Unit 8: Simulating Probabilities

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Connections

Probability
  • There are three types of probabilities mentioned that students sometimes confuse: theoretical probabilities (made using mathematical arguments), experimental probabilities (based on data), and simulated probabilities that come from simulation exercises and are used to approximate theoretical probabilities. We’ve discussed the differences between the former two in previous units and this unit discusses the latter.
Models
  • The assumptions under which one performs a simulation is a model. Remind students of this connection.
Inference
  • Though students will not learn formal inference using theoretical models (particularly, the normal model) until later in the course, remind them that they can make informal inference using simulated models. It will be very useful to compare the two methods in later units to show students the value of simulation-based inference.

  • Simulation-based inference will be extremely useful when assumptions used to make formal inference cannot be met.