3.15 Models: What is a model?

  • Q: In how far is a map a model of the reality?
  • Q: In how far is the mean(age) in this class a model of age in this class?


  • Behind any model there is a (joint) distribution
  • Model summarizes (joint) distribution with fewer parameters
    • e.g. a mean; or intercept/coefficents in linear model
  • Statistical Model (SM) (Wikipedia):
    • Class of a mathematical model (MM)
    • Embodies assumptions about generation of sample data from data of a larger population
    • Assumptions describe set of probability distributions
      • e.g. sampling distribution of reg. coefficent = normally or t-distributed
    • Inherent probability distributions distinguish SMs from MMs (but see also Nonparametric statistics)