>> And so how can Bayesian statistics in particular tell us more about the brain?

>> It's interesting that most of the literature recently

has been dominated by optimization methods,

a really simple methods that take the data and look at tiny pieces of it separately.

And so imagine that we have a big network in your brain, okay?

And so everyone in the study has a slightly different network,

and we'd like to know how are the features of the network related to

traits of that individual.

And so can we do that using non Bayesian methods?

Well, we could take little pieces of the network and just do a test separately for

the relationship between, say, IQ and this link in the network, get a p-value and

do that for every possible link in the network.

And then maybe do some sort of adjustment to avoid having too many false

discoveries.

So that turns out to do extremely badly, if you do tests.

The other thing people do in kind of modern statistics is to do an optimization

type of approach.

And so you try to take that brain network and

then maybe do some sort of singular value decomposition or

matrix factorization to learn some low-dimensional structure.

Then you can do that really fast, but the problem with that type of approach,

which has really dominated a lot of literature is that

it just gives you a point estimate, okay?

And so, let's say I want to study the relationship between

some mental health disorder or aging and brain structure, okay?

Well, if I just get a point estimate of that, that's just one guess or one, maybe,

best guess of what's going on.

It doesn't tell me how uncertain I am in that and so I can't really publish

an article on that or feel like I am confident about that result.

It might be that there's 10,000 other different relationships that are equally

consistent with the data, and I've just estimated one of them.

And so, the really distinct characteristic of Bayesian methods

is their ability to characterize uncertainty.

Uncertainty in scientific inferences, in this case.

And so I can say, what's the post to your probability that there's any

relationship between IQ and brain structure, say.

I can also say, well, what's the post to your probability in particular region

that there's a relationship between IQ and brain structure.

The other thing that people do is they will just take the data in the brain

network and they'll extract certain features.

They're called topological features of the network.

And they might take three, or four, or five of these different features and

then just do a statistical analysis based on that.

But that also fixates to some particular features, and

if you collect too many you'll end up having false positives.

In a Bayesian approach you can holistically model

the entire brain structure flexibly while allowing uncertainty.

So I think it's been quite exciting.

We've already found very intriguing relationships between brain structure and

Alzheimer's disease.

And also big differences between individuals having low creative

reasoning scores and high creative reasoning scores in terms of

connections in the frontal lobe across hemispheres and so it's been a lot of fun.