module indexstudent versionall modules1. From the task to the design matrix →

Notebook 0 — Roadmap

SWC ENC 2026 · behaviour module

Welcome. Over this day you'll rebuild, from the ground up, the statistical toolkit behind Figures 1–3 of Piet et al. (2024), Neuron — "Behavioral strategy shapes activation of the Vip-Sst disinhibitory circuit in visual cortex." This first notebook has no exercises; it's a map, so you know where the day is going and why each step matters.

The question

Mice performing the same task can solve it in different ways — different strategies — and those strategies can drift over the course of a session. The paper's task is visual change detection: a stream of images is shown, and the mouse is rewarded for licking when the image changes. A mouse might solve this by visually comparing each image to the last, or by timing — learning roughly how often changes come and licking on schedule.

The change-detection task (Fig. 1A).

The central problem of this module: given only the licking, how do we read out which strategy a mouse is using, and how it changes over time?

The approach

Piet et al. answer it with one model of when a licking bout starts, a logistic regression built from five candidate "strategy" regressors (a constant bias, a visual term, a timing term, and two omission terms). Fitting that model to a session recovers how much the mouse leans on each strategy; letting the weights drift recovers how that changes through the hour.

Why synthetic data? The real dataset is awkward to access, but there's a deeper pedagogical reason to avoid it: we learn a method best when we can check it against a known answer. So all day you'll analyze synthetic mice generated from the paper's own model, whose true strategy we chose. Every technique you build gets tested the same way — can we recover the truth we put in? That question is the spine of the whole module.

The day, notebook by notebook

The module comes in two parts. Part 1 (Notebooks 1–8) builds a model of one animal's behaviour — Notebooks 3–6 are a fit → evaluate → ablate cycle on mice with a fixed strategy, and Notebook 7 extends it to a mouse whose strategy drifts. Part 2 (Notebooks 9–11) steps up to a whole population and the statistics of comparing across it. Every notebook is short and self-contained — a bit of statistics, an exercise or two, a paper figure at the end — and any section can be skipped and left for self-study.

Part 1 — modelling one animal

#	Notebook	What you build	What you'll learn	Paper
1	Task → design matrix	licking bouts and the five-strategy design matrix	turning raw events into regressors — building a design matrix	Fig 1A, 1C
2	Meet the mice	how each strategy looks in behavior	generative models; reading a parameter off behavior	Fig 1B
3	Static model	logistic regression from its likelihood; weight recovery	the Bernoulli likelihood, maximum-likelihood/MAP fitting, gradient descent	Fig 1D
4	Evaluation	ROC, AUC, cross-validation	scoring predictions; ROC & AUC; cross-validation and overfitting	Fig 2A
5	Evidence & ablation	which strategies matter; the strategy index	model comparison; nested models & held-out likelihood; (opt.) Bayesian evidence & the Laplace approximation	Fig 2B, 2D
6	Mixtures	the cycle on mice that blend strategies	parameter recovery and identifiability when regressors overlap	Fig 2F
7	Dynamic model	the drifting-weight (random-walk) model	non-stationarity; priors as smoothing; the bias–variance trade-off	Fig 1D
8	Engagement (optional)	strategy vs. task engagement	latent-state estimation; separating independent axes of variation	Fig 3B

Part 2 — population-level inference

#	Notebook	What you build	What you'll learn	Paper
6+	(bonus section in Notebook 6)	a correlation & a linear fit	Pearson r, $R^2$, least-squares lines	Fig 2E
9	Individual differences	variance partitioning; a permutation test	is an effect more than chance? testing without distributional assumptions	Fig 2H
10	Multiple comparisons	t-tests; Bonferroni & Benjamini–Hochberg	keeping false positives in check across many tests	general tool
11	Hierarchical bootstrap	resampling for nested data	honest error bars when samples aren't independent	general tool

How the notebooks work

• Each notebook comes in two versions: a student copy with # YOUR CODE HERE blanks for you to fill, and a solutions copy with everything worked out.
• A small backend package, swcbehav, generates the synthetic mice and holds reference implementations of every technique. Each notebook imports what it needs from it, so you can run any notebook on its own.
• Wherever we can, an exercise ends by checking your result against ground truth — the recover-the-truth spine again, and each exercise tells you roughly what number to expect so you can spot a bug.
• Stuck on an exercise? Don't let it block your day. Every technique you implement also lives in the backend as sb.<name> (and fully worked out in the solutions copy), so you can drop that in, keep pace with the class, and circle back later — the sections are built so the rest still runs.

Run the cell below to confirm your environment is set up (select the "SWC Behaviour (.venv)" kernel if prompted). If it prints a mouse's weights and a plot appears, you're ready for Notebook 1.

import numpy as np
import matplotlib.pyplot as plt
import swcbehav as sb

# Generate one synthetic mouse and take a quick look -- no exercise here,
# just a check that everything is installed and importable.
sess = sb.make_mouse("visual", seed=0)
print("environment OK — generated a session with", len(sess.table), "image presentations")
print("this mouse's true strategy weights:", np.round(sess.true_weights[0], 1))
print("order: [bias, visual, omission, post_omission, timing]")

sb.plotting.plot_session_raster(sess, t0=560, t1=585)
plt.show()

environment OK — generated a session with 4800 image presentations
this mouse's true strategy weights: [-3.  5.  0.  0.  0.]
order: [bias, visual, omission, post_omission, timing]

Glossary — terms you'll meet

You don't need these yet; come back when a word trips you up. Each is defined properly where it first appears (in parentheses).

term	in plain words
design matrix / regressor	a table with one row per image and one column per candidate strategy; each column is a regressor (NB1)
bout	a burst of licks treated as one action (NB1)
Bernoulli / likelihood	a single yes/no trial; the likelihood is the probability the model assigns to all the data (NB3)
log-likelihood / nats	the log of the likelihood; "nats" is just its unit when you use natural log (NB3, NB5)
logit / log-odds / sigmoid	weights act on the log-odds of licking; the sigmoid maps them back to a probability (NB3)
MAP / prior	a fit that gently prefers small weights (a prior), rather than pure maximum-likelihood (NB3)
gradient descent	walk downhill on the error surface to fit the weights (NB3)
ROC / AUC	a curve of hit-rate vs false-alarm-rate; AUC is its area — the chance the model ranks a lick above a non-lick (NB4)
cross-validation / held-out	score the model on data it wasn't fit to, to avoid fooling yourself (NB4)
ablation / nested model	remove one strategy and see how much prediction suffers; the smaller model is nested in the full one (NB5)
model evidence / Laplace approximation	probability of the data with the weights averaged out; approximated by a Gaussian at the peak (NB5, optional)
strategy index	one number summarizing visual-vs-timing reliance (NB5)
correlation / R²	how tightly two quantities move together; R² is the fraction of variance explained (NB6)
permutation test / null	shuffle labels to build the "no real effect" distribution, then see if your result beats it (NB9)
variance explained (η²)	the fraction of spread due to group identity, e.g. mouse (NB9)
t-test / p-value	signal-over-noise for a mean; the p-value is how surprising it'd be under no effect (NB10)
FWER / FDR / Bonferroni / BH	ways to control false positives across many tests; BH controls the false-discovery rate (NB10)
bootstrap / hierarchical bootstrap	resample the data to get error bars; the hierarchical version resamples each level (mice, then sessions) for nested data (NB11)

Ready

That's the whole arc: from raw licks to a design matrix, to a fitted model, to knowing which strategy a mouse uses and how it drifts — each step checked against a truth you control. On to Notebook 1.

 module indexstudent versionall modules1. From the task to the design matrix →