Tutorial 1: Sequential Probability Ratio Test
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
- 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.