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So let's think about the inference. You want to generate beliefs about the world.
我們先來看推斷。在推斷中，我們要建立對于當前情景的“信念”。
So what are beliefs? Beliefs could be: where are my arms in space?
那么什么是信念？信念可以是我的胳膊在空間里的什么位置。
Am I looking at a cat or a fox?
也可以是我在看一只貓還是一只狐貍？
But we're going to represent beliefs with probabilities.
不過我們要把信念用概率來表示。
So we're going to represent a belief with a number between zero and one -- zero meaning I don't believe it at all, one means I'm absolutely certain.
所以在這里我們把所謂的信念表示成0到1之間的一個數--稱之為置信值，0表示完全不相信，1表示完全確信。
And numbers in between give you the gray levels of uncertainty.
到1之間就表示不同灰度的不確定程度。
And the key idea to Bayesian inference is you have two sources of information from which to make your inference.
然后注意，貝葉斯推斷的重點是我們靠兩個信息源來做出推斷。
You have data, and data in neuroscience is sensory input.
第一我們有數據，在神經科學里這個數據就是感官輸入進來的內容。
So I have sensory input, which I can take in to make beliefs.
所以感官輸入是其中一個信息源，用于生成我剛才說的“置信值 ”。
But there's another source of information, and that's effectively prior knowledge.
不過還有第二個信息源，事實上也就是先前的知識。
You accumulate knowledge throughout your life in memories.
因為我們在一生中在過去的記憶中積累知識。
And the point about Bayesian decision theory is it gives you the mathematics of the optimal way to combine your prior knowledge with your sensory evidence to generate new beliefs.
好了，貝葉斯決策論的重點就在于這個理論提供了一種計算方法，能找到最優的辦法來整合，知識積累和感官輸入這兩種信息源以生成新的置信值。
And I've put the formula up there. I'm not going to explain what that formula is, but it's very beautiful.
我現在把公式放在這里。我不詳細解釋這個公式了，但是這個公式非常漂亮。
And it has real beauty and real explanatory power.
不僅有和諧的內在美，還有實實在在的說服力。
And what it really says, and what you want to estimate, is the probability of different beliefs given your sensory input.
這個公式真正的用途，也就是我們要估測的結果，是給出我們感官輸入的情況下不同置信值出現的概率。
So let me give you an intuitive example.
現在我舉一個直觀的例子。
Imagine you're learning to play tennis, when you play tennis and you want to decide where the ball is going to bounce as it comes over the net towards you.
想象你現在在網球場練網球，當這個網球越過球網飛過來的時候，你要決定這個球落在哪里。
There are two sources of information Bayes' rule tells you.
根據貝葉斯的理論你現在有兩個信息源。
There's sensory evidence -- you can use visual information auditory information, and that might tell you it's going to land in that red spot.
一個是感官輸入--你的視覺和聽覺收到的信息，告訴你球應該會落在圖上的紅點處。
But you know that your senses are not perfect,
但是，你也知道自己的感官并不完美，
and therefore there's some variability of where it's going to land shown by that cloud of red, representing numbers between 0.5 and maybe 0.1.
所以球的落地點可能會有誤差--在圖上用這塊紅色區域來表示這個區域的概率在0.5和大概0.1附近浮動。
