---
title: "Trusting posteriors learned from simulations"
description: "Learn what a calibrated posterior promises, test a neural posterior with ranks and coverage, then catch a wrong simulator with importance weights."
canonical_url: "https://sandboxphysics.com/stories/simulation-based-inference/"
language: "en"
page_type: "story"
alternate_languages:
  zh-CN: "https://sandboxphysics.com/zh/stories/simulation-based-inference/"
last_modified: "2026-11-14"
---

# Trusting posteriors learned from simulations

Sandbox Physics · 2026-11-12

A neural network trained on simulations can return a posterior in seconds. Start with what a posterior and its 90% region promise, learn the rank and coverage tests that check the promise, and then see why a network can pass every test and still be wrong about real data.

1. L1 · Explainer

   ## [How can you tell whether a neural network's posterior deserves trust?](https://sandboxphysics.com/stories/simulation-based-inference/trusting-a-neural-posterior/)

   Test it on simulated data where the answer is known, compare it with an exact calculation, and check that the real data look like the simulations.

2. L1 · Chapter

   ## [What a posterior and a 90% credible region promise](https://sandboxphysics.com/stories/simulation-based-inference/posterior-and-credible-regions/)

   Build a posterior from a prior and a likelihood, find its 90% region on a grid, and see why the region catches the truth nine times in ten.

3. L2 · Chapter

   ## [Checking posterior calibration with ranks and coverage](https://sandboxphysics.com/stories/simulation-based-inference/rank-tests-for-posterior-calibration/)

   Simulation-based calibration ranks the true value among posterior draws. Flat ranks mean calibrated; humps, cups and slopes name the failure.

4. L3 · Chapter

   ## [Finding a wrong simulator with importance weights and residuals](https://sandboxphysics.com/stories/simulation-based-inference/model-mismatch-and-importance-weights/)

   Importance weights test the network against the assumed likelihood; a residual test checks the likelihood against the data. A hidden second mode can pass both.

5. L3 · Method

   ## [Recompute the ringdown posterior calibration](https://sandboxphysics.com/stories/simulation-based-inference/recompute-the-ringdown-calibration/)

   Run simulation-based calibration on a conjugate Gaussian model, then on a frozen neural posterior for a synthetic ringdown, with saved inputs and failure cases.

6. L4 · Paper guide

   ## [Reading the DINGO evidence: P–P plots, divergences and sample efficiency](https://sandboxphysics.com/stories/simulation-based-inference/reading-dingo-calibration-evidence/)

   A figure-by-figure guide to the 2021 DINGO letter and the 2023 importance-sampling letter, with what each test shows and how out-of-range data are flagged.