Models of Decision Making for Neuroscience

Simon Schug

October 2020

Normative Models


The world is riddled with uncertainty.

white-noise Noise

rotating-mask Ambiguity

aperture-problem Partial Information

Probability Theory

Probability theory is nothing but common sense reduced to calculation.

Pierre-Simon Laplace (1819)

Bayes’ Theorem

Given the state \(x\), the observation \(y\) and the hypothesis space \(\mathcal{H}\)

\[ P(x|y, \mathcal{H}) = \frac{P(y|x, \mathcal{H}) \cdot P(x| \mathcal{H})}{P(y| \mathcal{H})} \]

  • Likelihood: Probability of the observations given the explanation.
  • Prior: Probability of the explanation based on prior experiences.
  • Posterior: Probability of the explanation given the observations.

Posterior Update


Model Selection

What happens when we have multiple explanations \(\mathcal{H}_1, \mathcal{H}_2\) for the data? \[\mathcal{H}^* = arg \max_{\mathcal{H}_i} P(\mathcal{H}_i|y)\]

  • Find the most probable explanation by maximisation
  • Automatically embodies Occams’ Razor

How does Bayesian inference help us to study decision making?

Expected Utility Maximisation

\[ a^* = arg \max_a \int p(x | y) \cdot U(a, x) dy \]

  • Utility function \(U(x, a)\) encodes our own preferences
  • Choose the action that maximises utility!

Ideal-Observer Analysis

Derive a theoretically optimal model on how to perform a given task.


Perceptual Decision Making

In simple perceptual decision tasks, humans perform close to optimal. reference-ernst reference-körding

Monty Hall Problem


Process Models

Marr’s Levels of Analysis


Artificial Neural Networks

Study mathematical models of the brain.


Reinforcement Learning

Let artificial agents solve real tasks.


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