Presentation given by Caleb Madrigal at the Mythicist Milwaukee group on 2016-11-08. Video of presentation: https://www.youtube.com/watch?v=uymexoGtUVQ

1. Bayesian Probability: a tool for
communicating beliefs

2. Intro to Caleb
http://calebmadrigal.com/
caleb.madrigal@gmail.com

3. Monty Hall problem
"Suppose you're on a game show, and you're given the choice of three doors: Behind
one door is a car; behind the others, goats. You pick a door, say No. 1, and the host,
who knows what's behind the doors, opens another door, say No. 3, which has a goat.
He then says to you, "Do you want to pick door No. 2?" Is it to your advantage to
switch your choice?"
A: Switch
B: Stay with original door
C: Doesn't matter if you switch or stay

4. https://priceonomics.com/the-time-everyone-corrected-the-worlds-smartest/

5. Intro to Bayesian Probability

6. "Broadly speaking, there are two views on Bayesian probability that interpret the
probability concept in different ways. According to the objectivist view, the rules of
Bayesian statistics can be justified by requirements of rationality and consistency and
interpreted as an extension of logic. According to the subjectivist view, probability
quantifies a 'personal belief'."(https://en.wikipedia.org/wiki/Bayesian_probability)

8. Parts of formula:

9. Dice problemDice problem

10. https://github.com/calebmadrigal/probability-with-
python/blob/master/dice_problem_1.ipynb

11. Example application: roboticExample application: robotic
localizationlocalization

12. Bayesian Networks
Dice problem bayesian network for the first roll:
<>

13. (https://en.wikipedia.org/wiki/Bayesian_network)

14. Using a Bayesian Network, we can answer questions like, "What's the probability that
the sprinkler is/was on given that the grass is wet?"
P(Sprinkler | Grass Wet)

16. Though typically, I prefer to solve this using Monte
Carlo simulations:

17. Bayesian Network for pricing car insurance:

18. CPCS (Computer-based Patient Case Study) - used for
diagnosing medical conditions:

19. Application to ontological beliefs
3 big take-aways from Bayesian probability that we can apply to ontological beliefs:
Assign degrees of probability rather than Boolean (true/false) values
Use networks/graphs to show what other variables influence your beliefs
Update beliefs based on evidence

20. Let me demonstrate how this might look...
If you went to a believer and said you don't think there's a god, and the believer says,
"well, I think there is". That's not a very productive conversation. Obviously, it's better
to get into reasons.

27. Conclusion
Lessons learned from Bayesian Probability

28. Assign degrees of probability rather than Boolean (true/false) values
Unless you know a whole lot... you probably can't assign a 100% True or
False value
And doing so can be seen as either arrogance or ignorance
It's more intellectually honest/truthful to assign probabilities, as it implies
lack of knowledge (for 0% < p < 100%)
Also, it lowers the chance of your prematurely throwing out the truth
It would have been a mistake to throw out the 20-sided dice
hypothesis
Use networks/graphs to show what other variables influence your beliefs
Having such a network can help see what variables/assumptions are
influencing our beliefs. And can help us analyze our assumptions
It also helps keep the big picture in mind
Update beliefs based on evidence
Keep an open mind, and consider not just the evidence that fits your
current best hypothesis, but all the evidence (avoid selection bias)
If I think it's a 6-sided dice, I might be inclined to, say, only read
articles reporting on dice rolls 6 or less.

29. Questions?
More information:
http://www.greenteapress.com/thinkbayes/thinkbayes.pdf
https://github.com/CamDavidsonPilon/Probabilistic-Programming-and-
Bayesian-Methods-for-Hackers
https://github.com/calebmadrigal/probability-with-python