Successive approximation, Newton-Raphson was one nice example, but there's a whole class of things that get closer and closer, reducing your errors as you go along.
逐渐逼近,牛顿迭代是一个很好的例子,随着你不断的时行下去,你会不断的离结果越来越近,逐渐地减少误差。
So how do we go about measuring these things and what sorts of errors are in them, and how accurate are they?
那么我们该如何去评估,其中产生怎样的误差,它们又准确到什么程度
What do you think the error is going to be by failing to recognize that at the end of 6 times 10 to the 23rd I have over-counted some energy?
你们可能会发现,这将会有误差,在6乘以10的23次方的末端,我多余地引入了一些能量?
You've got survivorship bias taking out bad records and then you've got backfill bias adding good records.
生存偏差去掉了那些糟糕的记录,回填误差又加入了一些好的记录
So, it depends on your error bar in a sense.
因此,从某种意义上说它取决于误差棒。
It can be 5 dollars minus your error in pennies, if you won.
如果你赢了就是五美元减去你的误差
These numbers are so low they could be dismissed as people filling in the wrong things or making jokes or just being confused compared to-- stunningly superstitious high rankings.
这些比例低到,可以把它们当成人们填错表格,或者开玩笑,或者看不懂题目造成的误差,相比于…,那些高得吓人的比例。
as long as it's small and finite, will lead to some small infinite errors in the formula, but remember it's got to be in the end made to be vanishingly small.
只要它只是有限小,就会在公式中引起无限小的误差,但请记住,Δt最后变得难以察觉地小
You have to make those calculations and there are errors in that, but you come away with a population estimate of things like that.
你必须把这些都算进去,因为其中存在误差,但这样你会得出,整体人群摄取量的估算值
If you go onto some of the other foods in here you see that the error became even greater in some of these cases.
如果你们看表上的其他一些食物,一些例子的估算误差会更大
Any one of these things would introduce error, but when you start adding them altogether, you get considerable error, so that means--it shows several things.
这些事物都会引入误差,一旦误差集中起来,会变成严重的错误,那就意味着,表现如下
It leads to uncertainty in the measure.
它导致测量误差。
By the way, here's where the average error is in this particular study.
顺便一提,这是这个实验的平均误差值
Now here's how-- here's how the kind of errors that people make.
这就是人们如何造成的误差
As a consequence, there's a lot of variability and error in these dietary measurements.
结果就是,饮食测评中会有很多变数,和误差
So that's a big percentage error here and it was in the people's favor.
由于人们的一厢情愿,造成巨大的误差
So for all these reasons there's some error in this kind of thing.
以上种种原因,造成了研究中的误差
That's the hope, but of course, there's still error in that.
这便是所要的,但当然,其中仍然会有误差
I mean it's pretty easy to measure errors in some cases.
有些类型的误差是很容易测量的
So if there's any systematic bias going on in the way these things get graded it'll smooth itself out across the teaching fellows, so we'll have a fair grading system and things.
所以,如果在评分过程中,有任何系统性误差,都会由助教们尽量纠正过来,这样就有了公平的评分系统
But there's still a lot of error introduced.
但是这依然会造成巨大的误差
Okay, so you can see the size of the errors and you can see the problem with dietary assessment, and you can see the problem with how many calories get packed in processed foods.
你们看见了,误差的幅度很大,你们也明白了膳食评估的困难,你们也发现了,加工食品含有大量卡路里的问题
Now you can begin to see the kinds of errors that this method might produce because people forget, they can't remember exactly how much they ate of things, or they may not be willing to disclose everything they ate.
现在你就可以明白各种误差,是由人们的遗忘而产生的,他们无法准确记得吃了多少东西,他们不会透露所有自己吃的东西
You figure that most of those boxes are being eaten by somebody or another, there's some waste that you might calculate in, but there--error gets introduced there trying to estimate that, so you get a number on that.
你的计算中大部分食品,都被人们吃了,浪费的那些也要计算进来,但其中的误差,也要估算出来,最后得出一个数字
Highly educated people, a lot of you probably care a lot about food, think about labels, read them and things like that, not one person out of the 300-350 people in this room guessed correctly within ten percent margin of error.
你们受过高等教育,注意饮食健康,关注食品标签,等等,在10%的误差幅度下,在300-350个人中,没有一个人估计正确
All right now, now what I'd like you to do is just sort of do a guestimate in your mind of the percentage errors you might have made overall in these estimates, and I'll come back and ask you in a minute.
好了,现在,现在我希望你们,在脑海中估算下你们预测的百分误差,你们可以就总值做一个估算,我会在一分钟后问你们
Of course that depends on the accuracy of the self- reports that people are making on their own, and as you'll see in just a minute, there are errors in that and some of you may have experienced some of that yourself in keeping the dietary records.
当然这还取决于每个人自己完成的,个体调查的准确性,正如你马上会看到的,这其中有误差,而你们也可能经历过一些,你自己保存膳食记录时的误差
In this case people--bread, chips, and ham- they were estimating really large errors here.
对于面包,土豆片和火腿,人们的估算存在很大误差
And each time one of these errors occurs, or you get multiple errors that compound each other, then you've got a lot of potential error introduced in these messages.
每当有误差发生,或多重误差复合叠加,然后你所得到的信息,就会包含很多潜在的误差
Well we've talked about some of these already, but there are a ton of ways that inaccuracy can get introduced when you start assessing what people are eating.
我们已经讨论过一些了,但当你开始估算人们的饮食时,有很多方面,会造成误差
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