There are two sources of information Bayes' rule tells you.

So naive.

Naive justified honesty.

These are naive subjects.

Now I'm not naive.

Don't let's be naive.

But... you're so naive.

And what Bayes showed was a mathematical way that you could do that.

Oh Kit, you're so naive.

I know that I'm naive

Commoners are naive and easily frightened.

And a little naive too. Why?

Here is my naive advertising man's suggestion.

We'll see about that. You're being naive.

You're so naive, my dear old colleague.

And what Bayes' rule says is, given my beliefs, the action should in some sense be optimal.

Get rid of those kinds of naive ideas.

Now, here is another naive advertising man's question again.

Okay, we're naive, we're bright eyed and bushy tailed.

May I ask you a naive question, Mr Falco?

Oh, you dear man you dear, sweet, naive man.

You're being naive. Would you stop counting the chips?

And, you're so naive to have trusted my gun.

Gay and foolish, naive, shrewd, and heartbreaking all at once.

Here we've got naive subjects praising the robot Voice Nice robot.

We've nothing to worry about. He's as naive as a child.

It's just because of your naive way to estimate the votes.

And it all depends on the ideas of this guy, the Reverend Thomas Bayes, who was a statistician and mathematician in the 18th century.

You're so naive. You're like a little boy with a box of candy.

So as a naive New Zealander I thought, well I'll go to the Pentagon.

What was, for me, a very naive observation, turned out to be a disaster.

And essentially what Bayes did was to provide a mathematical way using probability theory to characterize, describe, the way that scientists find out about the world.

And yes, on a scale from one to over trusting, I am pretty damn naive.

Some naive person might try to sell one, but he'd never get away with it.

Even when she's a bother, she does it in a gay, naive, Southern belle way.

Through the infinite reaches of space... the problems of man seem trivial and naive indeed.

In 1974, I was young, I was naive, and I was pretty lost in my world.

And they take advantage of the innocent, the naive, the grieving, the needy people out there.

Now Ken and I are not naive, and we understand that you need to have rules.

In my defense, I'd say, as naive as this may sound, it's ultimately grounded in cynicism.

Why do you get naive now? I no longer understand you. Nobody can say if it's your child.

He wanted to give up the dangerous kind of science and keep the good bits. Now, that's absurdly naive for two reasons.

Now I thought, you know, if we just did good science, that would change medical practice. But, that was a little naive.

And what Bayes' rule says is that I should multiply the numbers on the red by the numbers on the green to get the numbers of the yellow, which have the ellipses, and that's my belief.

It is naive beyond description to think that having blocked this source of financial collapse, you have blocked all possible sources of financial collapse.