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, another by Wulfram Gerstner, and another by Idan Segev.

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

Sep 8,15 | Introduction; background on neuronal biophysics, regression, MCMC | Spikes introduction; Kass et al '05; Brown et al. '04 | Neuroscience review by Ella Batty. Regression notes |

Sep 22 | Signal acquisition: spike sorting, calcium imaging | Lewicki '98; Shoham et al '03; Pouzat et al '04, Pillow et al `13, Carlson et al '13, Pnevmatikakis et al '14 | EM notes |

Sept 29 | No class | ||

Oct 6 | Estimating time-varying firing rates | Kass et al (2003), Wallstrom et al (2008) | Generalized linear model notes |

Oct 13 | Linear-nonlinear Poisson cascade models: spike-triggered averaging; Poisson regression | Simoncelli et al. '04; Chichilnisky '01; Paninski '03; Sharpee et al. '04; Paninski '04; Weisberg and Welsh '94; Williamson et al '13 | Try these practice problems, courtesy of Dayan and Abbott; any problem in chapter 1; also problems 2-3 in chapter 2. |

Oct 20 | Expected log-likelihood; quadratic models; spike-triggered covariance; sparsity-promoting and rank-penalizing priors; hierarchical models. Experimental design. | Park and Pillow '11, Ramirez and Paninski, '13, Field, Gauthier, Sher et al '10, Ahrens et al '08, Lewi et al '09, Shababo et al '13, Soudry et al '15 | |

Oct 27 | Presentations of project ideas | Just two minutes each | |

Nov 3 | No class (University holiday) | ||

Nov 10 | 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. |

Nov 17 - Dec 1 | State space models; autoregressive models; Kalman filter; extended Kalman filter; fast tridiagonal methods. Applications in neural prosthetics, optimal smoothing of voltage/calcium traces, fitting common-input models for population spike train data, and analysis of nonstationary spike train data | HMM tutorial by Rabiner; Kalman filter notes by Minka; Roweis and Ghahramani '99; Huys et al '06; Paninski et al '04; Jolivet et al '04; Beeman's notes on conductance-based neural modeling; Wu et al '05; Brown et al '98; Smith et al '04; Yu et al '05; Kulkarni and Paninski '08; Paninski et al '10, Calabrese and Paninski '11; Vogelstein et al '10, Buesing et al '12, Vidne et al '12, Pfau et al '13. | state-space notes (need updating) |

Dec 8 | No class (office hours) | Stop by if you want to discuss your project. | |

Dec 15 | Project presentations | E-mail me your report as a pdf by Dec 18. |

Thanks to the NSF for support.