analysis:course-w16:week10
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| Both sides previous revision Previous revision Next revision | Previous revision Next revision Both sides next revision | ||
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analysis:course-w16:week10 [2016/02/15 10:18] mvdm [Estimating tuning curves] |
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. | ||
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| % get trial id for each sample | % get trial id for each sample | ||
| trial_id = zeros(size(Q_tvec_centers)); | trial_id = zeros(size(Q_tvec_centers)); | ||
| - | trial_idx = nearest_idx3(run_start,Q_tvec_centers); % NOTE: on non-Windows, use nearest_idx.m | + | trial_idx = nearest_idx3(metadata.taskvars.trial_iv.tstart,Q_tvec_centers); % NOTE: on non-Windows, use nearest_idx.m |
| trial_id(trial_idx) = 1; | trial_id(trial_idx) = 1; | ||
| trial_id = cumsum(trial_id); | trial_id = cumsum(trial_id); | ||
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| {{ :analysis:course-w16:dec_err.png?nolink&600 |}} | {{ :analysis:course-w16:dec_err.png?nolink&600 |}} | ||
| + | |||
| + | (Note, your plot might look a little different.) | ||
| Thus, on average our estimate is 2.14 pixels away from the true position. Earlier laps seem to have some more outliers of bins where our estimate is bad (large distance) but there is no obvious trend across laps visible. | Thus, on average our estimate is 2.14 pixels away from the true position. Earlier laps seem to have some more outliers of bins where our estimate is bad (large distance) but there is no obvious trend across laps visible. | ||
analysis/course-w16/week10.txt ยท Last modified: 2018/07/07 10:19 (external edit)
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