{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "c14bbecd",
   "metadata": {},
   "source": [
    "# The analysis toolbox: spikes, spectra and populations\n",
    "\n",
    "This tutorial walks through the measures added to `braintools.analysis` in 0.4. Each section builds data with a known answer and checks the measure against it:\n",
    "\n",
    "1. **Spike-train statistics** on a `SpikeTrains`: ISI, CV, CV2, LV, Fano factor, PSTH, correlograms, spike-triggered averages and spike-train distances.\n",
    "2. **Spectral analysis** of continuous signals: multitaper spectra, Morlet wavelets, band-pass filtering and phase synchrony.\n",
    "3. **Population analysis**: PCA, decoding, Granger causality and neuronal avalanches.\n",
    "4. **Resampling**: significance tests with jittered spikes and phase-randomised signals, and bootstrap confidence intervals.\n",
    "\n",
    "Every function here runs under `jax.jit` and `jax.vmap` and accepts `brainunit` quantities."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "4920fd3a",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-10-19T12:21:12.161493Z",
     "iopub.status.busy": "2026-10-19T12:21:12.161324Z",
     "iopub.status.idle": "2026-10-19T12:21:15.698380Z",
     "shell.execute_reply": "2026-10-19T12:21:15.697463Z"
    }
   },
   "outputs": [],
   "source": [
    "import brainunit as u\n",
    "import jax\n",
    "import jax.numpy as jnp\n",
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "\n",
    "from braintools.analysis import population, spectral, spike, stats\n",
    "from braintools.spike import SpikeTrains"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "50a909c9",
   "metadata": {},
   "source": [
    "## 1. Spike-train statistics\n",
    "\n",
    "We simulate two populations for 20 s at 0.1 ms resolution: 20 Poisson neurons (irregular, CV ≈ 1) and 20 regular neurons that fire every 50 ms with a little jitter (CV ≈ 0). A dense raster becomes a `SpikeTrains` with `SpikeTrains.from_dense`; its `capacity` is the largest spike count of any neuron."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "67f53e18",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-10-19T12:21:15.701213Z",
     "iopub.status.busy": "2026-10-19T12:21:15.700764Z",
     "iopub.status.idle": "2026-10-19T12:21:16.546069Z",
     "shell.execute_reply": "2026-10-19T12:21:16.545262Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "SpikeTrains(n_neurons=40, capacity=436, n_spikes=15892, t_start=0. ms, t_stop=20000. ms, overflow=False)"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "dt = 0.1 * u.ms\n",
    "n_steps = 200_000  # 20 s\n",
    "rng = np.random.default_rng(0)\n",
    "\n",
    "poisson = rng.random((n_steps, 20)) < 20.0 * 1e-4          # 20 Hz\n",
    "regular = np.zeros((n_steps, 20), dtype=bool)\n",
    "period = 500                                                 # 50 ms in steps\n",
    "for i in range(20):  # building the toy data on the host is fine\n",
    "    t = np.arange(rng.integers(0, period), n_steps, period)\n",
    "    t = np.clip(t + rng.integers(-5, 6, size=t.size), 0, n_steps - 1)\n",
    "    regular[t, i] = True\n",
    "\n",
    "trains = SpikeTrains.from_dense(np.concatenate([poisson, regular], axis=1), dt=dt)\n",
    "trains"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "6e10cf4c",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-10-19T12:21:16.548392Z",
     "iopub.status.busy": "2026-10-19T12:21:16.547973Z",
     "iopub.status.idle": "2026-10-19T12:21:18.445502Z",
     "shell.execute_reply": "2026-10-19T12:21:18.444711Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "CV   Poisson 0.99  regular 0.01\n",
      "CV2  Poisson 1.00  regular 0.01\n",
      "LV   Poisson 0.99  regular 0.00\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Fano factor (100 ms bins)  Poisson 0.98  regular 0.00\n"
     ]
    }
   ],
   "source": [
    "cv, cv2, lv = spike.cv(trains), spike.cv2(trains), spike.lv(trains)\n",
    "print('CV   Poisson %.2f  regular %.2f' % (cv[:20].mean(), cv[20:].mean()))\n",
    "print('CV2  Poisson %.2f  regular %.2f' % (cv2[:20].mean(), cv2[20:].mean()))\n",
    "print('LV   Poisson %.2f  regular %.2f' % (lv[:20].mean(), lv[20:].mean()))\n",
    "ff = spike.fano_factor(trains, bin_size=100 * u.ms)\n",
    "print('Fano factor (100 ms bins)  Poisson %.2f  regular %.2f' % (ff[:20].mean(), ff[20:].mean()))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ac0a4dcf",
   "metadata": {},
   "source": [
    "For a Poisson process CV, CV2, LV and the Fano factor are all close to 1; for the regular population they are close to 0. Undefined values (a neuron with fewer than two intervals) come back as `nan` rather than raising, so the statistics work inside `jit`.\n",
    "\n",
    "### PSTH and spike-triggered average\n",
    "\n",
    "`psth` aligns spikes to event times. Here a population responds 20 ms after each of 50 stimuli; the PSTH recovers the response latency."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "2a47cd6e",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-10-19T12:21:18.447483Z",
     "iopub.status.busy": "2026-10-19T12:21:18.447245Z",
     "iopub.status.idle": "2026-10-19T12:21:20.094156Z",
     "shell.execute_reply": "2026-10-19T12:21:20.093238Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "peak at 23 ms\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 600x300 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "events = np.arange(50) * 0.4 + 0.2            # stimulus times in s\n",
    "resp = rng.random((n_steps, 30)) < 5e-4         # 5 Hz background\n",
    "for e in events:\n",
    "    k = int(round((e + 0.020) / 1e-4))\n",
    "    resp[k:k + 50] |= rng.random((50, 30)) < 0.02  # 5 ms burst, 20 ms after the event\n",
    "resp_trains = SpikeTrains.from_dense(resp, dt=dt)\n",
    "\n",
    "rate, edges = spike.psth(resp_trains, events * u.second, window=(50 * u.ms, 100 * u.ms), bin_size=2 * u.ms)\n",
    "centers = (edges[:-1] + edges[1:]) / 2\n",
    "plt.figure(figsize=(6, 3))\n",
    "plt.bar(centers.to_decimal(u.ms), rate.mean(axis=1), width=2)\n",
    "plt.xlabel('time from stimulus (ms)'); plt.ylabel('rate (Hz)'); plt.title('PSTH')\n",
    "plt.tight_layout()\n",
    "print('peak at %.0f ms' % centers.to_decimal(u.ms)[int(jnp.argmax(rate.mean(axis=1)))])"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "553e6f7a",
   "metadata": {},
   "source": [
    "### Correlograms\n",
    "\n",
    "`cross_correlogram` compares neuron *i* of one `SpikeTrains` with neuron *i* of another. A copy of the Poisson trains delayed by 5 ms produces a peak at +5 ms; the auto-correlogram of the regular neurons shows their 50 ms period."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "b035bb68",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-10-19T12:21:20.096109Z",
     "iopub.status.busy": "2026-10-19T12:21:20.095886Z",
     "iopub.status.idle": "2026-10-19T12:21:22.406045Z",
     "shell.execute_reply": "2026-10-19T12:21:22.404973Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 900x300 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "delayed = np.roll(poisson, 50, axis=0)           # 5 ms later\n",
    "a = SpikeTrains.from_dense(poisson, dt=dt)\n",
    "b = SpikeTrains.from_dense(delayed, dt=dt)\n",
    "ccg, lags = spike.cross_correlogram(a, b, bin_size=1 * u.ms, max_lag=20 * u.ms)\n",
    "acg, alags = spike.auto_correlogram(trains.select(np.arange(20, 40)), bin_size=2 * u.ms, max_lag=150 * u.ms)\n",
    "\n",
    "fig, axes = plt.subplots(1, 2, figsize=(9, 3))\n",
    "axes[0].bar(lags.to_decimal(u.ms), ccg.sum(axis=0), width=1)\n",
    "axes[0].set(xlabel='lag (ms)', title='cross-correlogram (5 ms delay)')\n",
    "axes[1].bar(alags.to_decimal(u.ms), acg.sum(axis=0), width=2)\n",
    "axes[1].set(xlabel='lag (ms)', title='auto-correlogram (regular)')\n",
    "plt.tight_layout()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "758f3920",
   "metadata": {},
   "source": [
    "### Spike-train distances\n",
    "\n",
    "The ISI- and SPIKE-distances of Kreuz et al. are 0 for identical trains and grow as the trains diverge. Both compare neuron *i* of one `SpikeTrains` with neuron *i* of another and vectorise over neurons; jittering spikes by increasing amounts makes the distances grow."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "6c428b30",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-10-19T12:21:22.408915Z",
     "iopub.status.busy": "2026-10-19T12:21:22.408687Z",
     "iopub.status.idle": "2026-10-19T12:21:26.076182Z",
     "shell.execute_reply": "2026-10-19T12:21:26.075361Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "jitter   0.5 ms   ISI-distance 0.009   SPIKE-distance 0.005\n",
      "jitter   2.0 ms   ISI-distance 0.034   SPIKE-distance 0.018\n",
      "jitter   8.0 ms   ISI-distance 0.112   SPIKE-distance 0.064\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "jitter  32.0 ms   ISI-distance 0.277   SPIKE-distance 0.176\n"
     ]
    }
   ],
   "source": [
    "key = jax.random.key(1)\n",
    "widths = [0.5, 2.0, 8.0, 32.0]\n",
    "for w in widths:\n",
    "    jittered = stats.jitter_spikes(key, a, w * u.ms)\n",
    "    print('jitter %5.1f ms   ISI-distance %.3f   SPIKE-distance %.3f'\n",
    "          % (w, spike.isi_distance(a, jittered).mean(), spike.spike_distance(a, jittered).mean()))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5e63b52c",
   "metadata": {},
   "source": [
    "## 2. Spectral analysis\n",
    "\n",
    "A 10 Hz rhythm whose amplitude is modulated, plus a 40 Hz component and noise, sampled at 1 kHz. The multitaper estimate has much lower variance than a single periodogram; the Morlet transform shows when each rhythm is present."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "1c436ab3",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-10-19T12:21:26.078152Z",
     "iopub.status.busy": "2026-10-19T12:21:26.077963Z",
     "iopub.status.idle": "2026-10-19T12:21:27.998973Z",
     "shell.execute_reply": "2026-10-19T12:21:27.997956Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "alpha band power fraction 0.72\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1000x350 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fs = 1000.0\n",
    "t = np.arange(0, 8, 1 / fs)\n",
    "alpha = (1 + np.sin(2 * np.pi * 0.25 * t)) * np.sin(2 * np.pi * 10 * t)\n",
    "gamma = 0.5 * np.sin(2 * np.pi * 40 * t) * (t > 4)\n",
    "x = jnp.asarray(alpha + gamma + 0.5 * rng.standard_normal(t.size))\n",
    "\n",
    "freqs, psd = spectral.multitaper_psd(x, dt=1 * u.ms, nw=4.0)\n",
    "wfreqs = jnp.arange(4.0, 60.0, 1.0)\n",
    "tfr = spectral.morlet_transform(x, dt=1 * u.ms, freqs=wfreqs, n_cycles=7.0)\n",
    "\n",
    "fig, axes = plt.subplots(1, 2, figsize=(10, 3.5))\n",
    "axes[0].semilogy(freqs, psd); axes[0].set(xlim=(0, 80), xlabel='Hz', title='multitaper PSD')\n",
    "axes[1].imshow(jnp.abs(tfr), aspect='auto', origin='lower', extent=(0, 8, 4, 60), cmap='magma')\n",
    "axes[1].set(xlabel='time (s)', ylabel='Hz', title='Morlet power')\n",
    "plt.tight_layout()\n",
    "print('alpha band power fraction %.2f' % spectral.band_power(x, dt=1 * u.ms, band=(8, 12), nperseg=1000, relative=True))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "69865629",
   "metadata": {},
   "source": [
    "### Band-pass filtering and phase synchrony\n",
    "\n",
    "`bandpass` is a zero-phase Butterworth filter (it matches `scipy.signal.sosfiltfilt`) that runs inside `jit`. Two noisy signals sharing a 10 Hz rhythm with a fixed lag are phase-locked in the alpha band but not in an unrelated band: `plv` is high and `wpli` (insensitive to zero-lag volume conduction) is also high because the lag is non-zero."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "eaebaa77",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-10-19T12:21:28.001107Z",
     "iopub.status.busy": "2026-10-19T12:21:28.000907Z",
     "iopub.status.idle": "2026-10-19T12:21:29.833888Z",
     "shell.execute_reply": "2026-10-19T12:21:29.832921Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "band (8, 12)  PLV 0.99   PLI 0.99   wPLI 1.00\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "band (25, 35) PLV 0.05   PLI 0.02   wPLI 0.13\n"
     ]
    }
   ],
   "source": [
    "y = jnp.asarray(np.sin(2 * np.pi * 10 * t - 0.8) + 0.8 * rng.standard_normal(t.size))\n",
    "z = jnp.asarray(np.sin(2 * np.pi * 10 * t) + 0.8 * rng.standard_normal(t.size))\n",
    "for band in [(8, 12), (25, 35)]:\n",
    "    print('band %-8s PLV %.2f   PLI %.2f   wPLI %.2f' % (\n",
    "        band, spectral.plv(y, z, dt=1 * u.ms, band=band),\n",
    "        spectral.pli(y, z, dt=1 * u.ms, band=band), spectral.wpli(y, z, dt=1 * u.ms, band=band)))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b049c653",
   "metadata": {},
   "source": [
    "## 3. Population analysis\n",
    "\n",
    "### Low-dimensional structure and decoding\n",
    "\n",
    "100 neurons are driven by a 3-dimensional latent signal whose variances are in the ratio 9 : 4 : 1. PCA finds that three components explain almost all the variance. The participation ratio $(\\sum\\lambda)^2/\\sum\\lambda^2$ is an effective dimensionality that weights each dimension by its variance, so it comes out near $14^2/98 = 2$ rather than 3. `decode` then predicts which of four stimuli was shown from noisy population responses, with cross-validation."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "d6fc9e03",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-10-19T12:21:29.835782Z",
     "iopub.status.busy": "2026-10-19T12:21:29.835618Z",
     "iopub.status.idle": "2026-10-19T12:21:33.259443Z",
     "shell.execute_reply": "2026-10-19T12:21:33.258806Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "explained variance ratio of the first 4 PCs: [0.669 0.259 0.067 0.   ]\n",
      "participation ratio: 1.93\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "decoding accuracy per fold: [1.         0.94       0.97999996 0.98999995 0.96      ] (chance 0.25)\n"
     ]
    }
   ],
   "source": [
    "latent = rng.standard_normal((2000, 3)) * np.array([3.0, 2.0, 1.0])\n",
    "mixing = rng.standard_normal((3, 100))\n",
    "activity = jnp.asarray(latent @ mixing + 0.3 * rng.standard_normal((2000, 100)))\n",
    "res = population.pca(activity, n_components=10)\n",
    "print('explained variance ratio of the first 4 PCs:', np.round(res.explained_variance_ratio[:4], 3))\n",
    "print('participation ratio: %.2f' % population.participation_ratio(activity))\n",
    "\n",
    "labels = jnp.asarray(rng.integers(0, 4, size=400))\n",
    "templates = rng.standard_normal((4, 50))\n",
    "responses = jnp.asarray(templates[np.asarray(labels)] + 2.0 * rng.standard_normal((400, 50)))\n",
    "acc = population.decode(responses, labels, n_folds=5, model='lda', reg=0.1, key=jax.random.key(0))\n",
    "print('decoding accuracy per fold:', np.round(acc, 2), '(chance 0.25)')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0d643f12",
   "metadata": {},
   "source": [
    "### Granger causality and avalanches\n",
    "\n",
    "In a three-node chain x → y → z, conditional Granger causality finds the two direct links and no direct x → z link. `avalanches` splits a population count series into bursts separated by silence; for a critical branching process the branching ratio is close to 1."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "56a1b009",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-10-19T12:21:33.262323Z",
     "iopub.status.busy": "2026-10-19T12:21:33.262077Z",
     "iopub.status.idle": "2026-10-19T12:21:36.893880Z",
     "shell.execute_reply": "2026-10-19T12:21:36.892943Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "GC[target, source]:\n",
      "[[0.         0.         0.001     ]\n",
      " [0.55200005 0.         0.001     ]\n",
      " [0.001      0.60800004 0.        ]]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "avalanches: 181  branching ratio: 0.99\n"
     ]
    }
   ],
   "source": [
    "T = 5000\n",
    "xyz = np.zeros((T, 3))\n",
    "noise = rng.standard_normal((T, 3))\n",
    "for k in range(1, T):  # toy data generation on the host\n",
    "    xyz[k, 0] = 0.5 * xyz[k - 1, 0] + noise[k, 0]\n",
    "    xyz[k, 1] = 0.5 * xyz[k - 1, 1] + 0.8 * xyz[k - 1, 0] + noise[k, 1]\n",
    "    xyz[k, 2] = 0.5 * xyz[k - 1, 2] + 0.8 * xyz[k - 1, 1] + noise[k, 2]\n",
    "gc = population.granger_causality(jnp.asarray(xyz), order=2)\n",
    "print('GC[target, source]:')\n",
    "print(np.round(gc, 3))\n",
    "\n",
    "# a branching process with ratio sigma, restarted by rare external input\n",
    "sigma, counts = 1.0, np.zeros(20000, dtype=int)\n",
    "for k in range(1, counts.size):\n",
    "    counts[k] = rng.poisson(sigma * counts[k - 1]) + (rng.random() < 0.01)\n",
    "av = population.avalanches(jnp.asarray(counts))\n",
    "print('avalanches:', int(av.n), ' branching ratio: %.2f' % population.branching_ratio(jnp.asarray(counts)))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "fdf20f2c",
   "metadata": {},
   "source": [
    "## 4. Resampling and confidence intervals\n",
    "\n",
    "Is the 5 ms delayed coupling from section 1 significant? Compare the observed coincidence count with a null distribution built by jittering one train; `jax.lax.map` over the keys (vectorised in batches of 10) builds the whole null distribution in one compiled call. For continuous signals, `phase_randomize` keeps the power spectrum but destroys phase relations between signals. (It needs a broadband or noisy signal: a pure sinusoid is a single Fourier component, which phase randomisation merely shifts.) Finally, `bootstrap_ci` gives a confidence interval for any statistic."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "6d80396d",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-10-19T12:21:36.896938Z",
     "iopub.status.busy": "2026-10-19T12:21:36.896635Z",
     "iopub.status.idle": "2026-10-19T12:21:41.255323Z",
     "shell.execute_reply": "2026-10-19T12:21:41.254384Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "observed 8019, null mean 545.9, p = 0.000\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "PLV original 0.96, phase-randomised 0.22\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "mean CV of the Poisson neurons: 95% CI [0.969, 1.012]\n"
     ]
    }
   ],
   "source": [
    "def coincidences(b_trains):\n",
    "    ccg, _ = spike.cross_correlogram(a, b_trains, bin_size=1 * u.ms, max_lag=20 * u.ms)\n",
    "    return ccg[:, 25].sum()  # the +5 ms bin\n",
    "\n",
    "observed = coincidences(b)\n",
    "keys = jax.random.split(jax.random.key(2), 200)\n",
    "# lax.map with batch_size vmaps 10 keys at a time, bounding memory\n",
    "null = jax.lax.map(lambda k: coincidences(stats.jitter_spikes(k, b, 10 * u.ms)), keys, batch_size=10)\n",
    "print('observed %d, null mean %.1f, p = %.3f' % (observed, null.mean(), (null >= observed).mean()))\n",
    "\n",
    "# two signals sharing a narrow-band (8-12 Hz) noise driver with a 20 ms lag\n",
    "drive = np.asarray(spectral.bandpass(jnp.asarray(rng.standard_normal(t.size + 20)), dt=1 * u.ms, band=(8, 12)))\n",
    "p = jnp.asarray(drive[20:] + 0.02 * rng.standard_normal(t.size))\n",
    "q = jnp.asarray(drive[:-20] + 0.02 * rng.standard_normal(t.size))\n",
    "surr = stats.phase_randomize(jax.random.key(3), p)\n",
    "print('PLV original %.2f, phase-randomised %.2f' % (\n",
    "    spectral.plv(p, q, dt=1 * u.ms, band=(8, 12)), spectral.plv(surr, q, dt=1 * u.ms, band=(8, 12))))\n",
    "\n",
    "low, high = stats.bootstrap_ci(jax.random.key(4), cv[:20], jnp.nanmean, n_resamples=2000)\n",
    "print('mean CV of the Poisson neurons: 95%% CI [%.3f, %.3f]' % (low, high))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "cf105e8f",
   "metadata": {},
   "source": [
    "## Summary\n",
    "\n",
    "| Task | Functions |\n",
    "|---|---|\n",
    "| interval statistics | `spike.isi`, `cv`, `cv2`, `lv`, `fano_factor` |\n",
    "| event-aligned | `spike.psth`, `spike_triggered_average` |\n",
    "| pairwise timing | `spike.cross_correlogram`, `auto_correlogram`, `isi_distance`, `spike_distance` |\n",
    "| spectra | `spectral.multitaper_psd`, `spectrogram`, `morlet_transform`, `band_power` |\n",
    "| filtering and phase | `spectral.bandpass`, `analytic_signal`, `plv`, `pli`, `wpli` |\n",
    "| population | `population.pca`, `participation_ratio`, `cca`, `rdm`, `rsa`, `decode`, `mutual_information` |\n",
    "| collective dynamics | `population.kuramoto_order_parameter`, `granger_causality`, `avalanches`, `branching_ratio` |\n",
    "| resampling | `stats.jitter_spikes`, `shuffle_isi`, `phase_randomize`, `bootstrap_ci` |\n",
    "\n",
    "See the {doc}`API reference <../apis/analysis>` for every parameter."
   ]
  }
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