Bayesian Probability: a tool for communicating beliefs

Intro to Caleb

http://calebmadrigal.com/

caleb.madrigal@gmail.com

Monty Hall problem

"Suppose you're on a game show, and you're given the choice of three doors: Behindone 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 toswitch your choice?"

A: Switch

B: Stay with original door

C: Doesn't matter if you switch or stay

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

Intro to Bayesian Probability

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

Parts of formula:

Dice problemDice problem

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

Example application: roboticExample application: roboticlocalizationlocalization

Bayesian Networks

Dice problem bayesian network for the first roll:

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

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

Though typically, I prefer to solve this using MonteCarlo simulations:

Bayesian Network for pricing car insurance:

CPCS (Computer-based Patient Case Study) - used fordiagnosing medical conditions:

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

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 betterto get into reasons.

Conclusion

Lessons learned from Bayesian Probability

Assign degrees of probability rather than Boolean (true/false) valuesUnless 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 beliefsHaving 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 evidenceKeep 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.

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