Likelihood: How One Idea Reshaped Statistics
From tally tables to modern estimation -- and the much older twin the idea turns out to share with Bayesian inference
Traces statistics from pure data organization (tally tables, means, variances) through curve fitting -- correcting the record to show Gauss and Laplace attached a Normal-error probabilistic model to least squares within seven years of Legendre's model-free 1805 publication, not a century later -- through Pearson's 1894 method of moments, to Fisher's 1921-22 formalization of likelihood. Corrects a common historical inversion: inverse probability (Bayes 1763, Laplace, De Morgan's 1837 naming) predates Fisher's likelihood by a century and a half, and Fisher built likelihood in explicit opposition to it rather than statisticians later discovering Bayesian methods share the same machinery. Closes with likelihood's 20th-century descendants -- quasi-likelihood, partial likelihood, REML, and empirical likelihood -- and where each is used today.
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