Self-check: test your understanding

Goal of this page. A single place to test what you have learned. Each concepts page ends with a short Check your understanding quiz (with answers); this page collects them, then adds synthesis questions that span several pages — the kind of reasoning a real analysis demands.

Need a refresher on a term? Every term used in the quizzes is defined in the glossary, with HTML anchors you can deep-link to.

Per-topic quizzes

Work through the page, then try its quiz. Each links to the questions (answers are collapsible, right there on the page):

Topic

Quiz

Microelectrode recordings: spikes and the LFP

Check your understanding

Spike trains and point-process GLMs

Check your understanding

The LFP and spectral analysis

Check your understanding

Goodness-of-fit and decoding

Check your understanding

State-space models and EM

Check your understanding

Network connectivity and coupling

Check your understanding

Uncertainty and confidence intervals

Check your understanding

Rhythmic firing and the clinical microelectrode

Check your understanding

Synthesis questions

These cut across topics. Try to answer in a sentence or two before expanding.

  1. From electrode to encoding model. You are handed a single broadband extracellular trace and asked to build an encoding model of one neuron’s stimulus tuning. List the steps, in order, and name the nSTAT object or function at each.

  2. Two models, two verdicts. Model B has a lower AIC than model A, but model B leaves the time-rescaling KS band while model A stays inside it. Which do you report, and why doesn’t the lower AIC settle it?

  3. Useful vs. correct. In the place-cell capstone the place-field model decodes position several times better than chance, yet fails goodness-of-fit for nearly every cell. Explain how both can be true, and name two things you would add to the encoding model to close the gap.

  4. Correlation is not connection. Two neurons have a sharp peak at lag 0 in their cross-correlogram. Give two distinct explanations, only one of which is a direct synaptic connection, and say what analysis would help tell them apart.

  5. When the answer needs an interval. You report that a neuron’s stimulus coefficient is \(\beta_1 = 0.5\). A colleague asks whether the neuron is really stimulus-driven. What single additional quantity do you need, and how would you compute it from the GLM fit?

  6. Static vs. evolving tuning. You fit a GLM per trial and the stimulus coefficient seems to drift upward across a session. What model would you use to estimate that trajectory properly, and what does it give you that 100 independent per-trial fits do not?

  7. A rhythm is just a covariate. A neuron fires in time with a 5 Hz tremor and you have no external stimulus to regress against. Explain how you would still fit a point-process GLM that captures the rhythm, how you would prove it fit, and — using the same electrode — where you would look for the beta biomarker that drives adaptive DBS.

Show answers

  1. Filter → detect/sort → represent → specify → fit → check. Band-split the broadband trace (high-pass >300 Hz for spikes, low-pass <300 Hz for the LFP; see microelectrode recordings); detect and sort spikes into an nspikeTrain; build the stimulus as a Covariate; bundle data + model in a Trial and TrialConfig; fit with Analysis (or fit_poisson_glm) to get a FitResult; then check it with computeKSStats. See the spike-train GLM page.

  2. Report model A. AIC only ranks models relative to each other; it never certifies absolute fit. Leaving the KS band means model B is misspecified in absolute terms, so its lower AIC is the lowest score among inadequate models. Prefer the lowest-AIC model that also passes goodness-of-fit.

  3. Decoding only needs the model to rank positions correctly enough to pick the right one; goodness-of-fit asks whether the model reproduces the spiking exactly. The place-field model captures coarse spatial tuning (so it decodes) but omits spike history / refractoriness and the theta rhythm, and uses a single broad Gaussian bump — so KS rejects it. Add history terms and a richer spatial basis (e.g. Paper Example 04’s Zernike fields).

  4. (a) A direct synaptic connection from one to the other; (b) a shared common input (a stimulus or network rhythm) driving both. A connection typically shows a short, asymmetric, lagged peak; common input shows a symmetric peak near zero lag. Conditioning on the stimulus/other neurons in an ensemble GLM, or a Granger-style test, helps separate them. See network connectivity.

  5. You need the coefficient’s confidence interval (equivalently its standard error). Compute the Fisher information \(X^{\top} \mathrm{diag}(\lambda) X\), invert it for the covariance, take \(\mathrm{se} = \sqrt{\mathrm{diag}}\), and report \(\beta_1 \pm 1.96 \cdot \mathrm{se}\). If the interval excludes 0 the neuron is convincingly stimulus-driven. See uncertainty and confidence intervals.

  6. The state-space GLM (SSGLM), fit by EM. It treats the coefficient as a latent state evolving across trials and shares statistical strength between neighboring trials, giving a smoothed trajectory with credible intervals — far less noisy than 100 independent fits, and able to say whether the drift is real. See state-space models and EM.

  7. Build the rhythm itself as a periodic covariate — a sin/cos pair (or band-limited drive) at the tremor frequency — and fit the point-process GLM exactly as for any stimulus, with a history term for refractoriness. Prove it fit with the time-rescaling KS test: the rhythm-aware model stays in the band while a constant-rate model with the same mean rate is rejected for getting the timing wrong. Then low-pass the same electrode to a field potential and read beta-band (13–30 Hz) power with SignalObj.MTMspectrum (use spectrogram for burst structure). See Rhythmic firing and the clinical microelectrode.

Where to go next