Module 20: Statistical Models and Inference for Connectomics

Teaching Deck

Learning Objectives

• Choose statistical models aligned to connectomics question types
• Construct and justify appropriate null models for graph analyses
• Control multiplicity and uncertainty in high-dimensional motif tests
• Report inferential claims with explicit assumptions and limits

Session Outcomes

• Learners can complete the module capability target.
• Learners can produce one evidence-backed artifact.
• Learners can state one limitation or uncertainty.

Agenda (60 min)

• 0-10 min: Frame and model
• 10-35 min: Guided practice
• 35-50 min: Debrief and misconception correction
• 50-60 min: Competency check + exit ticket

Capability Target

Design and execute a connectomics inference plan that includes null-model choice, multiplicity control, uncertainty reporting, and explicit claim boundaries.

Concept Focus

1) Null models encode scientific assumptions

• Technical: null models should preserve relevant graph constraints (degree sequence, spatial limits, cell-class composition) while randomizing the tested structure.
• Plain language: your "chance baseline" must reflect biology and data collection realities.
• Misconception guardrail: a generic random graph is an adequate null for a connectome.

Core Workflow

• Question-to-test mapping
• Convert biological question into estimand(s), test set, and effect-size target.
• Null-model design
• Define null constraints and why they preserve key confounders.
• Inference execution
• Run model/tests with preregistered thresholds and multiplicity controls.
• Robustness checks
• Test sensitivity to preprocessing variant, sampling region, and parameter choice.
• Claim calibration
• Report supported, uncertain, and unsupported claims in separate blocks.

60-Minute Run-of-Show

• Read Technical Unit 09, section 2 — the worked reciprocity example across three null models.
• Bring one motif or connectivity claim from a paper you have read, with its stated null.
• 00:00-06:00 | Framing: the null is the scientific step
• Prompt: "Same graph, same motif, three null models, three different conclusions. Which one is right?"
• Establish that the answer depends on what the hypothesis treats as uninteresting.
• 06:00-18:00 | Worked example: reciprocity across nulls
• Instructor works the Unit 09 example live: 100 neurons, 1,200 edges, 210 reciprocal pairs.
• Erdos-Renyi gives 2.9x. Degree-preserving gives 1.4x. Degree-and-distance gives 1.14x, not significant.
• Think aloud about which null matches which hypothesis, not which gives the nicer number.
• 18:00-30:00 | Guided practice: write the uninteresting explanation
• In pairs, learners take their brought-in claim and write, in words, the sentence "this result would be uninteresting if ___".
• Then name the null that preserves exactly that.
• Instructor circulates asking "what does your null preserve, and what does it randomize?"
• 30:00-40:00 | Multiplicity
• Count the tests actually run, including unreported ones. Choose a correction and justify it.
• Surface the dependence problem: triad counts move together, so analytic p-values overstate confidence. Permutation inference respects the dependence.
• 40:00-50:00 | Robustness and error sensitivity
• Each learner names one preprocessing choice (synapse threshold, inclusion criteria, boundary handling) and states how they would test sensitivity to it.
• Introduce the error-simulation check: perturb the graph at measured merge and split rates, report the band.
• 50:00-57:00 | Competency check
• Each learner submits: estimand, null model with what it preserves, correction strategy, one robustness check, and one claim they will not make.
• 57:00-60:00 | Exit ticket
• "One result I now doubt, and the null model that would settle it."
• At 30 minutes: every pair can state their null in terms of what it preserves, not just its name. If not, re-teach before proceeding.
• At 50 minutes: learners distinguish an exploratory finding from a confirmatory one in their own write-up.

Misconceptions to Watch

• Misconception guardrail: a generic random graph is an adequate null for a connectome.
• Misconception guardrail: a small p-value speaks for itself, regardless of how many tests were run.
• Misconception guardrail: a hypothesis found in the data can be confirmed by the same data.

Studio Activity

Scenario: A team reports motif enrichment in one dataset and asks whether the claim generalizes.

Activity Output Checklist

• Evidence-linked artifact submitted.
• At least one limitation or uncertainty stated.
• Revision point captured from feedback.

Assessment Rubric

Minimum pass

• Null model is justified and the constraints it preserves are listed explicitly, in terms of what the hypothesis treats as uninteresting.
• Total test count — including tests run and not reported — is documented, and a named correction is applied against it.
• Claims are partitioned into exploratory and confirmatory blocks with different language in each.

Assessment Rubric

Strong performance

• Sensitivity analysis spans at least two preprocessing choices (synapse threshold, inclusion criteria), with results reported for each variant.
• Effect sizes with uncertainty intervals appear alongside every significance statement.
• Error-sensitivity band computed at measured merge and split rates, with the direction of merge bias named.
• Generalization boundary stated: which dataset, version, and region the claim covers, and what it says nothing about.

Assessment Rubric

Common failure modes

• Null model choice disconnected from the biological question.
• Selective reporting: significant outcomes shown, the full test count uncounted.
• Exploratory signal conflated with validated inference.
• Analytic p-values used where dependence between tests calls for permutation.

Exit Ticket

Write a 6-8 sentence inference note that includes:

1. hypothesis and estimand,
2. null-model assumptions,
3. multiplicity strategy,
4. one robust conclusion and one unresolved uncertainty.

References (Instructor)

• Bassett, Zurn, and Gold (2018) - model use in network neuroscience.
• Januszewski et al. (2018) - segmentation performance and uncertainty context.
• MICrONS/FlyWire/H01 analyses for cross-dataset inference constraints.

Teaching Materials

• Module page: /modules/module20/
• Slide page: /modules/slides/module20/
• Worksheet: /assets/worksheets/module20/module20-activity.md