The Fisher Information
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The Fisher Information quantifies how well an observation of a random variable locates a parameter value. It's an essential tool for measure parameter uncertainty, a problem that repeats itself throughout machine learning and statistics. In this video, I explain the Fisher Information rigorously and visually, starting in the one dimensional case and ending in the general case.
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Sources and Learning More
[1] provides a complete and deep explanation of the Fisher Information. It's captures the abstract/general perspective while making the idea concrete with examples. As is typically the case, the wikipedia article [2] was helpful. Also, section 8.2.2 of [3] explains the use of a theorem on the asymptotic normality of the MLE via the Fisher Information, which I didn't cover here, but certainly informed how I think it connects to parameter uncertainty.
[1] Ly A., Marsman M., Verhagen J., Grasman R., Wagermarkers E.J., (2017), A Tutorial on the Fisher Information, Department of Psychological Methods, University of Amsterdam, The Netherlands
[2] Fisher information, Wikipedia, https://en.wikipedia.org/wiki/Fisher_...
[3] Hastie, T., Tibshirani, R., & Friedman, J. H. (2009). The Elements of Statistical Learning: Data Mining, Inference, and Prediction. 2nd ed. New York: Springer.
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