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Tutorial 1: Sequential Probability Ratio Test

Difficulty level

This tutorial introduces the Sequential Probability Ratio Test between two hypotheses 𝐻𝐿 and 𝐻𝑅 by running simulations of a Drift Diffusion Model (DDM). As independent and identically distributed (i.i.d) samples from the true data-generating distribution coming in, we accumulate our evidence linearly until a certain criterion is met before deciding which hypothesis to accept. Two types of stopping criterion/stopping rule will be implemented: after seeing a fixed amount of data, and after the likelihood ratio passes a pre-defined threshold. Due to the noisy nature of observations, there will be a drifting term governed by expected mean output and a diffusion term governed by observation noise.

Overview of this tutorial:

  • Simulate Drift-Diffusion Model with different stopping rules
  • Observe the relation between accuracy and reaction time, get an intuition about the speed/accuracy tradeoff
Topics covered in this lesson
  • Introduction to the Sequential Probability Ratio Test (SPRT)
  • Accuracy vs stopping time
  • Drift diffusion model (DDM) with fixed thresholds
  • Accuracy vs threshold

Experience with Python Programming Language.

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