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

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.

Microelectrode. A fine metal/silicon probe that measures the extracellular voltage produced by nearby neural currents. See Microelectrode recordings.

Broadband signal. The raw wideband voltage from an electrode, before filtering — it contains both spikes and the LFP.

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.

EEG / ECoG. Field potentials recorded at the scalp (EEG) or cortical surface (ECoG); analyzed with the same SignalObj spectral tools as the LFP.

Single unit. Spikes attributed to one isolated neuron after spike sorting.

Multi-unit activity (MUA). Pooled spikes from several nearby neurons that could not be separated into single units.

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.

Tetrode / multi-electrode array. A probe with several nearby contacts; viewing each spike from multiple sites improves sorting accuracy.

Clinical microelectrode recordings and rhythms

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.

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.

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.

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.

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, Tinkhauser et al. 2017.

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

Point process. A probabilistic model for the timing of discrete events (spikes). The right framework for spike trains.

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.

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.

Homogeneous / inhomogeneous Poisson process. Point process with constant rate (\(\lambda\)) / time-varying rate (\(\lambda(t)\)) and no history dependence.

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.

Link function. The transform applied to the rate; nSTAT uses the log link so \(\lambda > 0\) and covariates act multiplicatively.

Covariate. An external (extrinsic) signal — stimulus, position, movement — that may drive firing. In nSTAT: Covariate, grouped in a CovColl.

Basis (e.g. spline). A set of functions used to expand a covariate so its effect on firing can be nonlinear.

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.

Ensemble / functional coupling. Dependence of one neuron’s firing on other neurons’, beyond shared stimulus drive.

AIC / BIC. Penalized-likelihood scores for comparing models of differing complexity (fit.AIC, fit.BIC). Lower is better — but confirm with goodness-of-fit.

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.

Goodness-of-fit and decoding

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.

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.

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.

Encoding vs. decoding. Encoding models predict spikes from stimulus/state (the GLM); decoding infers stimulus/state from spikes.

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.

Hybrid point-process filter (PPHF). Jointly estimates a discrete mode and a continuous state from spikes.

Kalman filter / smoother. Optimal recursive estimator of a latent state from Gaussian observations (e.g. LFP); the smoother uses the whole record.

Clusterless decoding. Decoding directly from spike-waveform features (“marks”) without spike sorting. nstat.extras.decoding.clusterless_bridge. See Denovellis et al. 2021.

Spectral analysis

Power spectral density (PSD). How a signal’s power is distributed across frequency.

Periodogram. The naive squared-FFT spectrum estimate; high variance and spectral leakage. SignalObj.periodogram.

Multitaper method. A low-variance, leakage-controlled spectrum estimate that averages over orthogonal Slepian (DPSS) tapers. SignalObj.MTMspectrum. See Thomson 1982, Mitra & Pesaran 1999.

Time–bandwidth product \(NW\). Sets the multitaper smoothing/resolution trade-off; the number of tapers is \(K \approx 2 \cdot NW - 1\).

Spectrogram. Power as a function of both time and frequency, from a sliding-window multitaper estimate. SignalObj.spectrogram.

See the Concepts overview for the full learning path and the Bibliography for sources.