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 |

Hierarchical Bayesian models | Estimating multiple neural encoding models |

Amortized inference | Spike sorting; stimulus decoding |

A couple good older online courses in computational neuroscience: one directed by Raj Rao and Adrienne Fairhall, and another by Wulfram Gerstner.

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

Sept 8, 15 | Intro and overview | Paninski and Cunningham, `18; International Brain Lab, '17, '22, '23a, '23b | Slides here. |

Sept 22 | Optogenetic circuit mapping | Hu et al '09, Shababo et al '13, Hage et al '19, Triplett et al '22, Antin et al '23, Triplett et al '23 | Guest lecture by Marcus Triplett. Background slides on Gaussian processes by J. Cunningham here. |

Sept 29 | Behavioral video analysis | DeepLabCut, DeepGraphPose, MoSeq, PS-VAE, SLEAP, Lightning-Pose, DAART | Guest lecture by Matt Whiteway and Dan Biderman. |

Thanks to the NSF for support.