#165 Hierarchical Sequential Sampling Modeling, with Alex Fengler

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Takeaways:

Q: What is HSSM and how does it relate to HDDM?
A: HSSM stands for hierarchical sequential sampling models, a generalization of HDDM (hierarchical drift diffusion models), the older toolbox for the same class of decision-making models, but HSSM is built from the ground up on simulation-based inference. That's what lets it handle any variation of the underlying process model, not just the ones with a tractable closed-form likelihood.

Q: What is the drift diffusion model and why has cognitive science relied on it so heavily?
A: The drift diffusion model treats a decision as a random walk that accumulates evidence until it crosses one of two boundaries, with parameters controlling boundary separation, starting bias, and drift rate. It's been used in thousands of published papers largely because it has a closed-form likelihood, which makes standard Bayesian and maximum-likelihood inference fast. Small variations on the model are often just as scientifically motivated, but if their likelihoods aren't analytically convenient, the literature using them stays sparse.

Q: What is a likelihood approximation network (LAN) and what does it actually learn?
A: A LAN is a neural network trained to take in a process's parameters and a trial's outcome and output how likely that outcome was, learned purely from repeated simulation rather than derived analytically. Once trained, it functions as a fast, reusable likelihood you plug directly into Bayes' rule, in place of a closed-form solution that may not exist for the model you actually want to fit.

Q: What's the difference between amortizing the likelihood and amortizing the posterior?
A: Amortizing the likelihood, HSSM's approach, means training a network once to approximate the likelihood, then reusing that same network across arbitrarily many downstream models: different priors, hierarchical structures, or regression backends, with no retraining. Amortizing the posterior directly, the approach tools like BayesFlow take, gives near-instant inference once trained, but locks the network into the specific scenario it was trained for. Neither is strictly better; it's a trade based on how much reuse you expect.

Chapters:
00:00:00 What is HSSM and how does it fit into the Bayesian inference landscape?
00:12:09 How did HSSM evolve from HDDM, and what does it apply to?
00:30:25 How do neural networks learn likelihoods for Bayesian inference?
00:37:01 What makes amortized Bayesian inference so flexible?
00:41:04 What are the real computational costs of amortized inference?
00:55:16 How does HSSM integrate with libraries like BayesFlow?
00:58:57 What does a live demo of HSSM and BayesFlow look like?
01:18:33 What is Bayesify and how does it score a paper's Bayesian workflow?
01:23:12 What new model classes are coming to the HSSM ecosystem?
01:30:12 How is AI reshaping development in the HSSM ecosystem?
01:38:42 How should society incentivize keeping hard cognitive skills alive?

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