# 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).

### 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

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

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

### 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