Today's clip is from episode 158 featuring Stefan Radev. In this conversation, Alex and Stefan explore a genuinely fascinating problem: how do you turn an expert's intuition into a mathematically valid prior distribution - and can AI help automate that process?

Alex explains that prior elicitation is essentially a translation problem. Experts don't walk around thinking in probability distributions - their knowledge lives in intuitions, rules of thumb, and rough ranges. The challenge is converting that into something a Bayesian model can actually use.

The traditional approach? Ask an expert for quantiles or a mean, then parameterize your prior with hyperparameters and simulate until the model-implied quantities match what the expert described. If your pipeline is differentiable end-to-end, you use gradient descent. If not, you fall back to something like Bayesian optimization. Either way, you're iterating toward a prior that genuinely reflects expert knowledge - not just a convenient assumption.

But the really exciting part is what came next. In a follow-up paper, they pushed this further: instead of optimizing within a fixed parametric family (say, a Gaussian), they replaced the prior entirely with a normalizing flow - a flexible generative network - and ran the same procedure. No assumed distribution family. Just let the data and the expert's knowledge shape the prior from scratch.

The catch? More flexibility means more non-identifiability and stability headaches. But the direction is clear: a fully automated, end-to-end pipeline for building priors from non-probabilistic expert knowledge. And in 2026, that pipeline could theoretically be driven by an agent.

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