Alexander Fengler, Krishn Bera
16/07/2026
Introduction to the
HSSM Ecosystem
Intro: Random Dot Motion Task
Let’s start with a simple experiment
Moving Dots Paradigm
Q: What is the dominant direction of motion?
Trials
Building a cognitive model
ndt
Starting point
a
choice up
choice down
z
Non-decision Time
v
Drift
The Drift Diffusion Model
Trials
Building a cognitive model
v
Drift
v
Drift
v
Drift
Subject specific notion of task difficulty…
Easier
Proposing an adjustment….
I propose that the
criterion is not
constant over time!
ndt
Starting point
a
z
Non-decision Time
v
Drift
Boundary Angle
People dynamically adjust the criterion to, e.g. avoid wasting too much time on a given decision!
Sounds reasonable intuitively.
Surely we would want to investigate it?
Mathematical Disconnect: Inference vs. Generation
Evaluate the density!
ndt
a
z
v
Data Generation
Inference
Produce (reaction time, choice) pairs!
As we said, usually simple…
5 lines of code here!
All about evaluating the likelihood many times!
Mathematical Disconnect: Inference vs. Generation
Data Generation
Inference
Mathematical Disconnect: Inference vs. Generation
Data Generation
Inference
Mathematical Disconnect: Inference vs. Generation
Inference
Observation :
Models with these mathematical
short-cuts are sparse,
when compared to the number of models we can easily simulate from!
Mathematical Disconnect: Inference vs. Generation
In undergraduate statistics classes we mostly (read pretty much always) are exposed to models for which we have both the likelihood and the DGP ….
. . .
. . .
Mathematical Disconnect: Inference vs. Generation
Data Generation
Inference
Mathematical Disconnect: Inference vs. Generation
Data Generation
Inference
Likelihood Approximation Networks (LANs)
Evaluation of the Neural Network is much faster than construction of empirical likelihoods!
Likelihood Surrogates broadly (LANs, NLEs, NREs ….)
Evaluation of the Neural Network is much faster than construction of empirical likelihoods!
Amortized Likelihoods: Flexibility
Amortized Likelihoods: Flexibility
Amortized Likelihoods: Flexibility
Surrogates
Analytical
Amortized Likelihoods: Flexibility
What we will try to achieve:
Also worth mentioning…
New analytical likelihoods (aDDM)
Gaze modulated drift parameter
Generalized algorithm for fast likelihood computation
Processes on parameters (1) (more on this later)
Processes on parameters (2) (upcoming)
Francesco Muia
Krishn Bera
Tony Chen
Lakshmi Govindarajan
Andrew Zhang
Sicheng
Liu
Michael J. Frank
Paul Xu
Carlo Paniagua
Aisulu Omar
END
Theoreticians
Computational Scientists
Likelihood Functions
Contribution Templates
Simulators
Inference Algorithms
Experimentalists
Simple Interface
Neural Covariates
Hierarchical Model
construction
Model Constructors
HSSM Ecosystem
Customized Education
Verify your work
The kind of research this powers:
Simulation
Surrogates
Inference