# Glossary

Plain-language definitions of the terms used across the Concepts pages and the
nSTAT API. Where a term maps to a specific object or method, the name is given
in `code font`.

## Recording and signals

<a id="action-potential"></a>
**Action potential (spike).** The brief (~1 ms) all-or-none electrical event a
neuron emits when it fires. nSTAT represents a neuron's spikes as a list of
times in an `nspikeTrain`.

<a id="microelectrode"></a>
**Microelectrode.** A fine metal/silicon probe that measures the extracellular
voltage produced by nearby neural currents. See
[Microelectrode recordings](microelectrode_recordings.md).

<a id="broadband-signal"></a>
**Broadband signal.** The raw wideband voltage from an electrode, before
filtering — it contains both spikes and the LFP.

<a id="local-field-potential"></a>
**Local field potential (LFP).** The low-frequency (~1–300 Hz) part of the
extracellular signal, reflecting summed synaptic/subthreshold currents of a
local population. Represented as a `SignalObj`. See
[The LFP and spectral analysis](lfp_and_spectral.md).

<a id="eeg-ecog"></a>
**EEG / ECoG.** Field potentials recorded at the scalp (EEG) or cortical
surface (ECoG); analyzed with the same `SignalObj` spectral tools as the LFP.

<a id="single-unit"></a>
**Single unit.** Spikes attributed to one isolated neuron after spike sorting.

<a id="multi-unit-activity"></a>
**Multi-unit activity (MUA).** Pooled spikes from several nearby neurons that
could not be separated into single units.

<a id="spike-sorting"></a>
**Spike sorting.** The pipeline (detect → extract features → cluster) that
turns a broadband trace into per-neuron spike trains. nSTAT assumes this is
already done; see [Lewicki 1998](https://pubmed.ncbi.nlm.nih.gov/10221571/).

<a id="tetrode-multi-electrode-array"></a>
**Tetrode / multi-electrode array.** A probe with several nearby contacts;
viewing each spike from multiple sites improves sorting accuracy.

## Clinical microelectrode recordings and rhythms

<a id="rhythmic-oscillatory-cell"></a>
**Rhythmic / oscillatory cell.** A neuron whose firing probability rises and
falls periodically, even without a changing stimulus. Modeled in nSTAT with a
periodic `Covariate` in the point-process GLM. See
[Rhythmic firing and the clinical microelectrode](rhythmic_firing_and_clinical_microelectrode.md).

<a id="tremor-cell"></a>
**Tremor cell.** A rhythmic cell whose firing is phase-locked to a few-hertz
(~3–8 Hz) limb tremor; characterized in the human subthalamic nucleus and
thalamus during DBS surgery. See
[Levy et al. 2000](https://pubmed.ncbi.nlm.nih.gov/11027240/).

<a id="deep-brain-stimulation"></a>
**Deep brain stimulation (DBS).** A therapy that delivers electrical stimulation
through an electrode implanted in a deep brain nucleus (e.g. the subthalamic
nucleus, STN) to treat Parkinson's disease and other disorders.

<a id="microelectrode-mapping-localization"></a>
**Microelectrode mapping / localization.** Advancing a recording microelectrode
millimetre by millimetre to identify a deep target from the firing-rate,
burstiness, and spectral signatures of each nucleus it passes through. A
latent-state / change-point problem. See
[Hutchison et al. 1998](https://pubmed.ncbi.nlm.nih.gov/9778260/).

<a id="beta-band"></a>
**Beta band (13–30 Hz).** A field-potential rhythm whose power in the STN tracks
Parkinsonian motor impairment; the feedback signal for **adaptive DBS**.
Estimated with `SignalObj.MTMspectrum`. See
[Little et al. 2013](https://pubmed.ncbi.nlm.nih.gov/23852650/),
[Tinkhauser et al. 2017](https://pubmed.ncbi.nlm.nih.gov/28334851/).

<a id="adaptive-dbs"></a>
**Adaptive (closed-loop) DBS.** Stimulation gated by a measured biomarker (e.g.
beta power) rather than delivered continuously — a decode-then-actuate loop.

## Point processes and modeling

<a id="point-process"></a>
**Point process.** A probabilistic model for the timing of discrete events
(spikes). The right framework for spike trains.

<a id="conditional-intensity-function"></a>
**Conditional intensity function (CIF), $\lambda(t \mid H_t)$.** The instantaneous
firing rate at time $t$ given the history $H_t$; $\lambda \cdot \Delta$ is the spike
probability in a small interval. The complete description of a point process.
In nSTAT: `CIF`, `CIFModel`, `LinearCIF`.

<a id="history"></a>
**History $H_t$.** Everything observed up to time $t$ — the neuron's own past
spikes, the ensemble's spikes, and covariates — that the CIF may depend on.

<a id="homogeneous-inhomogeneous-poisson-process"></a>
**Homogeneous / inhomogeneous Poisson process.** Point process with constant
rate ($\lambda$) / time-varying rate ($\lambda(t)$) and *no* history dependence.

<a id="generalized-linear-model"></a>
**Generalized linear model (GLM).** Here, a model of $\log \lambda(t \mid H_t)$ as a
linear sum of covariate, history, and ensemble terms. Fit by
`Analysis`/`fit_poisson_glm`; configured by `TrialConfig`. See
[Spike trains and point-process GLMs](spike_trains_and_glms.md).

<a id="link-function"></a>
**Link function.** The transform applied to the rate; nSTAT uses the **log**
link so $\lambda > 0$ and covariates act multiplicatively.

<a id="covariate"></a>
**Covariate.** An external (extrinsic) signal — stimulus, position, movement —
that may drive firing. In nSTAT: `Covariate`, grouped in a `CovColl`.

<a id="basis"></a>
**Basis (e.g. spline).** A set of functions used to expand a covariate so its
effect on firing can be nonlinear.

<a id="history-term-refractory-period"></a>
**History term / refractory period.** History covariates capture the neuron's
dependence on its own recent spikes; the dip just after a spike (no immediate
re-firing) is the refractory period.

<a id="ensemble-functional-coupling"></a>
**Ensemble / functional coupling.** Dependence of one neuron's firing on other
neurons', beyond shared stimulus drive.

<a id="aic-bic"></a>
**AIC / BIC.** Penalized-likelihood scores for comparing models of differing
complexity (`fit.AIC`, `fit.BIC`). Lower is better — but confirm with
goodness-of-fit.

<a id="state-space-glm"></a>
**State-space GLM (SSGLM).** A GLM whose coefficients evolve across trials (a
latent state), estimated by EM; captures learning. `nstColl.ssglm()`/`ssglmFB()`.
See [Smith & Brown 2003](https://pubmed.ncbi.nlm.nih.gov/12803953/).

## Goodness-of-fit and decoding

<a id="time-rescaling-theorem"></a>
**Time-rescaling theorem.** If the CIF is correct, integrating it between
spikes yields i.i.d. unit-rate exponential intervals — the basis of the KS
goodness-of-fit test. `FitResult.computeKSStats`. See
[Brown et al. 2002](https://pubmed.ncbi.nlm.nih.gov/11802915/).

<a id="kolmogorov-smirnov-test-ks-plot"></a>
**Kolmogorov–Smirnov (KS) test / KS plot.** A test of whether the rescaled
intervals match the expected distribution; the KS plot shows the empirical CDF
against the diagonal with confidence bands.

<a id="population-time-rescaling"></a>
**Population (marked) time-rescaling.** A joint goodness-of-fit test for a
*population* that catches inter-neuron coupling a per-neuron test misses.
`population_time_rescale`. See
[Tao et al. 2018](https://pubmed.ncbi.nlm.nih.gov/30298220/).

<a id="encoding-vs-decoding"></a>
**Encoding vs. decoding.** Encoding models predict spikes from
stimulus/state (the GLM); decoding infers stimulus/state from spikes.

<a id="point-process-adaptive-filter"></a>
**Point-process adaptive filter (PPAF).** Recursive Bayesian decoder — the
spiking analogue of the Kalman filter — that estimates a continuous state from
a population's spikes. `DecodingAlgorithms`. See
[Eden et al. 2004](https://pubmed.ncbi.nlm.nih.gov/15070506/).

<a id="hybrid-point-process-filter"></a>
**Hybrid point-process filter (PPHF).** Jointly estimates a discrete mode and
a continuous state from spikes.

<a id="kalman-filter-smoother"></a>
**Kalman filter / smoother.** Optimal recursive estimator of a latent state
from *Gaussian* observations (e.g. LFP); the smoother uses the whole record.

<a id="clusterless-decoding"></a>
**Clusterless decoding.** Decoding directly from spike-waveform features
("marks") without spike sorting. `nstat.extras.decoding.clusterless_bridge`.
See [Denovellis et al. 2021](https://pubmed.ncbi.nlm.nih.gov/34570699/).

## Spectral analysis

<a id="power-spectral-density"></a>
**Power spectral density (PSD).** How a signal's power is distributed across
frequency.

<a id="periodogram"></a>
**Periodogram.** The naive squared-FFT spectrum estimate; high variance and
spectral leakage. `SignalObj.periodogram`.

<a id="multitaper-method"></a>
**Multitaper method.** A low-variance, leakage-controlled spectrum estimate
that averages over orthogonal Slepian (DPSS) tapers. `SignalObj.MTMspectrum`.
See [Thomson 1982](https://doi.org/10.1109/PROC.1982.12433),
[Mitra & Pesaran 1999](https://pubmed.ncbi.nlm.nih.gov/9929474/).

<a id="time-bandwidth-product"></a>
**Time–bandwidth product $NW$.** Sets the multitaper smoothing/resolution
trade-off; the number of tapers is $K \approx 2 \cdot NW - 1$.

<a id="spectrogram"></a>
**Spectrogram.** Power as a function of both time and frequency, from a
sliding-window multitaper estimate. `SignalObj.spectrogram`.

---

See the [Concepts overview](index.md) for the full learning path and the
[Bibliography](bibliography.md) for sources.