## maximum likelihood: an introduction

“Basic Principle 0. Do not trust any principle.” L. Le Cam (1990)

Here is the abstract of a International Statistical Rewiew 1990 paper by Lucien Le Cam on maximum likelihood. ISR keeping a tradition of including an abstract in French for every paper, Le Cam (most presumably) wrote his own translation [or maybe wrote the French version first], which sounds much funnier to me and so I cannot resist posting both, pardon my/his French! [I just find “Ce fait” rather unusual, as I would have rather written “Ceci fait”…]:

Maximum likelihood estimates are reported to be best under all circumstances. Yet there are numerous simple examples where they plainly misbehave. One gives some examples for problems that had not been invented for the purpose of annoying maximum likelihood fans. Another example, imitated from Bahadur, has been specially created with just such a purpose in mind. Next, we present a list of principles leading to the construction of good estimates. The main principle says that one should not believe in principles but study each problem for its own sake.

L’auteur a ouï dire que la méthode du maximum de vraisemblance est la meilleure méthode d’estimation. C’est bien vrai, et pourtant la méthode se casse le nez sur des exemples bien simples qui n’avaient pas été inventés pour le plaisir de montrer que la méthode peut être très désagréable. On en donne quelques-uns, plus un autre, imité de Bahadur et fabriqué exprès pour ennuyer les admirateurs du maximum de vraisemblance. Ce fait, on donne une savante liste de principes de construction de bons estimateurs, le principe principal étant qu’il ne faut pas croire aux principes.

The entire paper is just as witty, as in describing the mixture model as “contaminated and not fit to drink”! Or in “Everybody knows that taking logarithms is unfair”. Or, again, in “biostatisticians, being complicated people, prefer to work out not with the dose y but with its logarithm”… And a last line: “One possibility is that there are too many horse hairs in e”.

### 4 Responses to “maximum likelihood: an introduction”

1. “It is hard to design experiments where the number of observations is strictly negative. Thus our best bet is to design them with n = 0 and uphold the faith.”

2. “Basic Principle 0. Do not trust any principle.” Logical conclusion: do not trust Basic Principle 0.

• Logical?! If you do not trust Basic Principle 0, you should not not trust any principle..!

• It does sound like a fallacy to me too. Actually similar to the Epimenides paradox: “All Cretans are liars.”, “All principles untrustworthy”

Principle 0 says, ‘all principles untrustworthy,’ but principle 0 is itself a principle; therefore it is itself untrustworthy. But if it is untrustworthy, what it says is not to be trusted, and consequently we can trust principles; but principle 0 is a principle, and therefore what it says is trustworthy; saying all principles are untrustworthy make principle 0 be itself untrustworthy. Hence we may go on alternately proving that principle 0 and all principles are trustworthy and untrustworthy without reaching convergence.

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