An introduction to bayesian statistics
- 2. 0 2000 4000 6000 8000 1960 1970 1980 1990 2000 2010 WOS "Bayesian" Citations by Year The rise of Bayesian statistics
- 4. So…What are Bayesian Statistics? 1) A fundamentally different approach to probability
- 5. So…What are Bayesian Statistics? 1) A fundamentally different approach to probability 2) An associated set of mathematical tools
- 6. Frequentists vs. Bayesian Round 1 Parameters fixed Data varies Data fixed Parameters Vary
- 8. Frequentists vs. Bayesian Round 1 Confidence Interval Credible Interval
- 9. Conditional Probability in 2 minutes
- 10. Conditional Probability in 2 minutes All possible outcomes
- 11. Conditional Probability in 2 minutes
- 12. Conditional Probability in 2 minutes
- 13. Conditional Probability in 2 minutes
- 14. Conditional Probability in 2 minutes
- 15. Conditional Probability in 2 minutes
- 16. Bayes’ Theorem
- 21. Frequentist vs. Bayesian Round 2 “The Strength of the Prior”
- 22. Sparse Data
- 23. Abundant Data
- 24. Uniform Prior
- 25. Where do Priors Come From?
- 26. So…What are Bayesian Statistics? 1) A fundamentally different approach to probability 2) An associated set of mathematical tools
- 27. How do you actually do this?
- 28. So how do you actually do this? 1. Analytical methods
- 29. So how do you actually do this? 1. Analytical methods 2. Grid approximation
- 30. So how do you actually do this? 1. Analytical methods 2. Grid approximation 3. Markov Chain Monte Carlo
- 31. MCMC • Algorithm for exploring parameter space
- 32. MCMC • Algorithm for exploring parameter space 1.Pick a starting point
- 33. MCMC • Algorithm for exploring parameter space 1.Pick a starting point 2.Propose a move
- 34. MCMC • Algorithm for exploring parameter space 1.Pick a starting point 2.Propose a move 3.Accept or decline move based on probability
- 35. MCMC • Algorithm for exploring parameter space 1.Pick a starting point 2.Propose a move 3.Accept or decline move based on probability • Time spent at each point approximates parameter distribution
- 36. MCMC • Algorithm for exploring parameter space 1.Pick a starting point 2.Propose a move 3.Accept or decline move based on probability • Time spent at each point approximates parameter distribution • E.g. Metropolis-Hastings, Gibbs sampling
- 37. MCMC 2D example
- 38. MCMC 2D example
- 39. So what does all this get us?
- 40. Bayesian methods really shine in complex (hierarchical) models…
- 43. Many benefits to this approach • Simultaneously estimate parameters • …as well as parameter relationships • “Borrow” strength across studies • Model comparison
- 44. So, is it a Bayesian Revolution?
- 45. Bayesian stats can do most things frequentist,
- 46. Bayesian stats can do most things frequentist, but… • Many simple models don‟t gain much • Better do something „boring‟ well than something exciting poorly
- 47. Bayesian stats can do most things frequentist, but… • Many simple models don‟t gain much • Better do something „boring‟ well than something exciting poorly • Don‟t be this guy
- 48. DO use Bayesian methods if • You have a complex model with many interacting parameters • You have „messy‟ data • You don‟t want to make assumptions about distributions
- 49. In Conclusion • Bayesian methods are powerful tools for ecological research • Like most things statistical, they are no substitute for thinking • They are here to stay, and you should at least be familiar with them
- 50. Great, I want to learn more! JAGS (Just Another Gibbs Sampler)