Seminar talk: Simulation-based Inference (SBI)
===============================================

:Date: 2026-03-16
:Tags: bayes, simulation-based inference, SNPE, seminar
:download:`Original slides <../_static/sbi-seminar.pptx>`

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 <https://github.com/PlayerPlanet/StimIQ>`_,
`EASE Health <https://ease-health.org>`_, and `QSVT4CRA <https://github.com/PlayerPlanet>`_.

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

1. Pick a forward model / simulator — encode the structure you understand.
2. Sample parameters :math:`\theta\sim p(\theta)`, run the simulator, observe
   :math:`x\sim p(x\mid\theta)`.
3. Train a neural posterior estimator (SNPE) — or an emulator, or a likelihood
   ratio network — directly on the :math:`(\theta, x)` pairs.
4. At inference time, condition on the observed data and let the amortised
   network give you :math:`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
------

.. figure:: ../_static/slides/sbi-seminar/sbi-image8.png
   :alt: Slide 2
   :width: 100%

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

.. figure:: ../_static/slides/sbi-seminar/sbi-image9.png
   :alt: Slide 4
   :width: 100%

   Slide 4.

.. figure:: ../_static/slides/sbi-seminar/sbi-image10.png
   :alt: Slide 4
   :width: 100%

   Slide 4.

.. figure:: ../_static/slides/sbi-seminar/sbi-image11.png
   :alt: Slide 4
   :width: 100%

   Slide 4.

.. figure:: ../_static/slides/sbi-seminar/sbi-image12.png
   :alt: Slide 5
   :width: 100%

   Slide 5.

.. figure:: ../_static/slides/sbi-seminar/sbi-image13.png
   :alt: Slide 5
   :width: 100%

   Slide 5.

.. figure:: ../_static/slides/sbi-seminar/sbi-image14.png
   :alt: Slide 6
   :width: 100%

   Slide 6.

.. figure:: ../_static/slides/sbi-seminar/sbi-image15.png
   :alt: Slide 6
   :width: 100%

   Slide 6.

.. figure:: ../_static/slides/sbi-seminar/sbi-image16.png
   :alt: Slide 8
   :width: 100%

   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.

.. figure:: ../_static/slides/sbi-seminar/sbi-image17.png
   :alt: Slide 8
   :width: 100%

   Slide 8.

.. figure:: ../_static/slides/sbi-seminar/sbi-image18.png
   :alt: Slide 8
   :width: 100%

   Slide 8.

.. figure:: ../_static/slides/sbi-seminar/sbi-image19.png
   :alt: Slide 8
   :width: 100%

   Slide 8.

.. figure:: ../_static/slides/sbi-seminar/sbi-image20.png
   :alt: Slide 9
   :width: 100%

   Slide 9.

.. figure:: ../_static/slides/sbi-seminar/sbi-image21.png
   :alt: Slide 9
   :width: 100%

   Slide 9.

.. figure:: ../_static/slides/sbi-seminar/sbi-image22.png
   :alt: Slide 9
   :width: 100%

   Slide 9.

.. figure:: ../_static/slides/sbi-seminar/sbi-image23.png
   :alt: Slide 9
   :width: 100%

   Slide 9.

.. figure:: ../_static/slides/sbi-seminar/sbi-image24.png
   :alt: Slide 13
   :width: 100%

   Slide 13.

.. figure:: ../_static/slides/sbi-seminar/sbi-image25.png
   :alt: Slide 14
   :width: 100%

   Slide 14.

.. figure:: ../_static/slides/sbi-seminar/sbi-image26.png
   :alt: Slide 14
   :width: 100%

   Slide 14.

Links
-----

- :download:`Download the original deck (PPTX) <../_static/sbi-seminar.pptx>`
- `sbi` library (the toolkit): https://www.mackelab.org/sbi/
- Course context — the special course in Simulation-based Inference at Aalto
  (early 2026) that ran alongside the talk.