並找出治療疾病的全新方法，
11:03
and preventative treatment and so on.
216
638000
3000
加以預防。
11:06
So that's, as I said, the little diversion on my main love.
217
641000
3000
這就是我所說的我的第二個嗜好。
11:09
Back to some of the more mundane issues of thinking about uncertainty.
218
644000
5000
現在我們回歸到現實面，來看看剛才我所說的不確定性，
11:14
Here's another quiz for you --
219
649000
2000
我要問各位另一個問題，
11:16
now suppose we've got a test for a disease
220
651000
2000
假設我們針對某項疾病研發了某種測試技術，
11:18
which isn't infallible, but it's pretty good.
221
653000
2000
雖然不是萬無一失，但尚稱良好，
11:20
It gets it right 99 percent of the time.
222
655000
3000
大約有99%的準確度。
11:23
And I take one of you, or I take someone off the street,
223
658000
3000
我請在座的一位或是街上隨便找個人，
11:26
and I test them for the disease in question.
224
661000
2000
來用這種技術檢驗是否得到了這種疾病，
11:28
Let's suppose there's a test for HIV -- the virus that causes AIDS --
225
663000
4000
假設是HIV病毒的檢驗試劑好了，就是愛滋病毒的檢驗試劑，
11:32
and the test says the person has the disease.
226
667000
3000
報告出來說這個人得病了。
11:35
What's the chance that they do?
227
670000
3000
那麼這個人真正得病的機率是多少？
11:38
The test gets it right 99 percent of the time.
228
673000
2000
試劑有99%的準確度，
11:40
So a natural answer is 99 percent.
229
675000
4000
大家自然會說這個人99%得了愛滋病，
11:44
Who likes that answer?
230
679000
2000
但誰會滿意這種答案？
11:46
Come on -- everyone's got to get involved.
231
681000
1000
拜託，每一個人都要參與啊...
11:47
Don't think you don't trust me anymore.
232
682000
2000
不要不信任我嘛...
11:49
(Laughter)
233
684000
1000
(笑聲)
11:50
Well, you're right to be a bit skeptical, because that's not the answer.
234
685000
3000
抱持懷疑態度是對的，因為這個答案不對，
11:53
That's what you might think.
235
688000
2000
你一定會這樣想。
11:55
It's not the answer, and it's not because it's only part of the story.
236
690000
3000
這個答案不對，但不是因為這個原因，
11:58
It actually depends on how common or how rare the disease is.
237
693000
3000
而是要看這種疾病的普遍程度來決定，
12:01
So let me try and illustrate that.
238
696000
2000
我來為各位解說一下。
12:03
Here's a little caricature of a million individuals.
239
698000
4000
假設這裡有一百萬人，
12:07
So let's think about a disease that affects --
240
702000
3000
我們來假設一種很罕見的疾病，
12:10
it's pretty rare, it affects one person in 10,000.
241
705000
2000
得病機率只有萬分之一，
12:12
Amongst these million individuals, most of them are healthy
242
707000
3000
所以在這一百萬人裡，大部分的人都是健康的，
12:15
and some of them will have the disease.
243
710000
2000
只有少數人會得病。
12:17
And in fact, if this is the prevalence of the disease,
244
712000
3000
如果這種疾病流行起來，
12:20
about 100 will have the disease and the rest won't.
245
715000
3000
也只有100個人會生病，其餘的人則不會生病。
12:23
So now suppose we test them all.
246
718000
2000
假設我們對全部的人做檢驗，
12:25
What happens?
247
720000
2000
會有什麼結果？
12:27
Well, amongst the 100 who do have the disease,
248
722000
2000
在這100個得病的人裡，
12:29
the test will get it right 99 percent of the time, and 99 will test positive.
249
724000
5000
以這99%準確度的試劑來檢驗，會有99個人呈陽性反應，
12:34
Amongst all these other people who don't have the disease,
250
729000
2000
而在其他沒有得病的人裡，
12:36
the test will get it right 99 percent of the time.
251
731000
3000
這個試劑的準確度還是99%，
12:39
It'll only get it wrong one percent of the time.
252
734000
2000
有1%的機會會出錯，
12:41
But there are so many of them that there'll be an enormous number of false positives.
253
736000
4000
但因為人數很多，所以假陽性的數量也就跟著變多。
12:45
Put that another way --
254
740000
2000
換個方式來說，
12:47
of all of them who test positive -- so here they are, the individuals involved --
255
742000
5000
在所有呈陽性反應的人裡，
12:52
less than one in 100 actually have the disease.
256
747000
5000
100個人裡只有不到一個人是真正染病的。
12:57
So even though we think the test is accurate, the important part of the story is
257
752000
4000
即使我們認為這種試劑很準確，
13:01
there's another bit of information we need.
258
756000
3000
但重點是我們還需要其他資訊來確認，
13:04
Here's the key intuition.
259
759000
2000
我們需要敏銳的洞察力。
13:07
What we have to do, once we know the test is positive,
260
762000
3000
一旦我們發現有人呈陽性反應，
13:10
is to weigh up the plausibility, or the likelihood, of two competing explanations.
261
765000
6000
我們就該去權衡二種不同解釋之間的可信度或可能性，
13:16
Each of those explanations has a likely bit and an unlikely bit.
262
771000
3000
每一種解釋都有可能的一面，也有不可能的一面。
13:19
One explanation is that the person doesn't have the disease --
263
774000
3000
你可以說這個人沒有染病，
13:22
that's overwhelmingly likely, if you pick someone at random --
264
777000
3000
這很有可能，因為你是隨機取樣的，
13:25
but the test gets it wrong, which is unlikely.
265
780000
3000
也就是說試劑出錯了，但這種機會不大。
13:29
The other explanation is that the person does have the disease -- that's unlikely --
266
784000
3000
你也可以說這個人確實是染病了，但這種疾病發生的機率很小，
13:32
but the test gets it right, which is likely.
267
787000
3000
試劑確實是準確的，這確實很有可能發生。
13:35
And the number we end up with --
268
790000
2000
最後我們得到的數據
13:37
that number which is a little bit less than one in 100 --
269
792000
3000
是比1%還稍小一點，
13:40
is to do with how likely one of those explanations is relative to the other.
270
795000
6000
也就是這二種解釋的發生的比例（幾乎是一比一百），
13:46
Each of them taken together is unlikely.
271
801000
2000
二者同時發生的可能性不高。
13:49
Here's a more topical example of exactly the same thing.
272
804000
3000
這裡還有一個很類似的例子，
13:52
Those of you in Britain will know about what's become rather a celebrated case
273
807000
4000
各位住在英國都知道一個很著名的案例，
13:56
of a woman called Sally Clark, who had two babies who died suddenly.
274
811000
5000
有個叫做莎莉．克拉克的婦人，她的二個嬰孩同時猝死，
14:01
And initially, it was thought that they died of what's known informally as "cot death,"
275
816000
4000
一開始大家都以為是猝死症，
14:05
and more formally as "Sudden Infant Death Syndrome."
276
820000
3000
正式名稱為嬰兒猝死症候群。
14:08
For various reasons, she was later charged with murder.
277
823000
2000
基於許多不同理由，莎莉被控謀殺，
14:10
And at the trial, her trial, a very distinguished pediatrician gave evidence
278
825000
4000
而在審判中，一位很知名的小兒科醫生做證說明，
14:14
that the chance of two cot deaths, innocent deaths, in a family like hers --
279
829000
5000
在他們這種家庭裡，也就是專業人士又不抽煙的家庭，
14:19
which was professional and non-smoking -- was one in 73 million.
280
834000
6000
二個嬰兒同時猝死的機率大約是7千3百萬分之一。
14:26
To cut a long story short, she was convicted at the time.
281
841000
3000
長話短說，她後來被定罪了。
14:29
Later, and fairly recently, acquitted on appeal -- in fact, on the second appeal.
282
844000
5000
但是後來，也就是最近的事，她在第二次上訴後獲判無罪。
14:34
And just to set it in context, you can imagine how awful it is for someone
283
849000
4000
請各位想想一下，如果有人失去了一個孩子，
14:38
to have lost one child, and then two, if they're innocent,
284
853000
3000
或甚至二個孩子，以清白之身卻被判謀殺定罪，
14:41
to be convicted of murdering them.
285
856000
2000
這是多麼殘忍的一件事。
14:43
To be put through the stress of the trial, convicted of murdering them --
286
858000
2000
就只為了紓解法庭所承擔的壓力，
14:45
and to spend time in a women's prison, where all the other prisoners
287
860000
3000
就把一個人以謀殺犯定罪，把她關進女子監獄，
14:48
think you killed your children -- is a really awful thing to happen to someone.
288
863000
5000
那裡的犯人都認為你殺了自己的小孩，這真是一件悲慘絕倫的事。
14:53
And it happened in large part here because the expert got the statistics
289
868000
5000
這個錯誤最主要是因為專家在二個不同的方面，
14:58
horribly wrong, in two different ways.
290
873000
3000
大錯特錯地引用了統計數據所造成。
15:01
So where did he get the one in 73 million number?
291
876000
4000
他怎麼得出7千3百萬分之一這個數據的？
15:05
He looked at some research, which said the chance of one cot death in a family
292
880000
3000
他看了某些研究文獻，裡頭說像莎莉這種家庭，
15:08
like Sally Clark's is about one in 8,500.
293
883000
5000
一個嬰孩猝死的機率約為8千5百分之一。
15:13
So he said, "I'll assume that if you have one cot death in a family,
294
888000
4000
他說：「先假設家裡已經有一個嬰孩猝死了，
15:17
the chance of a second child dying from cot death aren't changed."
295
892000
4000
第二個嬰孩猝死的機率與第一個相同。」
15:21
So that's what statisticians would call an assumption of independence.
296
896000
3000
這就是統計學所引用的獨立性假設，
15:24
It's like saying, "If you toss a coin and get a head the first time,
297
899000
2000
就好像是說：「若你第一次丟銅板得到一個人頭，
15:26
that won't affect the chance of getting a head the second time."
298
901000
3000
並不會影響你第二次再丟銅板，得到人頭的機率。」
15:29
So if you toss a coin twice, the chance of getting a head twice are a half --
299
904000
5000
所以，如果你丟一個銅板二次，那麼連丟二次都得到人頭的機率，
15:34
that's the chance the first time -- times a half -- the chance a second time.
300
909000
3000
就是第一次丟出銅板的機率，乘上第二次的機率（1/2＊1/2）。
15:37
So he said, "Here,
301
912000
2000
所以他才會說：「讓我們假設一下，
15:39
I'll assume that these events are independent.
302
914000
4000
假設這二個事件是獨立的，
15:43
When you multiply 8,500 together twice,
303
918000
2000
將8千5百乘二次，
15:45
you get about 73 million."
304
920000
2000
就會得到7千3百萬。」
15:47
And none of this was stated to the court as an assumption
305
922000
2000
但是這個前題假設並沒有在法庭上說明，
15:49
or presented to the jury that way.
306
924000
2000
也沒有對陪審團說明。
15:52
Unfortunately here -- and, really, regrettably --
307
927000
3000
很不幸也很遺憾的是，
15:55
first of all, in a situation like this you'd have to verify it empirically.
308
930000
4000
首先，像這種情形就該憑經驗先進行驗證，
15:59
And secondly, it's palpably false.
309
934000
2000
第二，這很明顯就是錯的。
16:02
There are lots and lots of things that we don't know about sudden infant deaths.
310
937000
5000
我們對於嬰兒猝死症所知真的不多，
16:07
It might well be that there are environmental factors that we're not aware of,
311
942000
3000
有可能是因為某些我們並不瞭解的環境因素所造成，
16:10
and it's pretty likely to be the case that there are
312
945000
2000
而這個個案更有可能是因為
16:12
genetic factors we're not aware of.
313
947000
2000
我們所不知道的基因缺陷所造成，
16:14
So if a family suffers from one cot death, you'd put them in a high-risk group.
314
949000
3000
所以當某個家庭裡有一個嬰孩猝死時，他們就算是高風險的家庭，
16:17
They've probably got these environmental risk factors
315
952000
2000
有可能存在著某些環境風險因子，
16:19
and/or genetic risk factors we don't know about.
316
954000
3000
或是有我們不知道的基因缺陷，或是二者都有。
16:22
And to argue, then, that the chance of a second death is as if you didn't know
317
957000
3000
真要計較起來，若完全不考慮這些因素，
16:25
that information is really silly.
318
960000
3000
就來計算第二個嬰孩的猝死機率，是很可笑的。
16:28
It's worse than silly -- it's really bad science.
319
963000
4000
甚至比可笑還糟，簡直就是爛透了的科學證據。
16:32
Nonetheless, that's how it was presented, and at trial nobody even argued it.
320
967000
5000
但這個數據就這樣被當成呈堂證供，法庭上也沒有人懷疑，
16:37
That's the first problem.
321
972000
2000
這就是第一個問題。
16:39
The second problem is, what does the number of one in 73 million mean?
322
974000
4000
第二個問題是，7千3百萬分之一代表著什麼？
16:43
So after Sally Clark was convicted --
323
978000
2000
當莎拉．克拉克被定罪之後，
16:45
you can imagine, it made rather a splash in the press --
324
980000
4000
你可以想見又在媒體上掀起了多大的波瀾，
16:49
one of the journalists from one of Britain's more reputable newspapers wrote that
325
984000
7000
英國某家聲譽卓著的報社記者
16:56
what the expert had said was,
326
991000
2000
就引用專家的話說：
16:58
"The chance that she was innocent was one in 73 million."
327
993000
5000
「莎拉清白的機率是7千3百萬之一」
17:03
Now, that's a logical error.
328
998000
2000
這犯了邏輯上的錯誤，
17:05
It's exactly the same logical error as the logical error of thinking that
329
1000000
3000
這個錯誤就和我們剛才所談到的疾病測試一樣，
17:08
after the disease test, which is 99 percent accurate,
330
1003000
2000
同樣具有邏輯上的錯誤，有人會以為試劑有99%的準確度，
17:10
the chance of having the disease is 99 percent.
331
1005000
4000
得到這種疾病的機率就是99%。
17:14
In the disease example, we had to bear in mind two things,
332
1009000
4000
在疾病試劑的例子裡，我們得記住二件事，
17:18
one of which was the possibility that the test got it right or not.
333
1013000
4000
其中之一是試劑的準確度，
17:22
And the other one was the chance, a priori, that the person had the disease or not.
334
1017000
4000
另一個則是人們染病的先驗機率。
17:26
It's exactly the same in this context.
335
1021000
3000
這和這個案子是一樣的情形，
17:29
There are two things involved -- two parts to the explanation.
336
1024000
4000
這個案子也有二種解釋的方向，
17:33
We want to know how likely, or relatively how likely, two different explanations are.
337
1028000
4000
我們得釐清這二種解釋發生的機率。
17:37
One of them is that Sally Clark was innocent --
338
1032000
3000
第一種解釋是莎拉是清白的，
17:40
which is, a priori, overwhelmingly likely --
339
1035000
2000
這在先驗機率上是很有可能的，
17:42
most mothers don't kill their children.
340
1037000
3000
大部分的母親都不會殺害自己的小孩。
17:45
And the second part of the explanation
341
1040000
2000
這種解釋的第二個部分是，
17:47
is that she suffered an incredibly unlikely event.
342
1042000
3000
莎拉的遭遇真的是令人難以置信，
17:50
Not as unlikely as one in 73 million, but nonetheless rather unlikely.
343
1045000
4000
雖然機率不像7千3百萬分之一那麼小，但確實是不太可能。
17:54
The other explanation is that she was guilty.
344
1049000
2000
第二種解釋是莎拉確實是有罪的，
17:56
Now, we probably think a priori that's unlikely.
345
1051000
2000
就先驗機率來說，這不太可能，
17:58
And we certainly should think in the context of a criminal trial
346
1053000
3000
而且我們當然認為在這起犯罪的審判中，
18:01
that that's unlikely, because of the presumption of innocence.
347
1056000
3000
一開始就要假設被告是無罪的，所以說莎拉有罪並不太可能。
18:04
And then if she were trying to kill the children, she succeeded.
348
1059000
4000
但若她真的想要殺害小孩，她也成功了，
18:08
So the chance that she's innocent isn't one in 73 million.
349
1063000
4000
所以她是清白的機率就不是7千3百萬分之一，
18:12
We don't know what it is.
350
1067000
2000
沒人知道是多少，
18:14
It has to do with weighing up the strength of the other evidence against her
351
1069000
4000
這個機率反而是和其他對她不利的證據和統計數據有關，
18:18
and the statistical evidence.
352
1073000
2000
得視證據強度而定。
18:20
We know the children died.
353
1075000
2000
我們只知道嬰孩死了，
18:22
What matters is how likely or unlikely, relative to each other,
354
1077000
4000
重要的是要找出這二種解釋
18:26
the two explanations are.
355
1081000
2000
之間的關聯性。
18:28
And they're both implausible.
356
1083000
2000
這二種解釋都無法使人信服，
18:31
There's a situation where errors in statistics had really profound
357
1086000
4000
有時統計上的錯誤所造成的影響，
18:35
and really unfortunate consequences.
358
1090000
3000
是很深遠且會造成不幸的。
18:38
In fact, there are two other women who were convicted on the basis of the
359
1093000
2000
事實上，還有有二位婦女因為這位小兒科醫生的證詞，
18:40
evidence of this pediatrician, who have subsequently been released on appeal.
360
1095000
4000
而被判有罪，但在後來的上訴後又被無罪釋放。
18:44
Many cases were reviewed.
361
1099000
2000
以往許多案子又被大家拿出來討論，
18:46
And it's particularly topical because he's currently facing a disrepute charge
362
1101000
4000
因此又掀起一波話題，因為這個醫生正被英國醫藥委員會
18:50
at Britain's General Medical Council.
363
1105000
3000
控以不名譽的罪名。
18:53
So just to conclude -- what are the take-home messages from this?
364
1108000
4000
結論是，這個故事帶給我們什麼樣的啟示？
18:57
Well, we know that randomness and uncertainty and chance
365
1112000
4000
我們知道隨機、不確定性及機率等，
19:01
are very much a part of our everyday life.
366
1116000
3000
都是我們日常生活的一部分，
19:04
It's also true -- and, although, you, as a collective, are very special in many ways,
367
1119000
5000
而雖然我們每一個人都與眾不同，
19:09
you're completely typical in not getting the examples I gave right.
368
1124000
4000
但就我所提出的問題沒有做出正確的回答這件事，這也是常態
19:13
It's very well documented that people get things wrong.
369
1128000
3000
很多過去的記錄顯示人們確實有時會做出錯誤判斷。
19:16
They make errors of logic in reasoning with uncertainty.
370
1131000
3000
在不確定的情況下，人們會犯下合理的邏輯錯誤。
19:20
We can cope with the subtleties of language brilliantly --
371
1135000
2000
人類可以運用精巧的語言，
19:22
and there are interesting evolutionary questions about how we got here.
372
1137000
3000
也能對人類本身的進化提出有趣的問題，
19:25
We are not good at reasoning with uncertainty.
373
1140000
3000
但我們就是不擅長預測不確定性，
19:28
That's an issue in our everyday lives.
374
1143000
2000
這是我們每天都必須面對的問題。
19:30
As you've heard from many of the talks, statistics underpins an enormous amount
375
1145000
3000
如同其他講者所提到的，統計學是其他許多科學研究的基礎，
19:33
of research in science -- in social science, in medicine
376
1148000
3000
不管是社會科學還是醫學都一樣，
19:36
and indeed, quite a lot of industry.
377
1151000
2000
還包括大部分的工業，
19:38
All of quality control, which has had a major impact on industrial processing,
378
1153000
4000
那些品質控制理論，對於工業流程管制具有重大的影響，
19:42
is underpinned by statistics.
379
1157000
2000
都是靠統計學做基礎。
19:44
It's something we're bad at doing.
380
1159000
2000
但這卻是我們所不擅長的事，
19:46
At the very least, we should recognize that, and we tend not to.
381
1161000
3000
至少我們該承認這一點，但我們卻沒人願意承認。
19:49
To go back to the legal context, at the Sally Clark trial
382
1164000
4000
回到法律層面，回到莎拉的案子上，
19:53
all of the lawyers just accepted what the expert said.
383
1168000
4000
所有的律師都接受這位專家的說法，
19:57
So if a pediatrician had come out and said to a jury,
384
1172000
2000
所以如果有一位小兒科醫生站出來對陪審團說，
19:59
"I know how to build bridges. I've built one down the road.
385
1174000
3000
「我知道如何建造橋樑，我已經在這條路上蓋了一座橋，
20:02
Please drive your car home over it,"
386
1177000
2000
請把你的車開上橋回家吧！」
20:04
they would have said, "Well, pediatricians don't know how to build bridges.
387
1179000
2000
陪審團會說：「小兒科醫生不是建造橋樑的專家，
20:06
That's what engineers do."
388
1181000
2000
這是工程師該做的事。」
20:08
On the other hand, he came out and effectively said, or implied,
389
1183000
3000
而在另一方面，這位醫師卻站出來發表專業意見，甚至暗示：
20:11
"I know how to reason with uncertainty. I know how to do statistics."
390
1186000
3000
「我知道如何解釋不確定性，我瞭解統計方法。」
20:14
And everyone said, "Well, that's fine. He's an expert."
391
1189000
3000
然後大家附和：「對，他是專家。」
20:17
So we need to understand where our competence is and isn't.
392
1192000
3000
我們必須瞭解每一個人的專長為何，
20:20
Exactly the same kinds of issues arose in the early days of DNA profiling,
393
1195000
4000
就像早期我們在描繪DNA時所引發的爭議一樣，
20:24
when scientists, and lawyers and in some cases judges,
394
1199000
4000
有些科學家、律師，或甚至法官，
20:28
routinely misrepresented evidence.
395
1203000
3000
都曾不斷地錯誤解讀他們所看到的證據。
20:32
Usually -- one hopes -- innocently, but misrepresented evidence.
396
1207000
3000
他們通常不是故意的，我們也衷心希望不是，但卻還是扭曲了證據的本質。
20:35
Forensic scientists said, "The chance that this guy's innocent is one in three million."
397
1210000
5000
鑑識專家說：「這傢伙清白的機率是三百萬分之一。」
20:40
Even if you believe the number, just like the 73 million to one,
398
1215000
2000
即使各位相信這個數據，就像先前提到的7千3百萬分之一那樣，
20:42
that's not what it meant.
399
1217000
2000
但這數據的意義並非如此，
20:44
And there have been celebrated appeal cases
400
1219000
2000
在英國和其他地方，
20:46
in Britain and elsewhere because of that.
401
1221000
2000
都有因為誤解數據而誤判的有名案例。
20:48
And just to finish in the context of the legal system.
402
1223000
3000
再讓我們回過頭來看看我們的法庭，
20:51
It's all very well to say, "Let's do our best to present the evidence."
403
1226000
4000
你大可以說：「我們得盡力將證據的原貌呈現出來。」
20:55
But more and more, in cases of DNA profiling -- this is another one --
404
1230000
3000
但是在DNA描繪的案例裡，一次又一次我們看到，這是另一個案例，
20:58
we expect juries, who are ordinary people --
405
1233000
3000
我們期望陪審團這些一般大眾，
21:01
and it's documented they're very bad at this --
406
1236000
2000
這些本來就對統計不甚在行在大眾，
21:03
we expect juries to be able to cope with the sorts of reasoning that goes on.
407
1238000
4000
我們竟然期望他們能解讀這些統計數據。
21:07
In other spheres of life, if people argued -- well, except possibly for politics --
408
1242000
5000
但在現實生活裡，如果有人爭論...嗯，除了政治話題之外，
21:12
but in other spheres of life, if people argued illogically,
409
1247000
2000
在現實生活裡，如果有人不合邏輯地爭論，
21:14
we'd say that's not a good thing.
410
1249000
2000
我們會說這樣做不好，
21:16
We sort of expect it of politicians and don't hope for much more.
411
1251000
4000
我們會認為這是政客做的事，因為我們對政客沒什麽太大的期望。
21:20
In the case of uncertainty, we get it wrong all the time --
412
1255000
3000
在面對不確定的事情時，我們總是犯錯，
21:23
and at the very least, we should be aware of that,
413
1258000
2000
但是至少我們應該知道我們會犯錯。
21:25
and ideally, we might try and do something about it.
414
1260000
2000
並希望我們能嘗試去減少錯誤的發生。
21:27
Thanks very much.
415
1262000
1000
謝謝各位！
ABOUT THE SPEAKER
Peter Donnelly - Mathematician; statisticianPeter Donnelly is an expert in probability theory who applies statistical methods to genetic data -- spurring advances in disease treatment and insight on our evolution. He's also an expert on DNA analysis, and an advocate for sensible statistical analysis in the courtroom.
Why you should listen
Peter Donnelly applies statistical methods to real-world problems, ranging from DNA analysis (for criminal trials), to the treatment of genetic disorders. A mathematician who collaborates with biologists, he specializes in applying probability and statistics to the field of genetics, in hopes of shedding light on evolutionary history and the structure of the human genome.
The Australian-born, Oxford-based mathematician is best known for his work in molecular evolution (tracing the roots of human existence to their earliest origins using the mutation rates of mitochondrial DNA). He studies genetic distributions in living populations to trace human evolutionary history -- an approach that informs research in evolutionary biology, as well as medical treatment for genetic disorders. Donnelly is a key player in the International HapMap Project, an ongoing international effort to model human genetic variation and pinpoint the genes responsible for specific aspects of health and disease; its implications for disease prevention and treatment are vast.
He's also a leading expert on DNA analysis and the use of forensic science in criminal trials; he's an outspoken advocate for bringing sensible statistical analysis into the courtroom. Donnelly leads Oxford University's Mathematical Genetics Group, which conducts research in genetic modeling, human evolutionary history, and forensic DNA profiling. He is also serves as Director of the Wellcome Trust Centre for Human Genetics at Oxford University, which explores the genetic relationships to disease and illness.
Peter Donnelly | Speaker | TED.com