Statistical concept / technique | Neuroscience application |
---|---|

Point processes; conditional intensity functions | Neural spike trains; photon-limited image data |

Time-rescaling theorem for point processes | Fast simulation of network models; goodness-of-fit tests for spiking models |

Bias, consistency, principal components | Spike-triggered averaging; spike-triggered covariance |

Generalized linear models | Neural encoding models including spike-history effects; inferring network connectivity |

Regularization; shrinkage estimation | Maximum a posteriori estimation of high-dimensional neural encoding models |

Laplace approximation; Fisher information | Model-based decoding and information estimation; adaptive design of optimal stimuli |

Mixture models; EM algorithm; Dirichlet processes | Spike-sorting / clustering |

Optimization and convexity techniques | Spike-train decoding; ML estimation of encoding models |

Markov chain Monte Carlo: Metropolis-Hastings and hit-and-run algorithms | Firing rate estimation and spike-train decoding |

State-space models; sequential Monte Carlo / particle filtering | Decoding spike trains; optimal voltage smoothing |

Fast high-dimensional Kalman filtering | Optimal smoothing of voltage and calcium signals on large dendritic trees |

Markov processes; first-passage times; Fokker-Planck equation | Integrate-and-fire-based neural models |

More recently, a couple good online courses in computational neuroscience have appeared: one directed by Raj Rao and Adrienne Fairhall, and another by Wulfram Gerstner.

Date | Topic | Reading | Notes |
---|---|---|---|

Sept 4 | Intro and overview | Paninski and Cunningham, `18; International Brain Lab, '17 | |

Sept 11 | Signal acquisition: spike sorting | Lewicki '98; Pachitariu et al '16; Lee et al '17; Calabrese and Paninski '11 | EM notes; Blei et al review on variational inference |

Sept 18 | Signal acquisition: single-cell-resolution functional imaging | Overview: Pnevmatikakis
and Paninski '18; Compression and
denoising: Buchanan
et al '18; Demixing: Pnevmatikakis et al '16; Zhou et al '18; Friedrich et al '17b; Lu et al '17; Giovanucci et al '17; Deconvolution: Deneux et al '16; Picardo et al '16; Friedrich et al '17a; Berens et al '18 | HMM tutorial by Rabiner; HMM notes |

Thanks to the NSF for support.