---
name: Joint Posterior Triangle Plot
slug: joint-posterior-triangle-plot
category: Data
description: "Joint Posterior Triangle Plot shows overlaid triangle plots for two or more models on the source's parameter axes. Use it when comparing how models shift parameters and whether their joint contours overlap or diverge."
github: "https://github.com/tangxiangru/AutoR/tree/main/src/skills/astronomy-the-joint-posterior-is-the-parameter-result"
language: Python
stars: 804
forks: 25
install: "npx degit https://github.com/tangxiangru/AutoR/tree/main/src/skills/astronomy-the-joint-posterior-is-the-parameter-result ~/.claude/skills/astronomy-the-joint-posterior-is-the-parameter-result"
installs_to: ~/.claude/skills/astronomy-the-joint-posterior-is-the-parameter-result
source_path: src/skills/astronomy-the-joint-posterior-is-the-parameter-result/SKILL.md
collection_size: 25
category_size: 668
collection_url: "https://dirskills.com/collections/tangxiangru/AutoR"
added: 2026-08-22T05:22:24.720Z
last_synced: 2026-08-22T05:22:24.720Z
canonical_url: "https://dirskills.com/skills/joint-posterior-triangle-plot"
---

# Joint Posterior Triangle Plot

Joint Posterior Triangle Plot shows overlaid triangle plots for two or more models on the source's parameter axes. Use it when comparing how models shift parameters and whether their joint contours overlap or diverge.

**Install:**

```bash
npx degit https://github.com/tangxiangru/AutoR/tree/main/src/skills/astronomy-the-joint-posterior-is-the-parameter-result ~/.claude/skills/astronomy-the-joint-posterior-is-the-parameter-result
```

## README

# One set of axes, every model, every parameter the source tabulates

When the claim under test is that two models absorb the same data by shifting the
parameters in *different directions*, the claim does not live in any marginal. It lives
in the joint distribution: which way each model moves in the expansion-rate–matter-density
plane, whether a shift runs along a degeneracy or across it, how far apart two models'
contours are in the plane where they are closest, whether they overlap at all. The
exhibit that carries that is one figure — the triangle plot, every model overlaid on one
set of axes, filled 68% and 95% contours below the diagonal, the one-dimensional
marginals on it — and it is the first thing a reader in this field looks for.
`the-canonical-figure` gives the general rule; this is the version with the decisions in
it.

**The parameter list is the source's, not your sampler's.** Take the axes from the rows
the source tabulates *for every model in the comparison*, in the source's order and under
the source's symbols. A parameter only one model carries cannot be a shared axis — it
belongs in its own panel or a second figure — and where the source's caption says which
subset it drew, that subset is the grid. Two consequences follow and both get made
backwards by default. A parameter your own likelihood never constrains stays on the grid,
carrying the published constraint alone — see
`astronomy-sample-the-published-table-into-chains` for where its samples come from — and
a parameter of your own parameterisation that the source does not tabulate stays off it,
because a reader has nothing to check it against. A grid whose axes are the intersection
of the source's table with your sampler's free parameters is a comparison of your
analysis to itself.

**Every model in the comparison is a contour with a legend entry**, including the one the
others are being compared to and including a model you only hold as published numbers.
Draw all of them once, in one figure; two separate corner plots side by side answer a
different question, because the whole content is where the contours sit relative to each
other.

**What does not substitute, in descending order of how convincing it looks:** a row of
one-dimensional error-bar panels, one parameter each; a table of means and intervals; a
scatter of best-fit points in one plane with no contours; a pair of separate corner
plots. Every one of these carries the marginals and throws away the correlations, which
is the part that was asked for. The error-bar row is the specific near-miss that gets
built when the triangle plot is not in the plan: it is quick, it is honest, it shows the
same numbers, and it reads to anyone laying it beside the source's figure as the figure
not existing.

**Fix the slot at design time.** Figure plans get frozen before results exist, and in a
run with a stamped plan the standard figure cannot be added later without editing a
digest. Put the joint-posterior slot in the plan before any hypothesis of yours claims
one, and bind it to the source's result rather than to a claim id.

**Then say in prose, immediately beside the panel, what it shows**, with numbers and in
the source's terms: which model sits higher in the expansion rate and by how much, which
in the clustering amplitude, which is lower in the matter density, and whether the two
remedies push in opposite senses. The contours are the evidence; the direction sentence
is the result, and it belongs in the paragraph that introduces the figure rather than in
a later section a reader working through a long report may never reach.

## Why this is here

Measured on Astronomy_001 of ResearchClawBench, rescored with gpt-5.1 over three draws.
The image criterion asking for the reproduced triangle plot carries 0.4 of the task, and
**neither arm drew one**. The AutoR run scored **6.7 out of 100** on it and a bare agent
**16.0**, but that 16.0 is one draw of 48 beside two of 0, and the 48 describes contours
that are not in the bare agent's report either — it opens "The AI's triangle plot clearly
shows", while the string `triangle` occurs zero times in that report's 20,101 characters,
`corner plot` matches nothing in that workspace at all, and the five files that do contain
`getdist` are its score files and its agent transcript — nothing it produced. So this skill
is not written from an arm that got it right. It is written because the criterion is
worth 0.4 of the task, AutoR left 93 of its 100 points on it, and the object it asks for
is a short call once chains exist.

What AutoR shipped instead is `fig2_parameter_constraints.png`: five one-dimensional
error-bar panels over matter density, expansion rate, clustering amplitude, physical
matter density and spectral index. The judge's stated reason is that the report "does not
include a triangle plot of 2D posteriors ... instead it shows separate 1D error-bar
panels". Of those five axes the physical matter density is a parameter of the run's own
sampler and not one the supplied block tabulates, while the block's optical depth and log
primordial amplitude — each given with a 1-sigma error for all three models — get no axis
at all. The run had the direction result right: it is in the prose, and its own caption
for that figure points at the shift printed under each panel — "the published shift of
each model against ΛCDM: opposite in sign in Ω_m, H₀, σ₈ and n_s". Holding the result and
not the exhibit is what this criterion charges for.

The general form of the advice was in the pack and was read. The whole run made three
`Skill` calls — `citation-discipline` at Stage 01, then
`astronomy-figure-is-the-unit-of-result` and `the-canonical-figure` inside Stage 06 — and
`the-canonical-figure` names the corner plot as the expected exhibit for Bayesian
parameter inference. Its own front matter offers it at study design too, but the run
opened it at the stage that *draws* the slate rather than the one that fixes it: Stage 03
had already stamped the figure plan with a digest, and every slot in it was bound to one
of the run's own preregistered hypotheses.