Method library WORKFLOW / 038

Research workflow/4 steps

Bayesian regression discontinuity with credible intervals (CausalPy)

@causalpy ✓ P D · Jun 29, 2026 · 1k views

@misc{causalpy,
  title        = {CausalPy},
  author       = {PyMC Labs},
  howpublished = {\url{https://causalpy.readthedocs.io/}},
  note         = {Software / documentation}
}

In the margins · Peer notes@rahul_nair · Nice that the bandwidth refit is built in as a robustness step. The estimate moving with the window is the whole R… 2

The method workspace

Follow the analysis.

Select a node to explore the method

Method mapInput → 4 steps → output

START WITHInput data

ARRIVE ATResults

Read step 01

Inside the methodReasoning, equations & implementation

Data prep

Running variable, threshold, outcome

Step notesField note & discussion1

Data preparation — shapes the raw inputs into what the estimator expects.

What happens here

Treatment switches on at the cutoff c. Identification rests on continuity of everything else at c.

Formula

\tau=\lim_{x\downarrow c}\mathbb E[Y\mid X{=}x]-\lim_{x\uparrow c}\mathbb E[Y\mid X{=}x]

Reads fromNot specified Feeds intoNot specified

Key code

import causalpy as cp
# x running variable, cutoff c, treated = (x >= c)

Reference / docs ↗

Discussion on this step (0)

StatsOtterDiscussion starter · Editorial note

Before using this step, make its assumptions and its output explicit. A useful peer note explains what you would check, what could go wrong, or what would change your interpretation.

Questions to explore

Which assumption matters most here, and what evidence could challenge it?
What would you check before passing this output to the next step?

Peer discussion

Bring your experience, a question, or a different perspective.

Estimation

A Bayesian model each side of the cutoff

Step notesField note & discussion1

The core estimate — where the causal quantity itself is computed.

What happens here

Fit a flexible trend with a treatment indicator; the coefficient on the indicator is the discontinuity, with a prior and full posterior.

Formula

Y\sim\mathcal N\big(f(X)+\tau\,\mathbb 1\{X\ge c\},\ \sigma^2\big)

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Key code

result = cp.pymc_experiments.RegressionDiscontinuity(
    df, formula='y ~ 1 + x + treated',
    running_variable_name='x', treatment_threshold=0.5)

Reference / docs ↗

Discussion on this step (0)

StatsOtterDiscussion starter · Editorial note

Before using this step, make its assumptions and its output explicit. A useful peer note explains what you would check, what could go wrong, or what would change your interpretation.

Questions to explore

Which assumption matters most here, and what evidence could challenge it?
What would you check before passing this output to the next step?

Peer discussion

Bring your experience, a question, or a different perspective.

Inference

Posterior & 94% credible interval for the jump

Step notesField note & discussion1

Uncertainty quantification — standard errors, intervals, and aggregation.

What happens here

Instead of a single number ± SE, you get the whole posterior of the discontinuity — summarised as a credible interval.

Formula

p(\tau\mid \text{data})\propto p(\text{data}\mid\tau)\,p(\tau);\quad \text{report }CI_{94\%}

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Key code

result.summary()   # discontinuity, CI_94%
result.plot()

Reference / docs ↗

Discussion on this step (0)

StatsOtterDiscussion starter · Editorial note

Before using this step, make its assumptions and its output explicit. A useful peer note explains what you would check, what could go wrong, or what would change your interpretation.

Questions to explore

Which assumption matters most here, and what evidence could challenge it?
What would you check before passing this output to the next step?

Peer discussion

Bring your experience, a question, or a different perspective.

Robustness check

Bandwidth & functional-form sensitivity

Step notesField note & discussion1

A robustness check — does the headline result survive a different lens?

What happens here

Refit on a narrow window and with different trends; a discontinuity that survives is one you can defend.

Formula

\hat\tau(h)\ \text{stable across bandwidths }h\ \Rightarrow\ \text{credible}

Reads fromNot specified Feeds intoNot specified

Key code

cp.pymc_experiments.RegressionDiscontinuity(
    df, ..., epsilon=0.2)   # restrict near the cutoff

Reference / docs ↗

Discussion on this step (0)

StatsOtterDiscussion starter · Editorial note

Before using this step, make its assumptions and its output explicit. A useful peer note explains what you would check, what could go wrong, or what would change your interpretation.

Questions to explore

Which assumption matters most here, and what evidence could challenge it?
What would you check before passing this output to the next step?

Peer discussion

Bring your experience, a question, or a different perspective.

Data contract

Inputs & data

A running variable with a known threshold, a binary treatment that switches on at the cutoff, and an outcome.

Show data format & exampleHide example

Format — x (running variable), y (outcome), treatment = 1{x ≥ cutoff}.

import causalpy as cp
result = cp.pymc_experiments.RegressionDiscontinuity(
    df, formula='y ~ 1 + x + treated', running_variable_name='x',
    treatment_threshold=0.5)
result.plot()

Read the evidence

Results & interpretation

2 figures Workflow discussion 2

01FigureBayesian RD: the posterior-mean fit with a 94% credible band on each side of the cutoff — the jump at the red threshold is the estimated effect.

02FigureA bandwidth-restricted refit using only points near the cutoff: the discontinuity estimate shifts — exactly why bandwidth is a robustness check, not a footnote.

Figures reproduced from CausalPy — PyMC Labs — unofficial community showcase; all credit to the original authors.

Context & interpretation

⚠️ Unofficial community showcase of causalpy. Not affiliated with the authors; all credit to them.

Fit a model on each side of the cutoff, put a posterior on the jump, and report a credible interval for the discontinuity — plus an honest look at how it moves with the bandwidth.

Peer notes

Discuss the workflow (2)

2

@elise_dubois · Jun 29, 2026

A full posterior on the discontinuity beats a point estimate ± SE for communicating uncertainty to non-stats stakeholders.
0

@rahul_nair · Jun 29, 2026

Nice that the bandwidth refit is built in as a robustness step. The estimate moving with the window is the whole RD ballgame.

1

@elise_dubois · Jun 29, 2026

Exactly — I always show the narrow-window and full-sample fits next to each other so nobody thinks the number is bandwidth-free.