Bayes and Bool Walk into a Bar
summary
Scala code constructs a probability monad with map/flatMap, sampling-based density and discretization, and a simple API to generate users, dice/coin games and Normal(30,5) ages. It runs millions of samples to estimate mean/median/variance and also uses the Figaro library to represent models and perform inference, showing exact variable elimination and approximate Metropolis–Hastings. Concrete examples include a disease-test posterior (~2.9% given 0.1% prevalence and 90% sensitivity) and an alarm/burglary model (~37% burglary posterior when John calls).
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chapters (21)
- 0:00Introduction
- 0:19About me
- 0:47Acknowledgments
- 1:09A few words about the title
- 1:45What’s on the agenda
- 2:40Use cases
- 3:18Data generation
- 4:44Key concepts
- 5:06Measurable space
- 10:39Probability measure
- 11:16Random variable
- 12:29Example
- 16:19Density
- 19:29How to define a probability distribution in functional programming?
- 22:24Defining descriptive statistics
- 27:19We can tackle problems the other way around
- 27:56Figaro
- 30:29Back to conditional probabilities
- 31:38Bayes’ theorem: application
- 35:15Conclusion
- 37:09Thank you for your attention
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