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>> Hi I'm David.

Â I work a lot in Bayesian statistical methods and so I've been doing that for

Â about 20 or 25 years now and a lot of it is motivated by high

Â dimensional interesting biomedical applications.

Â >> Could you tell us about some of the application in

Â Bayesian methods in the health data that you're working with?

Â >> Yeah, we have a whole enormous variety of high dimensional health data that

Â we're motivated by.

Â I think that there's been this enormous profusion of high dimensional really

Â complicated data in a variety of fields, and so I just give one example

Â that we're really excited about lately which is neurosciences.

Â And so there's a lot of new imaging technology that allows you to actually

Â measure the connection structure in an individual's brain and so

Â you guys can go in and do a brain scan called a diffuse intenser imaging scan.

Â And also get structural imaging, and based on that imaging scan, you can actually

Â recreate the fibers connecting different regions of your brain.

Â And so you guys might be wired slightly differently, and

Â that might be related to your personality traits,

Â 1:27

tendency to have depression, creativity, intelligence in different domains.

Â And so we'd like to kind of figure out those relationships and so

Â we've been working on that a lot.

Â Lately using Bayesian methods and so the data are really intriguing.

Â They're kind of curves linking up different regions of the brain.

Â They have a network type structure and we're trying to build models for

Â discovering low dimensional structure

Â in the brain related to phenotypes like intelligence, creative reasoning, etc.

Â 1:59

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

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

Â has been dominated by optimization methods,

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

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

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

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

Â traits of that individual.

Â And so can we do that using non Bayesian methods?

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

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

Â do that for every possible link in the network.

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

Â discoveries.

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

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

Â type of approach.

Â And so you try to take that brain network and

Â then maybe do some sort of singular value decomposition or

Â matrix factorization to learn some low-dimensional structure.

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

Â which has really dominated a lot of literature is that

Â it just gives you a point estimate, okay?

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

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

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

Â best guess of what's going on.

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

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

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

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

Â And so, the really distinct characteristic of Bayesian methods

Â is their ability to characterize uncertainty.

Â Uncertainty in scientific inferences, in this case.

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

Â relationship between IQ and brain structure, say.

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

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

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

Â network and they'll extract certain features.

Â They're called topological features of the network.

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

Â then just do a statistical analysis based on that.

Â But that also fixates to some particular features, and

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

Â In a Bayesian approach you can holistically model

Â the entire brain structure flexibly while allowing uncertainty.

Â So I think it's been quite exciting.

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

Â Alzheimer's disease.

Â And also big differences between individuals having low creative

Â reasoning scores and high creative reasoning scores in terms of

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

Â 5:18

In general, Bayesian statistics if you kind of back up in time,

Â there's been these different kind of revolutions essentially.

Â And so prior to the onset of Markov Chain Monte Carlo methods in the late 80s,

Â early 90s,

Â it was more of a small philosophical field where people would work on toy problems.

Â And then once we had more computational tools,

Â it sort of exploded into being a very applied driven, applied motivated

Â field that could have a substantial impact on lot of application areas.

Â But that's kind of changing a little recently, as with the data becomes so

Â big, that these traditional algorithms that people were using in the 90s,

Â early 2000s, no longer usable.

Â And so one of the really exciting things in Bayesian statistics is trying to design

Â completely new algorithms, new ways to do inferences, new types of models for

Â really hugely high dimensional complicated data while allowing uncertainty.

Â Can we talk to people in computer science and machine learning, and figure out ways

Â to kind of scale up algorithms using big computing systems, distributed computing.

Â And that's been really interesting and intriguing,

Â while also maintaining theoretical guarantees that these methods do well.

Â So that's been a big part of our work and

Â there's been an explosion in this area in general, I think.

Â 6:38

>> Can you tell us a bit more about the application of Bayesian

Â methods to big data?

Â >> Yeah, so it's interesting because what people mean by big data exactly.

Â And so, a lot of the people in the literature are working on

Â Bayesian methods have been focused on big data meaning really large sample sizes.

Â And so that we might have a 100 million subjects or something.

Â But, if you don't have a really large sample size, but

Â the number of variables you're collecting isn't that big, and

Â you're doing something like say, a logistic regression, which is a toy

Â example people almost always use in motivating these types of methods,

Â then actually, there's often not that much motivation for

Â doing a Bayesian approach relative to some fast optimization approach.

Â Because, I have 50 parameters and I have a 100 million sample size,

Â well, my posterior distribution might be essentially,

Â really super concentrated right around something that we would get

Â by just doing say maximum likely estimation.

Â And so the really interesting problems in big data are when you actually

Â have really large numbers of variables or you're trying to fit a really flexible

Â model like a non-parametrical model or you have something like rare events.

Â So, for example, in computational advertising, we might be looking at people

Â going from a large number of websites to a small set of websites, client websites.

Â And so there might be hundreds of thousands websites and

Â then a hundred client websites, and those transitions can be really rare.

Â And so, even though you have millions of people, you have rare events.

Â And so, then we found that the uncertainty in those transitions is super important.

Â And so, if you just do an optimization approach, you might be quite misled.

Â