Models of Learning

• Introduction

  1. Task description

• Reinforcement Learning

  1. Theory
     • Rescorla-Wagner
     • SoftMax
  2. Data plotting
  3. Simulation
     • Example participants
     • More participants
     • Explore Parameters
     • Grid Search
     • Marginal distributions
     • Summary values
  4. Real data
     • Fit the data
     • Statistical inference
  5. Review
     • Modelling how-to

• Bayesian Learning

  1. Coin tossing
     • Probability
     • Likelihood
     • Uncertainty
     • Learning
     • Review
  2. Bandit task
     • Updating
     • Transition function
     • Learning rate

Developed by
Jill O'Reilly
Hanneke den Ouden
-August 2015

Marginal distributions for α and β

Most of the time we will be interested in the value of each parameter, not in this full 2D 'likelihood landscape'.

In order to achieve this, we can for each parameter, or dimension, 'collapse' or 'marginalise' this plot over the other dimensions.

What do you think the marginal distributions for α and β look like?

?

Marginal distributions for α and β

• To get the parameter distribution for α, we sum the 2D likelihood plot along the vertical dimension.
• To get the parameter distribution for β, we sum the 2D likelihood plot along the horizontal dimension.

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