### Citations

472 | Multivariate density estimation
- Scott
- 1992
(Show Context)
Citation Context ... (13). ThesHistogram bin width selection for time-dependent Poisson processes 7261 mechanism for this scaling is the same as that for Scott’s choice of the number of bars used to construct histograms =-=[13]-=-. The scaling relation is dependent on the smoothness of the probability modulation. In the case that the rate function fluctuates in a zigzag form, as when modulated by the Ornstein– Uhlenbeck proces... |

151 |
Introduction to theoretical neurobiology, (Vol. 2.) Cambridge:
- Tuckwell
- 1988
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Citation Context ...sider the situation that we observed n sequences of point events, or spikes, repeatedly derived from time-dependent Poisson processes characterized by the same time-dependent rate of occurrence, λ(t) =-=[10, 11]-=-. With this set of data, one constructs a time histogram ˜λ�(t) to infer the underlying rate of occurrence λ(t). The time histogram takes the form of a bar graph, consisting of bars of bin width � ali... |

26 |
Abbott L 2001 Theoretical Neuroscience
- Dayan
(Show Context)
Citation Context ... time-dependent Poisson process with rate of occurrence λ(t). From the set of spike sequences, a time histogram ˜λ�(t) of bin width � is constructed. experiments are carried out using time histograms =-=[8, 9]-=-. In constructing a time histogram, one has to determine the bin width. A small bin width is necessary for capturing the details of the time dependence of the spike rate. If the bin width is too small... |

25 | Filtering and detection for doubly stochastic Poisson processes,” - Snyder - 1972 |

5 |
Lewis P A W 1966 The Statistical Analysis of Series of Events (London
- Cox
(Show Context)
Citation Context ...sider the situation that we observed n sequences of point events, or spikes, repeatedly derived from time-dependent Poisson processes characterized by the same time-dependent rate of occurrence, λ(t) =-=[10, 11]-=-. With this set of data, one constructs a time histogram ˜λ�(t) to infer the underlying rate of occurrence λ(t). The time histogram takes the form of a bar graph, consisting of bars of bin width � ali... |

1 |
et al 1996 Spikes: Exploring the Neural Code
- Rieke
(Show Context)
Citation Context ...must repeat the same trial a number of times to extract the actual signal of each neuron. The signal, or the message, is considered to underlie the rate of occurrence with which the spikes are evoked =-=[1]-=-. If the underlying rate is given apriorias a function of time, one would employ the maximum likelihood estimates to determine its parameters. In the general circumstance in which the underlying rate ... |

1 | Beneˇs V E 1980 Recursive nonlinear estimation of a diffusion acting as the rate of an observed Poisson process - Boel |

1 | et al 1999 Discrete time filters for doubly stochastic Poisson processes and other exponential noise models Int - Manton |

1 | et al 2002 Statistical analysis of temporal evolution in single-neuron firing rates Biostatistics 3 1 - Ventura |

1 | A C and Brown E N 2003 Estimating a state-space model from point process observations Neural Comput - Smith |

1 | et al 2003 Pattern filtering for detection of neural activity, with examples from HVc activity during sleep zebra fiches Neural Comput - Chi |

1 |
Tsubo Y 2001 Modeling spiking behaviour of neurons with time-dependent Poisson processes Phys
- Shinomoto
(Show Context)
Citation Context ...re not generated when λ(t) � 0. Negative values of λ(t) that may occur in the Ornstein–Uhlenbeck process result in errors in the analysis. The following analytical results are reliable for σ 2τ/µ ≪ 1 =-=[12]-=-. The mean squared error E� defined in (1) for a particular realization of the Ornstein– Uhlenbeck process, λ(t), is expected to be self-averaging in the limit of a long observation time, T →∞, and in... |