Small Worlds and Large Worlds

schifferl
February 21, 2018

McElreath, R. Statistical Rethinking: A Bayesian Course with Examples in R and Stan. (CRC Press/Taylor & Francis Group, 2016).

Small worlds and large worlds





A bag of four marbles



  • Consider a bag of four marbles
  • Marbles are either blue or white
  • Divine all possible combinations
  • Call these conjectures



  • Consider the 1 blue, 3 white conjecture
  • Draw three times with replacement
  • How many ways to produce:
    • Blue, white, blue

A bag of four marbles





A bag of four marbles





ways <- c(0, 3, 8, 9, 0)

ways / sum(ways)
[1] 0.00 0.15 0.40 0.45 0.00

Definitions



Parameter - An index of possible explanations
Likelihood - Relative number of ways to produce a parameter
Prior Probability - Prior plausibility of produce specific value of a parameter
Posterior Probability - Updated plausibility of a parameter given observations

Globe toss



Globe toss

  • Model (story)
  • Update (prior)
  • Evaluate (BIC)

Globe toss

Bayes' theorem




Condition Priors

  • Given your data, construct a prior
  • Produce a likelihood for a parameter
  • Calculate a posterior
  • Grid approximation
  • Quadratic approximation
  • Markov chain Monte Carlo