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 5 | Intro and overview | Paninski and Cunningham, `17 | |

Sept 5 | 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 12 | Neuroscience review by Gonzalo Mena | ||

Sept 19 - Oct 3 | Signal acquisition: calcium imaging | Demixing: Pnevmatikakis
et al '16; Zhou
et al
'16; 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 '17 | HMM tutorial by Rabiner; HMM notes |

Oct 10-17 | Poisson regression models; estimating time-varying firing rates; hierarchical models for sharing information across cells | Kass et al (2003), Wallstrom et al (2008), Batty et al (2017), Cadena et al (2017), Seely et al (2017) | Generalized linear model notes |

Oct 24 | Presentations of project ideas | Just two minutes each | |

Oct 31 | Expected log-likelihood. Network models. Optimal experimental design. | Ramirez and Paninski, '14, Field et al '10, Lewi et al '09, Shababo et al '13, Soudry et al '15 | |

Nov 7 | No class (University holiday) | ||

Nov 14 | Point processes: Poisson process, renewal process, self-exciting process, Cox process; time-rescaling: goodness-of-fit, fast simulation of network models | Brown et al. '01, Mena and Paninski '14 | Uri Eden's point process notes; supplementary notes. |

Thanks to the NSF for support.