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analysis:course-w16:week10 [2016/02/16 14:01]
mvdm [Quantifying decoding accuracy]
analysis:course-w16:week10 [2017/01/05 15:16]
mvdm [Bayesian decoding]
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 In general, from the [[http://​en.wikipedia.org/​wiki/​Poisson_distribution | definition of the Poisson distribution]],​ it follows that In general, from the [[http://​en.wikipedia.org/​wiki/​Poisson_distribution | definition of the Poisson distribution]],​ it follows that
  
-\[P(n_i|\mathbf{x}) = \frac{(\tau f_i(\mathbf{x}))^{n_i}}{n_i!} e^{-\tau f_i (x)}\]+\[P(n_i|\mathbf{x}) = \frac{(\tau f_i(\mathbf{x}))^{n_i}}{n_i!} e^{-\tau f_i (\mathbf{x})}\]
  
 $f_i(\mathbf{x})$ is the average firing rate of neuron $i$ over $x$ (i.e. the tuning curve for position), $n_i$ is the number of spikes emitted by neuron $i$ in the current time window, and $\tau$ is the size of the time window used. Thus, $\tau f_i(\mathbf{x})$ is the mean number of spikes we expect from neuron $i$ in a window of size $\tau$; the Poisson distribution describes how likely it is that we observe the actual number of spikes $n_i$ given this expectation. $f_i(\mathbf{x})$ is the average firing rate of neuron $i$ over $x$ (i.e. the tuning curve for position), $n_i$ is the number of spikes emitted by neuron $i$ in the current time window, and $\tau$ is the size of the time window used. Thus, $\tau f_i(\mathbf{x})$ is the mean number of spikes we expect from neuron $i$ in a window of size $\tau$; the Poisson distribution describes how likely it is that we observe the actual number of spikes $n_i$ given this expectation.
analysis/course-w16/week10.txt ยท Last modified: 2018/07/07 10:19 (external edit)