butterfly_effect
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- Dec 1, 2016
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Here is the problem, from a paper by Kording 2014:
Let’s say we have a monkey opening and closing its hand, while we record from its primary motor cortex. We want to decode how the monkey is moving the hand, maybe to build a prosthetic device. Let us say the monkey wants to open the hand 80% of the time and close it otherwise (prior p(open)=.8). Let us say we record the number of spikes from a neuron related to hand opening which gives 10+−3 spikes (mean+−sd) when the hand is open and 13+−3 spikes when the hand is closed. How could we estimate if the hand should be open based on both the spikes and the prior knowledge?
This seems like it should be simple to me, just using the 68-95-99.7 rule and Baye's Law.
Given p(open|spikes) = p(open)*p(spikes|open) / (p(open)*p(spikes|open) + p(closed)*p(spikes|closed))
p(open) = 0.8, the prior
p(closed) = 0.2
p(spikes|open) = p(>19 spikes) in the open distribution, which is 3 sds above the mean, so this would be 0.0015.
p(spikes|closed) = p(>19 spikes) in closed distribution, which is 2 sds above the mean, so 0.025.
p(open|spikes) = 0.8*0.0015 / (0.8*0.0015 + 0.2*0.025) = 0.19
But apparently the answer is supposed to be 47%? I can't figure out what's wrong with my approach...
Let’s say we have a monkey opening and closing its hand, while we record from its primary motor cortex. We want to decode how the monkey is moving the hand, maybe to build a prosthetic device. Let us say the monkey wants to open the hand 80% of the time and close it otherwise (prior p(open)=.8). Let us say we record the number of spikes from a neuron related to hand opening which gives 10+−3 spikes (mean+−sd) when the hand is open and 13+−3 spikes when the hand is closed. How could we estimate if the hand should be open based on both the spikes and the prior knowledge?
This seems like it should be simple to me, just using the 68-95-99.7 rule and Baye's Law.
Given p(open|spikes) = p(open)*p(spikes|open) / (p(open)*p(spikes|open) + p(closed)*p(spikes|closed))
p(open) = 0.8, the prior
p(closed) = 0.2
p(spikes|open) = p(>19 spikes) in the open distribution, which is 3 sds above the mean, so this would be 0.0015.
p(spikes|closed) = p(>19 spikes) in closed distribution, which is 2 sds above the mean, so 0.025.
p(open|spikes) = 0.8*0.0015 / (0.8*0.0015 + 0.2*0.025) = 0.19
But apparently the answer is supposed to be 47%? I can't figure out what's wrong with my approach...
