.. _bda-do-the-inferences-from-the-model-make-sense:

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Do the Inferences from the Model Make Sense?
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**Part 2 · Stage 6 · 🔍 Model Checking & Comparison**  ·  Lesson 041 of 144  ·  *intermediate*

:doc:`◀ Previous · The Place of Model Checking in Applied Bayesian Statistics <040-the-place-of-model-checking-in-applied-bayesian-statistics>`   ·   :doc:`Next · Posterior predictive checking ▶ <042-posterior-predictive-checking>`   ·   :doc:`↑ Section <index>`


.. important::

   **✨ AI-generated content.** This page was written with the assistance of an
   AI language model and is provided as a learning aid. Despite careful
   review, it may still contain mistakes, omissions, or out-of-date
   information. Whether you are new to the topic, a team lead, or a senior
   practitioner, treat it as a starting point rather than an authoritative
   reference: read it critically and independently verify anything you act on
   (code, commands, figures, and factual claims) against official
   documentation and primary sources before relying on it.

The cheapest check
--------------------

Before any simulation, before any :math:`p`-value, look at the answer and ask whether it is **possible**.
This costs nothing and catches a startling share of real errors — coding mistakes, unit confusions,
mis-specified priors, sign flips. External knowledge that never entered the model is exactly what makes
the check informative.

What to look at
-----------------

Read the posterior against what you already know:

* **Magnitude.** Is a coaching effect of 28 SAT points plausible, given that the test is designed to
  resist short-term preparation? Is an odds ratio of 400 credible, or a symptom of separation?
* **Sign and direction.** Does the coefficient point the way theory demands? A negative dose effect in
  a toxicity assay is a red flag, not a discovery.
* **Physical constraints.** Probabilities in :math:`[0,1]`, variances positive, rates non-negative,
  populations integral.
* **Derived quantities.** Push draws through the functions you care about — an LD50, a predicted count,
  a break-even price — and see whether the implied statements are absurd.
* **Extremes.** Look at the widest intervals and the most-shrunken groups. Do they behave as the
  structure of the data predicts?

External validation
---------------------

The strongest version compares model output with information **deliberately excluded** from the fit:
held-out data, a later replication, an independent measurement, a published estimate. Agreement is
weak evidence for the model; sharp disagreement is strong evidence against it, and localises the fault.

.. code-block:: python

   import numpy as np, arviz as az
   post = idata.posterior
   # 1. do parameters respect their constraints?
   assert float(post["tau"].min()) >= 0
   # 2. do derived quantities land in plausible ranges?
   ld50 = -post["alpha"] / post["beta"]
   np.percentile(ld50, [2.5, 50, 97.5])       # compare with known chemistry
   # 3. does the model's implied prediction match a value you did not fit to?
   az.summary(idata, var_names=["mu"])        # against the published meta-analytic estimate

Being wrong usefully
----------------------

An implausible inference has three possible causes, in decreasing order of frequency: a **bug**, a
**bad prior**, or a **wrong likelihood**. Rule them out in that order — check the data pipeline and
units first, then simulate from the prior, then question the model. And keep the caveat honest: a
result that merely *surprises* you may be the finding. The check is against what is **impossible** or
**incoherent**, not against what is merely unexpected.

.. hint::

   **Related lessons:** :doc:`The Place of Model Checking in Applied Bayesian Statistics <040-the-place-of-model-checking-in-applied-bayesian-statistics>`  ·  :doc:`Posterior predictive checking <042-posterior-predictive-checking>`  ·  :doc:`Weakly Informative Prior Distributions <019-weakly-informative-prior-distributions>`  ·  :doc:`Debugging Bayesian computing <068-debugging-bayesian-computing>`

.. seealso::

   **Source article** Adapted (context, re-expressed) in our own words from: `https://insightful-data-lab.com/2025/11/10/do-the-inferences-from-the-model-make-sense/ <https://insightful-data-lab.com/2025/11/10/do-the-inferences-from-the-model-make-sense/>`__ (insightful-data-lab.com).

.. tags:: purpose: reference, topic: data analysis, domain: bayesian, level: intermediate