Mean squared likelihood score as Fisher-information estimate

Read the equation

For a scalar parameter, Fisher information is the expected square of the derivative of log likelihood. The implementation averages squares of the supplied scores. It estimates that information only when the inputs actually are likelihood-score samples drawn from the intended model; arbitrary scalar scores merely produce a mean square.

Terms & definitions

How it works

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Assumptions & limits

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Original context

func MutualInformation(px, py, pxy []float64) float64 {
	hx := ShannonEntropy(px)
	hy := ShannonEntropy(py)
	hxy := ShannonEntropy(pxy)
	return hx + hy - hxy
}

// FisherInformation computes I(θ) = E[(∂log p/∂θ)²]
func FisherInformation(scores []float64) float64 {
	if len(scores) == 0 {
		return 0.0
	}

	sum := 0.0
	for _, s := range scores {
		sum += s * s
	}
	return sum / float64(len(scores))

FisherInformation computes I(θ) = E[(∂log p/∂θ)²]

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