It'll take you from knowing nothing to being able to fully apply Bayes' theorem or multiple linear regression.

它将带你从一无所知到能够完全应用贝定理或多元线性回归。

You understand the heart of Bayes' theorem.

您了解贝定理的核心。

And that requires us to talk about Bayes rule and also probability density functions.

这需要我们讨论贝则和概率密度函。

For this case, we do have a Bayes rule, once more.

对于这种情况，我们再次有贝则。

So this plot is meant to show usage of Bayes.

所以这个图是为了展示贝的用法。

I was reading through a Bayes book that carried through this argument about the prosecutor's fallacy.

我在阅读一本贝的书，这本书贯穿了关于检察官谬误的论点。

When did we start calling it Bayes?

我们什么时候开始叫它贝?

This, my friends, is Bayes' theorem.

我的朋友们，这就是贝定理。

It's very commonly used to introduce the topic of bayes rule in  probability.

它非常常用于介绍概率中的贝则主题。

In the context of Bayes' theorem, this value also has a special name, it's the " likelihood" .

在贝定理的背景下，这个值还有一个特殊的名字，那就是“可能性”。

I think that's what this notation says, but we don't see so clearly Bayes' theorem.

我认为这就是这个符号所说的，但我们没有那么清楚地看到贝定理。

The logic there is completely the same but the Bayes factor  that you compute is going to look different.

逻辑完全相同，但您计算的贝因子看起来会有所不同。

Now let's contrast this  with the usual way that Bayes rule is written, which is a bit more complicated.

现在让我们将其与贝则的通常编写方式进行对比，贝则的编写方式稍微复杂一些。

What that would mean is that our  Bayes factor is 90 instead of 10, the test is doing more work for us.

这意味着我们的贝因子是 90 而不是 10，测试为我们做了更多的工作。

In our example this number is 10. This is the Bayes factor, also sometimes called the likelihood ratio.

在我们的示例中， 该字为 10。 这是贝因子，有时也称为似然比。

Each answer to that question gives you a new Bayes factor, a new thing that you multiply by your odds.

这个问题的每个答案都会给你一个新的贝因子，一个你乘以你的赔率的新东西。

The reason I don't like using this notation in general, even though I can see Bayes' Theorem, is that bar usually means given.

即使我可以看到贝定理，我通常不喜欢使用这种表示法的原因是 bar 通常表示给定。

Wo taking this more honest representation of it,   let's compare our two versions of Bayes rule.

让我们比较一下贝则的两个版本。

But with the other formula, to do that you have to recompute everything each time, you can't  leverage a pre-computed Bayes factor the same way.

但对于另一个公式， 要做到这一点， 您必须每次都重新计算所有内容，您不能以相同的方式利用预先计算的贝因子。

The upshot, and this is the key mantra underlying Bayes' theorem, is that new evidence should not completely determine your beliefs in a vacuum; it should update prior beliefs.

结果是，新的证据不应该在真空中完全决定你的信念，这也是贝定理的关键原则。它应该更新先前的信念。