Seminar talk: Simulation-based Inference (SBI)#

Date:

2026-03-16

Tags:

bayes, simulation-based inference, SNPE, seminar

Original slides

A seminar talk I gave alongside the special course in Simulation-based Inference that ran at Aalto in early 2026 — the same course that anchored the work in StimIQ, EASE Health, and QSVT4CRA.

SBI is the method I keep coming back to whenever a problem is hard to likelihood but easy to simulate. Instead of writing down \(p(x\mid\theta)\) analytically and inverting it, you:

  1. Pick a forward model / simulator — encode the structure you understand.

  2. Sample parameters \(\theta\sim p(\theta)\), run the simulator, observe \(x\sim p(x\mid\theta)\).

  3. Train a neural posterior estimator (SNPE) — or an emulator, or a likelihood ratio network — directly on the \((\theta, x)\) pairs.

  4. At inference time, condition on the observed data and let the amortised network give you \(p(\theta\mid x)\).

The slides work through:

  • Why SBI. Likelihood-free settings (stochastic simulators, agent-based models, implicit models) where MCMC is stuck because the likelihood isn’t a closed-form expression. The motivating examples are the ones I actually use: migraine risk under a mechanistic “digital shadow,” DBS parameter optimisation in Parkinson’s, credit-risk on the LUMI supercomputer.

  • The three families. Neural posterior estimation (SNPE-A/B/C), neural likelihood estimation (NLE), neural ratio estimation (NRE). When each one is the right tool.

  • Calibration. A posterior isn’t useful if you can’t tell whether it’s honest. The calibration / coverage diagnostic on slide 8 — empirical coverage vs. credibility level — is the one I lean on. A well-calibrated posterior hugs the diagonal; an overconfident one falls below it.

The honest framing in the talk — and the one that shapes everything I build now — is that SBI is honest about what it doesn’t know. You get a full posterior, not a point estimate; and the simulator encodes your structural beliefs explicitly, so when the posterior is wide you can trace it back to a modelling choice.

Slides#

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Slide 2 — the canonical SBI loop: simulate, train, condition.#

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Slide 8 — empirical-coverage diagnostic. The yellow curve hugging the diagonal is a well-calibrated posterior; below it, the model is overconfident. This is the slide I keep coming back to.#

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