§15 Population Coding — Tuning Curves and Fisher Information
f(θ) = fmax · exp(-(θ - θpref)² / (2σ²)) + fbase
J(θ) = Σi (∂fi/∂θ)² / σ²noise
Var(θ̂) ≥ 1/J(θ) (Cramér–Rao lower bound)
J(θ) = Σi (∂fi/∂θ)² / σ²noise
Var(θ̂) ≥ 1/J(θ) (Cramér–Rao lower bound)
Population coding theory describes how the nervous system represents external stimuli precisely through the activity of a population of neurons. Each neuron has a tuning curve (preferring a particular stimulus value); Fisher information quantifies coding precision, and the Cramér–Rao bound gives the minimum variance achievable by any unbiased decoder.
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