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#92 How to Make Decision Under Uncertainty, with Gerd Gigerenzer
Episode 924th October 2023 • Learning Bayesian Statistics • Alexandre Andorra
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I love Bayesian modeling. Not only because it allows me to model interesting phenomena and learn about the world I live in. But because it’s part of a broader epistemological framework that confronts me with deep questions — how do you make decisions under uncertainty? How do you communicate risk and uncertainty? What does being rational even mean?

Thankfully, Gerd Gigerenzer is there to help us navigate these fascinating topics. Gerd is the Director of the Harding Center for Risk Literacy of the University of Potsdam, Germany.

Also Director emeritus at the Max Planck Institute for Human Development, he is a former Professor of Psychology at the University of Chicago and Distinguished Visiting Professor at the School of Law of the University of Virginia. 

Gerd has written numerous awarded articles and books, including Risk Savvy, Simple Heuristics That Make Us Smart, Rationality for Mortals, and How to Stay Smart in a Smart World.

As you’ll hear, Gerd has trained U.S. federal judges, German physicians, and top managers to make better decisions under uncertainty.

But Gerd is also a banjo player, has won a medal in Judo, and loves scuba diving, skiing, and, above all, reading.

Our theme music is « Good Bayesian », by Baba Brinkman (feat MC Lars and Mega Ran). Check out his awesome work at https://bababrinkman.com/ !

Thank you to my Patrons for making this episode possible!

Yusuke Saito, Avi Bryant, Ero Carrera, Giuliano Cruz, Tim Gasser, James Wade, Tradd Salvo, William Benton, James Ahloy, Robin Taylor,, Chad Scherrer, Zwelithini Tunyiswa, Bertrand Wilden, James Thompson, Stephen Oates, Gian Luca Di Tanna, Jack Wells, Matthew Maldonado, Ian Costley, Ally Salim, Larry Gill, Ian Moran, Paul Oreto, Colin Caprani, Colin Carroll, Nathaniel Burbank, Michael Osthege, Rémi Louf, Clive Edelsten, Henri Wallen, Hugo Botha, Vinh Nguyen, Marcin Elantkowski, Adam C. Smith, Will Kurt, Andrew Moskowitz, Hector Munoz, Marco Gorelli, Simon Kessell, Bradley Rode, Patrick Kelley, Rick Anderson, Casper de Bruin, Philippe Labonde, Michael Hankin, Cameron Smith, Tomáš Frýda, Ryan Wesslen, Andreas Netti, Riley King, Yoshiyuki Hamajima, Sven De Maeyer, Michael DeCrescenzo, Fergal M, Mason Yahr, Naoya Kanai, Steven Rowland, Aubrey Clayton, Jeannine Sue, Omri Har Shemesh, Scott Anthony Robson, Robert Yolken, Or Duek, Pavel Dusek, Paul Cox, Andreas Kröpelin, Raphaël R, Nicolas Rode, Gabriel Stechschulte, Arkady, Kurt TeKolste, Gergely Juhasz, Marcus Nölke, Maggi Mackintosh, Grant Pezzolesi, Avram Aelony, Joshua Meehl, Javier Sabio, Kristian Higgins, Alex Jones, Gregorio Aguilar, Matt Rosinski, Bart Trudeau and Luis Fonseca.

Visit https://www.patreon.com/learnbayesstats to unlock exclusive Bayesian swag ;)

Links from the show:

Abstract

by Christoph Bamberg

In this episode, we have no other than Gerd Gigerenzer on the show, an expert in decision making, rationality and communicating risk and probabilities. 

Gerd is a trained psychologist and worked at a number of distinguished institutes like the Max Planck Institute for Human Development in Berlin or the University of Chicago. He is director of the Harding Center for Risk Literacy in Potsdam. 

One of his many topics of study are heuristics, a term often misunderstood, as he explains. We talk about the role of heuristics in a world of uncertainty, how it interacts with analysis and how it relates to intuition.

Another major topic of his work and this episode are natural frequencies and how they are a more natural way than conditional probabilities to express information such as the probability of having cancer after a positive screening. 

Gerd studied the usefulness of natural frequencies in practice and contributed to them being taught in high school in Bavaria, Germany, as an important tool to navigate the real world.

In general, Gerd is passionate about not only researching these topics but also seeing them applied outside of academia. He taught thousands of medical doctors how to understand and communicate statistics and also worked on a number of economical decision making scenarios.

In the end we discuss the benefits of simpler models for complex, uncertain situations, as for example in the case of predicting flu seasons.


Transcript

This is an automatic transcript and may therefore contain errors. Please get in touch if you're willing to correct them.

Transcripts

Speaker:

Gert Gigerentzer, welcome to Learning

Vision Statistics.

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I'm glad to be here.

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Yeah, thanks a lot for taking the time.

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I am very happy to have you on the show.

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A few patrons have asked for your episode,

so I'm glad to have you here today.

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And thank you very much to all of you in

the Slack, in the LBS Slack who

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recommended Gert for an episode on the

show.

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And yeah, I have a lot of questions for

you because you've done a lot of things.

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You have a lot of, there is a lot of

questions I want to ask you on a lot of

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different topics, but first, as usual,

let's start with your origin story.

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Geert, and basically, how did you come to

the world of study of rationality and

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decision-making under uncertainty?

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Now, I have been observing myself, how I

make decisions.

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For instance, in an earlier career, I was

a musician playing dixieland, jazz, and

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other things.

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And when I did my PhD work, I had to make

a decision.

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Was I want to continue a career on the

stage as a musician or to try an academic

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career?

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Mm-hmm.

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And for me, music was the safe option,

because I knew, and also I earned much

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more money than an assistant professor.

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And an academic career, I couldn't know

whether I could make it, whether I would

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ever become a professor, but it was the

risky option.

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So this is, if you want an initial story,

I decided then to take the uncertainty at

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risk.

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That makes sense.

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And so that was like pretty early in your

career, or is that something that came

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later on when you already had started

studying other things, or you started

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doing that as soon as you started your

undergrad studies?

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What came later was that I learned about

theories about decision making, and some

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of them I found very unrealistic and

strange, and about topics that were not

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really the topics where I thought are

important, like which job do you take,

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what do you do with the rest of your life,

but were of monetary gambles, was it you

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want a hundred dollars for sure, or two

hundred with a probability of 0.4?

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or six.

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And I also spent an important year of my

life at the Center for Interdisciplinary

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Research in Bielefeld on a group called

the Probabilistic Revolution.

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That's an international and

interdisciplinary group that investigated

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how science changed from a deterministic

worldview to a probabilistic one.

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And I learned so much.

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I was one of the young guys in this group.

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There were people like Thomas Kuhn, Ian

Hacking, Nancy Cartwright.

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And that also taught me something.

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It's important not to read in your own

discipline and do what the others do.

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But to fall in love is a topic like

decision making and uncertainty in the

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real world.

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And then read everything.

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that people have written about that.

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And that means from areas like biology,

animal behavior, to economics, to

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sociology, to the history of science.

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Yeah, that was something really

interesting when preparing the episode

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with you to see the whole arc of your

career being basically around these topics

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that you've studied really a lot and

in-depth.

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So that was really super interesting to

notice.

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And so something I'm wondering is, if you

remember...

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how you first got introduced to Bayesian

methods.

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Now, for instance, I read Fisher's book,

Statistic Methods and

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Mm-hmm.

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Thomas Bayes for having the insight not to

publishing his paper.

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Because, according to Fisher, that's not

what you need in science.

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And I got very much interested in the

fights between statisticians, in something

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that could be called insult and injury.

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And Fisher, for instance, in the same

book, he destroys Carl Pearson, his

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successor, saying

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the terrible weakness of his mathematical

and scientific work flowed from his

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incapacity of self-criticism.

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So if you want to get anyone interested in

statistics, then start with the

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controversies.

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That's my advice.

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And the pity is that in the textbooks, in

psychology certainly,

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All the controversies have been

eliminated, one doesn't mention them, and

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talks as if there would be only one kind

of statistics.

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So that could be Fisher's null hypothesis

testing, which has been turned in a very

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strange ritual, Fisher never would accept,

or on the other side there are also

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Bayesians who think it's the only tool in

the toolbox.

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And the knees of that attitude is

realistic, it's more religious.

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There is a statistical toolbox.

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And there are different instruments and

you need to look at the problem to choose

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the right one.

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And also within bass, there are so many

different kinds of bassianism.

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There's not one.

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64,000.

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It's a lot.

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Yeah, so, okay, that makes it clear.

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And that helps me also understand your

work because, yeah, something I saw is in

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your work, you often emphasize the role of

heuristics in decision-making.

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So I'm curious if you could explain how

Bayesian thinking and heuristics intersect

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and...

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how do these approaches complement each

other in navigating uncertainty?

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First, the term heuristic is often

misunderstood.

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I mean the term in the sense that Herbert

Simon used it to make a computer program

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smart, or the Gestalt psychologist used

it, or Einstein used it in the title of

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his Nobel Prize winning paper of 1905.

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I don't use it in the sense that it has

been very popular in psychology and other

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fields.

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as heuristics and biases.

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That's a clear misunderstanding.

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So to make it very short, in a world that

Jimmy Savage, who is often called the

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father of Bayesian statistics, called a

small world where the entire state space

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is known and nothing else can happen.

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In that world,

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This is the ideal world for Bayesianism

and also for most of statistics.

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In a world where you do not know the state

space that the economist Frank Knight

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called uncertainty, or as I have called

true uncertainty or radical uncertainty,

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you can't optimize by definition.

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You cannot find the best solution.

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And here...

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People and other animals, just like

managers and scientists, use heuristics.

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So a heuristic is a rule that helps you,

under uncertainty, to find a good

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solution.

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For instance, Polia, the mathematician

distinguished between analysis and

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heuristics.

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You need heuristics to find a proof and

you need analysis to check.

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whether it was right.

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Most important, heuristics and analysis

are not opposites, as it's now become very

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popular in system one and system two

theories.

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They're not opposites.

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They go together.

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And for instance, a study of 17 noble

laureates reported that almost all of them

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attributed there.

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success from going back and forth between

heuristics slash intuition or analysis.

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So that's an important thing.

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It's not binary opposites.

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So your question, where does Bayes meet

heuristics?

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Now, of course, for instance, in the

determination of the prior probability

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distribution, uniform

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That's also known as one over N.

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So you divide, for instance, your assets

equally over the funds or the stocks that

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you have.

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It's a reasonable assumption when you know

little.

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And just as one over n is reasonable, in

some situations it's not always.

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And the real challenge is to find out in

what situation does a certain heuristic or

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does space work, and where does it not

work.

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That's what I call the study of ecological

rationality.

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So in short, there's no single tool that's

always the best.

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We need to face...

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The difficult question, can we identify

the structure of environments where a

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simple heuristic like equal distribution

or imitate others works and where does it

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mislead?

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Hehehe

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Yeah, yeah, this is really interesting

because something also I'm always like, I

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always try to reconcile and actually you

talk about it in your book, Gut Feelings,

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The Intelligence of the Unconscious.

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And you talk also about intuitions and how

they can sometimes outperform more complex

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analytical processes.

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And this is a claim that you can see in a

lot of fields, right?

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From, I don't know, politics to medicine

to sports, when basically people don't

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really want the analytical process to be

taken too seriously because maybe it

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doesn't go, it doesn't confirm their...

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Yeah.

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their previous analysis or their own bias.

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So what I'm wondering is how do Bayesian

methods in your research, how do Bayesian

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methods accommodate the role of intuitive

judgment and how can individuals strike a

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balance between intuitive thinking and the

systematic updating of beliefs that we use

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under Bayesian reasoning?

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So let me first define what I mean by

intuition.

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So intuition is a kind of unconscious

intelligence that is based on years of

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experience with a topic where one feels

quickly what one should do, what one

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should not do, but one cannot explain it.

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So when a doctor sees a patient and the

doctor may feel something is wrong with

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that patient but cannot explain it, that's

an intuition based on years of experience.

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And then the doctor will go on and do

tests and analysis in order to find out

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what's wrong if there's something.

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So remember, intuition and analysis are

the same.

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always go together.

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It's a big error what we have today in

so-called dual processing theories, where

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they're presented as opposites.

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And then usually one side is always right,

like analysis and intuition is blamed, and

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heuristics are blamed if things go wrong.

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I see.

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Yeah.

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And so how does that then integrate into

the Bayesian framework according to you?

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Like in the systematic analysis of beliefs

that we have in the Bayesian framework.

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So applications of Bayes use heuristics

such as 1 over n, so equal distribution,

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equal priors.

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And they also use a more silent

independence assumption and such things.

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But I would not phrase the problem as how

to integrate heuristics in the Bayesian

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framework.

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I would also not say...

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how to integrate Bayes in the heuristics

framework.

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I think of both, so there are many

Bayesian methods and also other

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statistical methods, the old optimizing

methods, and there are heuristic methods

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which are non-optimizing methods.

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I think of them as part of an adaptive

toolbox that humans have, that they can

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use, and the real art is the choice of the

right.

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tool.

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So when I should use base and what kind of

base or when should I use a heuristic, a

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social heuristic, for instance do what

Alex tells me to do or for instance simple

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heuristics like take the best which just

go lexicographically through reasons and

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stop with the first one that allows to

make a decision.

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And that's the question of ecological

rationality.

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I see.

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And do you have, yeah, do you have

examples?

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Bayes' rule is a rule that is reasonable

to apply in situations where the world is

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stable, where no unexpected things happen,

where you have good estimates for the

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priors and also good estimates for the

likelihoods.

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For instance, mammography screening is a

case.

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So...

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We know that the, or we can expect that

the results of mammography screening won't

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change very much.

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We have to take in account that the base

rates differ from country to country or

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from group to group.

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But besides that, it is a good framework

to understand what is the probability that

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a person has breast cancer.

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if she tests positive.

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Mm-hmm.

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But that's a good situation.

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But if you have something which is highly

volatile, like, okay, I worked with the

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Bank of England on a method for

regulation, for banking regulation, and

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that role is highly volatile, and you're

not getting very far with standard

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statistical methods.

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But you may evaluate whether a bank is in

troubles.

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by something that we call a fast and

frugal tree that only looks at maybe three

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or four important variables and doesn't

combine them in a way as base or as linear

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models do, but lexicographic.

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Why?

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Because, so if you first look, for

instance, think about medical diagnosis.

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If your heart fails, a good kidney cannot

compensate that.

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And this is the idea of lexicographic

models.

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And a number of heuristics are

lexicographic, as opposed to compensatory

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models like Bayes or linear regressions.

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Oh, I see, okay.

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Yeah, continue.

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Yeah, I have myself trained about a

thousand doctors in understanding and

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doing Bayesian diagnosis and Bayesian

thinking.

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And you should realize that most doctors

and also most gynecologists would not be

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able to answer the question I posed

before.

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What is the...

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probability that a woman has breast cancer

in screening when the mammogram is

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positive.

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And if I give them the numbers in

conditional probabilities, they're equally

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lost.

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Alex, I do a test with you.

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Are you ready?

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So the point will be, I give you the

information in, as usual, in conditional

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probabilities.

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And I hope you will be confused.

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And also, to readers, the listeners.

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And then I give you the same.

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information in what we call natural

frequencies.

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And then insight will come.

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Ready?

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Okay.

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So assume you conduct a mammography

screening.

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What you know is that among the group of

women who participates, there is a one

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percent chance that a woman has breast

cancer undetected.

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You also know that the probability that a

woman has positive if she

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as breast cancer is 90%.

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And you know that the probability that

women should test positive if she does not

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have breast cancer is 9%.

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Okay?

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You have a base rate of 1%, a sensitivity

or hit rate of 90%, and a falls alarm rate

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of 9%.

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Now a woman in that group just tested

positive and you know nothing.

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about her because it's creamy, ask you,

doctor, tell me, do I now have breast

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cancer?

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Or how certain is it?

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99%, 90, 50, please tell me.

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What do you say?

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If there is now fog in your mind, that's

the typical situation of most doctors.

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Mm-hmm.

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And there have been conclusions made in

psychological research that the human mind

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has not evolved to think statistically, or

here, the Bayesian way.

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Now the problem is not in the mind, the

problem is in the representation of the

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information.

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Conditional probabilities are something

quite new.

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And few of us have been trained in it.

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Now how did humans...

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before Thomas Bass.

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Mm-hmm.

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or animals do based on reasoning, not

conditional probabilities, but what we

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call natural frequencies.

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That is, I give you first a demonstration,

then explain what it is.

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Okay, we use the same situation.

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You do the mammography screening and

translate the probabilities into concrete

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frequencies.

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Okay?

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Think about a hundred women.

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We expected one of them has breast cancer

and she likely tests positive.

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That's the 90%.

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Among the 99 who do not have breast

cancer, we expected another 9 will

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nevertheless test positive.

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So we have a total of 10 who test

positive.

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Question, how many of them do actually

have cancer?

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It's one out of 10.

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So a woman who tests positive in screening

has most likely not cancer.

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That's good news.

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So that's natural frequencies and you

basically see through.

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And natural frequencies, we call them

because they're not relative frequencies.

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They're not normalized.

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You start with a group like 100 and you

just break it down.

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And then the computation becomes very

simple.

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just imagine Bayes rule for this problem.

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And then natural frequencies does the

computation, the representation.

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It's just one out of the total number of

positives, 10.

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That's all.

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And once doctors have learned that and

tried with a few problems, they can

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generalize it and use the method for other

problems.

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And then we can avoid.

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the errors that are currently still in

place and also doctors can better

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understand what tests like HIV tests or

pregnancy tests actually mean.

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And the interesting theoretical point is,

as Herbert Simon said, the solution to the

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problem is in its representation.

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And he asked it from the Gestalt

Psychologist.

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Yeah, this is really interesting.

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I really love the...

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And in a way that's quite simple, right,

to just turn to natural frequencies.

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So I really love that because it gives a

simple solution to a problem that is

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indeed quite pronounced, right?

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Where it's just like when you're...

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Even if you're trained in statistics, you

have to make the conscious effort of not

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falling into the fallacy of...

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thinking, well, if the woman has a

positive test and the test has a 99% hit

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rate, she's got a 99% probability of

having breast cancer.

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I have one part of my brain which knows

that completely because I deal with

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statistics all the time, but there is

still the intuitive part of my brain,

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which is like, wait, why should I even

wonder if that's the true answer?

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So I like the fact that natural

frequencies

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kind of an elegant and simple solution to

that issue.

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And so I will put in the show notes your

paper about natural frequencies and also

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the one you've written about HIV screening

and how that relates to natural

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frequencies.

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So that's in the show notes for listeners.

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And I'm also curious, basically

concretely,

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how you did that with the professionals

you've collaborated with.

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Because your work has involved

collaborating with professionals from

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various domains.

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That means physicians, that means judges.

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I'm curious how you have applied these

principles of risk communication in

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practice with these professionals and what

challenges.

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and what successes have emerged from these

applications.

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Yeah, so I have always tried to connect my

theoretical work with practical work.

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So in that case of the doctors, I have

been teaching continuing medical education

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for doctors.

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So the courses that I give, they are

certified and the doctors gets points for

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that.

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and it may be a group of 150 or so doctors

who are assembled to a day or two days of

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continuing medical education, and I may do

two hours with them.

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And that has been for me a quite

satisfying experience because the doctors

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are grateful because they have muddled

through these things for their lives.

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And now they realize there's a simple

solution.

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They can learn within a half an hour or

so.

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And then it sticks for the rest of their

lives.

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I've also trained in the US, so I have

lived many years in the US and taught as a

345

:

professor at the University of Chicago.

346

:

And I have trained together with a program

from George Mason University, US Federal

347

:

Churches.

348

:

These are very smart people and I enjoyed

that.

349

:

So these trainings were...

350

:

and in illustrious places like Santa Fe.

351

:

And the churches were included and their

partners also included.

352

:

And there was also a series of things like

about how to understand fibers.

353

:

And I was teaching them how to understand

risks and decision making and heuristics.

354

:

And...

355

:

If you think that federal churches who are

among the best ones in the US would

356

:

understand Bayes' rule, good luck.

357

:

No, there may be a few, most not.

358

:

And actually, by the way, Bayes' rule is

forbidden in UK law.

359

:

interesting.

360

:

And so, but going back, these are examples

of training that every psychologist could

361

:

do.

362

:

But you have to leave your lab and go

outside and talk to doctors and have

363

:

something to offer them for teaching.

364

:

By now, the term natural frequencies is a

standard term in evidence-based medicine.

365

:

And I'm very...

366

:

proud about that.

367

:

And many, there's also a review, a

Cochrane's review has looked at various

368

:

representations and found that natural

frequencies are among the most powerful

369

:

ones.

370

:

And we have with some of our own students

who were more interested in children than

371

:

in doctors, we have posed us the question,

can we teach children?

372

:

and how early.

373

:

And one of the papers I sent you, it's a

paper in the Journal of Experimental

374

:

Psychology General, I think two years ago,

has for the first time tested fourth

375

:

graders, fifth graders, sixth graders, and

second graders.

376

:

So when we did this with the teachers,

they were saying, and they were looking at

377

:

the problems,

378

:

They were saying, no, that's much too

difficult.

379

:

The children will not be able to do that.

380

:

They haven't even had fractions.

381

:

But you don't need fractions.

382

:

And for instance, when we use problems,

they are more childlike.

383

:

So here we put that type of problems.

384

:

And when they are in natural frequencies,

385

:

And the numbers are two-digit numbers.

386

:

You can't do larger numbers with fourth

graders.

387

:

Then the majority of the fourth graders

got the exact Bayesian answer.

388

:

Of course, with conditional probabilism,

it would be totally lost.

389

:

And also we have found that some, maybe

20% of the second graders find the

390

:

Bayesian answer.

391

:

The title of the paper is Our Children

Intuitive Basients.

392

:

Yeah, it's in the show notes.

393

:

And again, it's in the representation.

394

:

It's a channel message in mathematics,

that representation of numbers matter.

395

:

And if you don't believe it, just think

about doing a calculation or base rule

396

:

with Roman numerals.

397

:

Good luck.

398

:

And that's well known in mathematics.

399

:

For instance, the physicist...

400

:

Feynman has made a point that

mathematically equally forms of a formula,

401

:

or despite their mathematically

equivalent, they're not psychologically

402

:

the same.

403

:

Because, as I said, you can see new

directions, new guesses, new theories.

404

:

In psychology, that is not always

realized.

405

:

And what Feynman, Richard Feynman was

talking about would be called framing in

406

:

psychology.

407

:

And by many of my colleagues, it's

considered an error to pay attention to

408

:

framing.

409

:

It's not.

410

:

It's an enabler for intelligent

decision-making.

411

:

Yeah, this is fascinating.

412

:

I really love that.

413

:

And I really recommend your, your paper

that you that you're talking about.

414

:

Do children have Bayesian intuitions?

415

:

Because first, I really love the

experiment.

416

:

I found that super, super interesting to

watch that.

417

:

And also, yeah, as you were saying,

418

:

in a way, the conclusion that we can draw

from that and basically how this could be

419

:

integrated into how statistics education

is done, I think is extremely important.

420

:

And actually, yeah, I wanted to ask you

about that.

421

:

Basically, if you, what would be the main

thing you would change in the way

422

:

statistical education is done?

423

:

Well, so you're mainly based in Germany,

so I would ask in Germany, maybe just in

424

:

general in Europe, since our countries are

pretty close on a lot of metrics.

425

:

So I guess what you're saying for Germany

could also be applied for a lot of other

426

:

European countries.

427

:

it's actually starting to change.

428

:

So some of my former post-docs are now

professors, and some are in education.

429

:

And for instance, they have done

experiments in schools in Bavaria, where

430

:

the textbooks have, in the 11th class,

have base rule.

431

:

And they show trees, but with relative

frequencies.

432

:

not natural frequencies.

433

:

And I've run a study which basically

showed that when pupils learn in these

434

:

textbooks base rules with relative

frequencies or conditional probabilities,

435

:

and you test them later,

436

:

90% can't do it anymore.

437

:

They've done something like rote learning.

438

:

Never understood it.

439

:

And then, in class, teachers taught the

students natural frequencies they had

440

:

never learned before.

441

:

And then 90% could do it.

442

:

Something they had never heard of.

443

:

Thanks for watching!

444

:

so my former students convinced the

Bavarian government with this study.

445

:

And now natural frequencies and thus

understandable base is part of the mass

446

:

curriculum in Bavaria.

447

:

So that's a very concrete example where

one can help young persons to understand.

448

:

And when they will be older and will be

doctors or have another profession where

449

:

they need base, they will not be so

blocked and have to muddle through and not

450

:

understand.

451

:

And if there are patients, then they know

what to ask and how to find out what a

452

:

positive HIV screening test really means

or a positive COVID test and what

453

:

information one needs for that.

454

:

So I think that statistical literacy is

one of the most important topics that

455

:

should be taught in school.

456

:

We still have an emphasis on the

mathematics on certainty, of certainty.

457

:

So algebra, geometry, trigonometry,

beautiful systems.

458

:

But what's most important for everyone in

later life is not geometry, it's

459

:

statistical thinking.

460

:

I mean in practical life.

461

:

And we are missing to do that.

462

:

The result is that...

463

:

If you test people, including medical

professionals, or we have tested

464

:

professional lawyers, with problems that

require Bayesian thinking, most are lost.

465

:

And the level of statistical thinking

is...

466

:

is often so low that you really can't

imagine it.

467

:

Here's an example.

468

:

Two years ago, the Royal Statistical

Society of London asked members of

469

:

parliament whether they would be willing

to do a simple statistical test.

470

:

And about 100 agreed.

471

:

The first question was, if you throw a

fair coin twice, what's the chance that it

472

:

will land twice on head?

473

:

Now, if you think that every member of

parliament understands that there are four

474

:

possibilities and two heads or two...

475

:

So two heads are, that's one in fourth?

476

:

No.

477

:

About half understood and the others not.

478

:

And the most wrong guess was it's still a

half.

479

:

It's just an illustration of the level of

statistical thinking in our society.

480

:

And I don't think if we would test German

politicians, we would do much better.

481

:

And that's a, you might say, yeah, who

cares about coins?

482

:

But look, there was COVID with all these

probabilities.

483

:

There is investment.

484

:

There are taxes.

485

:

There are tons of numbers that need to be

understood.

486

:

And if you have politicians that don't

even understand the most basic things,

487

:

what can we expect?

488

:

No, for sure.

489

:

I completely agree.

490

:

And these are topics we already tackled in

these podcasts, especially in episode 50,

491

:

where I had David Spiegelhalter here on

the podcast.

492

:

And we talked about these topics of

communication of uncertainty and all these

493

:

very interesting topics, especially

education and how

494

:

how to include all that in the education.

495

:

So that these are very interesting and

important topics and I encourage people to

496

:

listen to that episode, number 50 with

David Spiegelhauter.

497

:

I will put it in the show notes.

498

:

Yeah.

499

:

I may add here that David and I have been

working together for many years.

500

:

And he has been conducting the Wynton

Center for Evidence Communication or Risk

501

:

Communication in Cambridge.

502

:

And I'm still directing the Harding Center

for Risk Literacy.

503

:

And both centers were funded by the same

person, David Harding, a London Investment

504

:

Banker, who had insight that there's a

problem.

505

:

But the rest of philanthropists don't

really seem to realize that it would be

506

:

important to fund these centers.

507

:

The Wyndham Center is now closed down.

508

:

which is a great pity.

509

:

And yeah.

510

:

So there's very little funding for.

511

:

So there's funding for research.

512

:

So when I do the studies like this,

children, there's lots of funding for

513

:

that.

514

:

But the moment you apply what you learn

into the real world to help the society,

515

:

funding stops.

516

:

Except for...

517

:

Philanthropes like David Harding.

518

:

Mm-hmm.

519

:

Any idea why that would be the case?

520

:

They are the research agencies they think

they have not realized the problem that

521

:

science is more than having publications.

522

:

but that much of the science that we have

is actually useful.

523

:

That's being realized in, if it's about

engineering, and it's about patent, yes,

524

:

but that there are similar positive tools

that help people like natural frequencies

525

:

to understand their world, and that you

can teach them, and then you need a few.

526

:

guys who just go out and teach doctors,

lawyers or school children.

527

:

That is not really in the mind of

politicians.

528

:

Yeah, which is, which clearly is a shame,

right?

529

:

Because you can see how important

probabilistic thinking is in a lot of, in

530

:

a lot of fields.

531

:

And, and, and especially in politics,

right?

532

:

Even electoral forecasting, which is

something I've done a lot.

533

:

Probabilistic thinking is absolutely,

absolutely of utmost importance.

534

:

And yet, it's not there yet.

535

:

and not a lot of interest in developing

this, at least in France, which is where I

536

:

have done these experiments.

537

:

That's always been puzzling to me,

actually.

538

:

And even in sports, one of the recent

episodes I've done about soccer analytics

539

:

with Maximilian Goebel, well,

540

:

That was also an interesting conversation

about the fact that basically the methods

541

:

are there to use the data more

efficiently, but a lot of European

542

:

football clubs don't really use them for

some reason, which for me is still a

543

:

mystery because that would help them make

better use of their finite resources and

544

:

also be more competitive.

545

:

So.

546

:

Yeah, that's definitely something I'm

passionate to understand.

547

:

So yeah, thanks a lot for doing all that

work.

548

:

I'm here to try and help us understand all

that.

549

:

everyone can help here.

550

:

And for instance, most people are with the

doctors at some point, like COVID-19 or

551

:

HIV tests or cancer screening.

552

:

And everyone could ask the doctor, what's

the probability that I actually have the

553

:

disease?

554

:

or the virus, if it is positive.

555

:

And then you likely will learn that your

doctor doesn't know that.

556

:

Or excuse.

557

:

Then you can help your doctor understand

that.

558

:

And bring a natural frequency tree and

show them.

559

:

I've done this with many doctors, but

quite a few.

560

:

Over here, I said, I'm training doctors.

561

:

I've trained more than 1,000, my own

researcher from the Harding Center, I've

562

:

trained more than 5,000 extra.

563

:

And the last time I was with my home

physician, I spent maybe 50 minutes with

564

:

him.

565

:

and 40 minutes explaining him on the

internet where he finds reliable

566

:

information.

567

:

The problem is not in the doctor's mind,

the problem is in the education, at the

568

:

medical departments, where doctors learn

lots of things, but one thing they do not

569

:

learn, statistical thinking.

570

:

Mm-hmm.

571

:

Yeah.

572

:

with very few exceptions.

573

:

And I'm curious, did you do some follow-up

studies on some courts of those doctors

574

:

where you basically taught them those

tools, it seemed to work in the moment

575

:

when they applied it, and then I'm curious

basically of the retention rate of these

576

:

methods, basically is it something like,

oh yeah, when you force them in a way to

577

:

use them, yeah, they see it's useful,

that's good.

578

:

But then when you go away, they just don't

use them anymore.

579

:

And they just refer to the previous way

they were doing things, which is of

580

:

course, suboptimal.

581

:

So yeah, I'm curious how that...

582

:

continuing medley education, I have about

90 minutes and I teach them many things,

583

:

not just natural frequencies.

584

:

And when I teach them natural frequencies,

somewhere in the beginning, and I test

585

:

them towards the end.

586

:

So that's, yeah, a short time, a little

bit more than an hour.

587

:

There is no way for me to find these

doctors again.

588

:

But we have done follow-up studies up to

three months with students and teaching

589

:

them how to translate conditional

probabilities in natural frequencies.

590

:

And the interesting thing is that the

performance, which is after the training,

591

:

around 90%, that means 90% of all tasks,

they get exactly right.

592

:

After several months it stays at the same

level.

593

:

Whereas in the control group where they

are taught conditional probability,

594

:

exactly your problem is there.

595

:

So they learn it not as well as natural

frequencies, but then a few days later it

596

:

goes away and after three months they are

basically down with the story.

597

:

Yeah.

598

:

Some representations do not stick in the

minds.

599

:

And frequency representations do, if they

are not relative frequencies.

600

:

Yeah, this is definitely super

interesting.

601

:

So basically to make it stick more, the

idea would be definitely use more natural

602

:

frequencies.

603

:

Is that what you were saying?

604

:

Yes, and of course it doesn't hurt if you

continue thinking this way and do some

605

:

exercise.

606

:

Hmm, yeah.

607

:

Yeah, yeah.

608

:

I see.

609

:

And something I'm also curious about and

that a lot of, a lot of beginners ask me a

610

:

lot is what about priors, right?

611

:

So I'm curious in your job, how did you

handle priors and the challenges regarding

612

:

confirmation bias, persistence of...

613

:

persistence of incorrect beliefs.

614

:

So in a more general way, what I'm asking

is, how can individuals, particularly

615

:

decision makers in fields like law or

medicine that you know very well, avoid

616

:

the pitfalls associated with biased prior

beliefs and harnessing the power of

617

:

patient reasoning?

618

:

Yeah, so in the medical domain,

particularly in diagnostics, the priors

619

:

are usually from, they're usually

frequencies and they are estimated by

620

:

studies.

621

:

There's always the possibility that a

doctor might adjust the frequency base

622

:

rate a bit because he or she has some kind

of belief that

623

:

this patient's main op-e exactly from that

group.

624

:

But again, there's huge uncertainty about

priors.

625

:

And also, one should not forget, there's

also uncertainty about likelihoods.

626

:

Often in Beijing, the discussion centers

among priors.

627

:

How do you know the likelihoods?

628

:

So for instance, the, take the mammography

problem again, the probability that you

629

:

test positive if you don't have cancer, so

which I in the example gave is 9%, which

630

:

is roughly correct, but it varies.

631

:

It depends on the age of the woman.

632

:

It depends on quite a number of factors.

633

:

And one should not forget that

634

:

Also the likelihoods have to have some

kind of subjective element and judgment.

635

:

And then there's a third more general

assumption, namely the assumption that all

636

:

these terms, the likelihoods and the base

rates, which are from somewhere, maybe a

637

:

study in Boston, would actually apply to a

study in Berlin.

638

:

Mm-hmm.

639

:

And I can name you a few more assumptions.

640

:

For instance, that the world would be

stable, that nothing has happened.

641

:

There's no different kind of cancer that

has different statistics.

642

:

So one always has to assume a stable world

to do base.

643

:

And one should be aware that it might not

be.

644

:

And that's why I use the term statistical

thinking.

645

:

Because you need to think about the

assumptions all the time and about the

646

:

uncertainty in the assumptions.

647

:

And also realize that often, particularly

if you have more complex problems, not

648

:

just one test, but many, and many other

variables, you might, in these situations,

649

:

where Bayes slowly gets intractable.

650

:

Mm-hmm.

651

:

You might think using a different

representation, like what we call a fast

652

:

and frugal tree, that's a simple way.

653

:

It's just like think about a natural

frequency tree, but it is an incomplete

654

:

one, where you basically focus on the

important parts of the information and

655

:

don't even try to estimate the rest in

order to avoid estimation error.

656

:

And that's the key logic of heuristics.

657

:

Under uncertainty, the big danger is that

you overfit.

658

:

You overfit the data.

659

:

You have wrongly assuming that the future

is like the past.

660

:

And in order to avoid overfitting, as the

bias-variance dilemma shows in more

661

:

detail, one needs to make things more

simple.

662

:

Maybe not too simple, but more simple.

663

:

and trying to estimate all conditional

probabilities may give you a great fit,

664

:

but not good predictions.

665

:

Yeah, so thanks a lot for this perfect

segue to my next question, because this is

666

:

a recurring theme in your work and in your

research, simplicity.

667

:

You often emphasize simplicity in

decision-making strategies.

668

:

And so that was something I was wondering

about, because, well, I, of course, love

669

:

Bayesian methods.

670

:

They are extremely powerful.

671

:

They are, most of the time,

672

:

really intuitive to interpret, especially

the model parameters.

673

:

But they are complex sometimes.

674

:

And they appear even more complex than

they are to people who are unfamiliar with

675

:

them, precisely because they are

unfamiliar with them.

676

:

So anything you're unfamiliar with seems

extremely complex.

677

:

So

678

:

I'm wondering how we can bridge the gap

between the complexity of patient

679

:

statistics, whether real or fantasized,

and the need for simplicity in practical

680

:

decision-making tools, as you were talking

about, especially for professionals and

681

:

the general public, because these are the

audiences we're talking about here.

682

:

Now there are two ways.

683

:

One is you stay within the Bayesian

framework and for instance avoid

684

:

estimating conditional probabilities.

685

:

And that would be what's called naive

Bayes.

686

:

And naive Bayes can be amazingly good.

687

:

It has also the advantage that is much

more easy to understand than regular

688

:

Bayes.

689

:

The second option is to leave the Bayesian

framework.

690

:

and study how adaptive heuristics can give

you what base makes too complicated.

691

:

And also there's too much overfitting.

692

:

For instance, if we have studied

investment problems, so assume you have a

693

:

sum of money and want to invest it in N

assets.

694

:

How do you do it?

695

:

And there are basic methods that tell you

how to weigh your money in each of these

696

:

in assets.

697

:

There is Markowitz Nobel Prize winning

method that's standards of statistics, the

698

:

mean variance portfolio that tells you how

you should do that.

699

:

But when Harry Markowitz made his own

investments for the time after his

700

:

retirement...

701

:

You might think he used his Nobel Prize

winning optimization method.

702

:

No, he didn't.

703

:

He used a simple heuristic that's called 1

over n, or divide equally, the same as a

704

:

Bayesian equal prior.

705

:

And a number of studies have asked how

good is 1 over n compared to the Nobel

706

:

Prize?

707

:

Winning Markowitz model and also modern

variants including Bayesian methods.

708

:

The short answer is that 1 over n is

mostly as good as Markowitz and also

709

:

better, and also the most modern

sophisticated models that use any kind of

710

:

complexity cannot really beat it.

711

:

The more interesting question is the

following.

712

:

Can we identify in what situation

713

:

A heuristic like 1 over n or any other of

the complicated models is ecologically

714

:

rational.

715

:

Because before we have talked about

averages.

716

:

And you can see, so 1 over n has no free

parameter, very different from base.

717

:

That means nothing needs to be estimated

from data.

718

:

It actually doesn't need any data.

719

:

Thus, in the statistical terms of bias and

variance, it may have a bias, and likely

720

:

it has.

721

:

So bias is the difference from the average

investment to the true situation, but it

722

:

has no variance because it doesn't

estimate any parameters from data.

723

:

And variance means it's the deviation.

724

:

of individual estimates from different

samples around the average estimate.

725

:

And since there is no estimate, there is

no variance.

726

:

So Markowitz or Bayesian models, they

suffer from both errors.

727

:

And the real question is whether the sum

of bias and variance of one method is

728

:

larger than

729

:

of the other one.

730

:

And then ecologically rational it means,

let me illustrate this with the, with

731

:

Markowitz versus Van der Weyne.

732

:

So if you have more, if n is larger, then

you have more parameters to estimate

733

:

because the covariances, they just

increase.

734

:

That means more measurement error.

735

:

So you can...

736

:

derived from that, that in situations

where we have a large number of assets,

737

:

then the complex methods will likely not

be as good.

738

:

While 1 over n doesn't have more

estimation error, it has none anyhow.

739

:

And then another thing is, if the true

distribution of

740

:

the so-called optimal weights that you

only can know in the future, is highly

741

:

skewed.

742

:

Then 1 over n is not a good model for

that.

743

:

But it's roughly equal, then that's the

case.

744

:

So these are, and then sample size plays a

role for the estimation.

745

:

So the more data you have, the Bayesian or

Markowitz model will profit, while it

746

:

doesn't matter.

747

:

for the 1 over n heuristic because it

doesn't even look at the data.

748

:

So that's the kind of ecological

rationality thinking.

749

:

And there are some estimates just to give

you some flesh into that.

750

:

One study has asked, one study that found

that mostly in seven out of eight, I

751

:

think, tests 1 over n made more money in

terms of Sharpe ratio and similar.

752

:

criteria than the optimal Markowitz

portfolio and with 10 years of data.

753

:

So they asked the question how many years

of data would one need so that the

754

:

estimates get precise so that eventually

the complex model outperforms the simple

755

:

heuristic.

756

:

And that depends on the number of assets

you have.

757

:

And if they are 50, for instance, then the

estimate is you need 500 years of stock

758

:

data.

759

:

So in the year 2500, we can turn to the

complex models, provided the same stocks

760

:

are still around in the stock market in

the first place.

761

:

That's a very different way to think about

a situation.

762

:

It's the Herbert Simonian way, or don't

think about a method by itself, and don't

763

:

ever believe that a method is rational in

every situation.

764

:

But think about how this method matches

with the structure of environment.

765

:

And that's a much more difficult question

to answer than just claiming that

766

:

something is optimal.

767

:

Yeah, I see.

768

:

That's interesting.

769

:

I love the very practical aspect of that.

770

:

And also that, I mean, in a way that focus

on simplicity is something I found also

771

:

very important in the way of basically

thinking about parsimony.

772

:

Why make something more difficult when you

don't have to?

773

:

And it's something that I always use also

in my teaching, where I teach how to build

774

:

a model.

775

:

Don't start with the hierarchical time

series model, but start with a really

776

:

simple linear regression, which is just

one predictor, maybe.

777

:

And don't make it hierarchical yet, even

though that makes sense.

778

:

the problem at hand because from a very

practical standpoint if the model fails

779

:

and it will at first if it's too complex

you will not know which part to take apart

780

:

right and to and to make better so it's

just the parsimony makes it way easier to

781

:

build the model and also to choose the

prior right just don't make your priors

782

:

turn complicated find good enough priors

because you won't find

783

:

Find good enough priors and then go with

that.

784

:

I mean, the often use of the term optimal

is mostly misleading.

785

:

Under uncertainty or interactability, you

cannot find the optimal solution and prove

786

:

it.

787

:

It's an illusion.

788

:

And under uncertainty, so when you have to

make predictions, for instance, about the

789

:

future and you don't know whether the

future is like the past,

790

:

quite simple heuristics outperform highly

complex methods.

791

:

An example is, remember when Google

engineers try to predict the flu with a

792

:

system that's called Google Flu Trends.

793

:

and it was a secret system and it started

with 45 variables, they were also secret,

794

:

and the algorithm was secret.

795

:

And it ran from 2008 till 2015.

796

:

And at the very beginning in 2009 the

swine flu occurred.

797

:

And out of season in the summer.

798

:

And Google flew trends, so the big data

algorithm had learned that the flu is high

799

:

in the winter and low in the summer.

800

:

So it underestimated the flu-related

doctor visits, which was the criterion.

801

:

And the Google engineers then tried to

revise the algorithm to make it better.

802

:

And here are two choices.

803

:

One is what I call the complexity

illusion, namely you have a complex

804

:

algorithm and the high uncertainty, like

the flu is a virus that mutates very

805

:

quickly, and it doesn't work.

806

:

What do you do now?

807

:

You make it more complex.

808

:

And that's what the Google engineers did.

809

:

So they used a revision with about 160

variables, also secret.

810

:

and thought they would solve the problem,

but it didn't improve at all.

811

:

The opposite reaction would have been...

812

:

You have a complex and high uncertain

problem.

813

:

You have a complex algorithm.

814

:

It doesn't work.

815

:

What do you do now?

816

:

You make it simpler.

817

:

Because you have too much estimation

error.

818

:

The future isn't like the past.

819

:

We have tested those published paper on a

very simple heuristic that just takes one

820

:

data point.

821

:

So remember that.

822

:

Google Flu Trends estimated next week's or

this week's flu-related doctor visits.

823

:

So the one data point algorithm is you

take the most recent data, it's usually

824

:

one week or two weeks in the past, and

then make the simple prediction that's

825

:

what it will be this or next week.

826

:

That's a heuristic called the recency

heuristic, which is well documented in

827

:

human thinking, is often mistaken as a

bias heuristic.

828

:

And we showed it for the entire run of

Google Flu Trends for eight years.

829

:

The simple heuristic outperformed Google

Flu Tense in all updates, about a total, I

830

:

think, three updates.

831

:

for every year and for each of the updates

and reduce the error by about half.

832

:

You can intuitively see that.

833

:

So a big data algorithm gets stuck like if

something unexpected happened like in the

834

:

swine flu.

835

:

The recency heuristic can quickly adapt to

the new situation and

836

:

So that's another example showing that you

always should test a simple algorithm

837

:

first.

838

:

And you can learn from the human brain.

839

:

So the heuristics we use are not what the

heuristics and bios people think, always

840

:

second best.

841

:

No.

842

:

You need to see in a situation of high

uncertainty.

843

:

Pick a right heuristic.

844

:

A way to find it is to study what humans

do in these situations.

845

:

I call this psychological AI.

846

:

Yeah, I love that.

847

:

Um, and actually that, so before closing

up the show that, um, sets us up nicely

848

:

for one of my last questions, which is a

bit more, uh, formal thinking.

849

:

Because so you, you've been talking about

AI and, and these decision-making science.

850

:

So I'm wondering how you see the future of

decision science.

851

:

And where do vision statistics fit into

this evolving landscape, especially

852

:

considering the increasing availability of

data and computational power?

853

:

And that may be related to your latest

book.

854

:

Yeah.

855

:

My latest book is about, it's called How

to Stay Smart in a Smart World, and it

856

:

teaches one thing, a distinction between

stable worlds and unstable worlds.

857

:

Stable worlds are like what the economist

Frank Knight called a situation of risk,

858

:

where you can calculate the risk as

opposed to uncertainty.

859

:

That's unstable worlds.

860

:

If you have a stable world,

861

:

That's the world of optimization

algorithms, at least if it's fractable.

862

:

And here more data helps, because you can

fine-tune your parameters.

863

:

If you have to deal with an unstable

world, and that's most of things are

864

:

unstable, are not just viruses, but human

behavior.

865

:

And complex algorithms typically do not

help in predicting human behavior.

866

:

In my book I have a number of examples.

867

:

And here you need to study smart adaptive

heuristics that help.

868

:

And for instance, we are working with the

largest credit rating company in Germany.

869

:

And they have...

870

:

intransparent, secret, complex algorithms.

871

:

That has caused an outcry in the public

because these are decisions that decide

872

:

whether you are considered for, if you

want to rent a flat or not, and other

873

:

things.

874

:

And we have shown them that if they make

the algorithms simpler.

875

:

then they actually get better and more

transparent.

876

:

And that's an interesting combination.

877

:

Here is one future about solving the

so-called XAI problem.

878

:

First try a simple heuristic, that means a

simple algorithm, and see how good it is.

879

:

And not just test competitively, a handful

of complex algorithms.

880

:

Because the simple algorithm may be

881

:

do as well or better than the complex

ones.

882

:

And also they are transparent.

883

:

And that means that doctors, for instance,

may accept an algorithm because they

884

:

understand it.

885

:

And a responsible doctor would not really

want to have a neural network diagnostic

886

:

system that he or she doesn't understand.

887

:

So the future of decision making would be,

if you want it in a few sentences, take

888

:

uncertainty serious.

889

:

and distinguish it from situations of

risk.

890

:

We are not foreign, I hear this.

891

:

And second, take heuristics seriously and

don't confuse them with viruses.

892

:

And third...

893

:

If you can, go out in the real world and

study decision making there.

894

:

How firefighters like Gary Klein make

decisions, how chess masters make

895

:

decisions, how scientists come up with

their theories.

896

:

And you will find that standard decision

theory that's geared on small worlds of

897

:

calculated risk will have little to tell

you about that.

898

:

and then have the courage to study

empirically what experience people do, how

899

:

to model this as heuristics and find out

their ecological rationality.

900

:

That's what I see will be the future.

901

:

Nice.

902

:

Yeah, I find that super interesting in the

sense that it's also something I can see

903

:

as an attractive feature of the patient

modeling framework from people coming to

904

:

us for consulting or education, where the

fact that the models are clear on the

905

:

assumptions.

906

:

and the priors and the structure of the

model make them much more interpretable.

907

:

And so way less black boxy than classic AI

models.

908

:

And that's, yeah, definitely a trend we

see and it's also related to causal

909

:

inference.

910

:

People most of the time wanna know if X

influences Y and in what way, and if that

911

:

is, you know, predictable way.

912

:

And so for that causal inference,

913

:

fits extremely well in the Bayesian

framework.

914

:

So that's also something I'm really

curious about to see evolve in the coming

915

:

years, especially with some new tools that

start to appear.

916

:

Like I had Ben Vincent lately on the show

for episode 97, and we talked about causal

917

:

pi and how to do causal inference in PyMC.

918

:

And now we have the new do operator.

919

:

in Pintsy, which helps you do that.

920

:

So, yeah, I really love seeing all those

tools coming together to help people do

921

:

more causal inference and also more state

of the art causal inference.

922

:

And for the curious, we will do with

Benjamin Vincent a modeling webinar in the

923

:

coming weeks, probably in September, where

he will demonstrate how to use the

924

:

Dooperator in PIMC.

925

:

So if you're curious about that, follow

the show.

926

:

And if you are a patron of the show, you

will get early access to the recording.

927

:

So if you want to support the show with...

928

:

Cafe latte per month.

929

:

Um, I, uh, I'm really, um, uh, thanking

you from the bottom of my heart.

930

:

Um, well, Gert, um, I have so many other

questions, but I think, I think it's a

931

:

good time to, to stop.

932

:

Uh, I've already taken a lot of your time,

so I want to be mindful of that.

933

:

Um, but before letting you go.

934

:

I'm going to ask you the last two

questions I ask every guest at the end of

935

:

the show.

936

:

Number one, if you had unlimited time and

resources, which problem would you try to

937

:

solve?

938

:

I would try to solve the problem to

understanding the ecological rationality

939

:

of strategies, particular heuristics.

940

:

Hmm.

941

:

That's a next.

942

:

Yeah.

943

:

You're the first one to answer that.

944

:

And that's a very precise answer.

945

:

I am absolutely impressed.

946

:

And second question, if you could have

dinner with any great scientific mind,

947

:

dead, alive, or fictional, who would it

be?

948

:

Oh, I would love to have dinner with two

women.

949

:

The first one is a pioneer of computers,

Ada Lovelace.

950

:

And the second one is a woman of courage

and brain, Marie Curie.

951

:

The only woman who got two Nobel Prizes.

952

:

And Marie Curie said something very

interesting.

953

:

Nothing in life.

954

:

is to be feared.

955

:

It is only to be understood.

956

:

Now is the time to understand more so that

we may fear less." Kori said this when she

957

:

discovered that she had cancer and was

soon to die.

958

:

extremely inspiring.

959

:

Yeah, thanks, Edgar.

960

:

That's really inspiring.

961

:

But having courage is something that's

very important for every researcher.

962

:

And also having courage to look forward,

to dare, to find new avenues, rather than

963

:

playing the game of the time.

964

:

Well, on that note, I think, well, thank

you for coming on the show, Gert.

965

:

That was an absolute pleasure.

966

:

I'm really happy that we could have that

more, let's say epistemological discussion

967

:

than we're used to on the podcast.

968

:

I love doing that from time to time.

969

:

Also filled with applications and

encourage people to take a look at the

970

:

show notes.

971

:

I put.

972

:

your books over there, some of your

papers, a lot of resources for those who

973

:

want to dig deeper.

974

:

So thank you again, Gert, for taking the

time and being on this show.

975

:

It was my pleasure.

976

:

Bye bye.

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