## The day I invented Bayesian Lasso…

**G**eorge Casella remarked to me last month in Padova that, once he and Trevor Park published ** The Bayesian Lasso** in JASA, they received many claims for prior discovery of “Bayesian Lasso”! So, as a joke, let me add my claim as well! Indeed, in the first (1994) edition of

**, I included an example in Chapter 4 (Example 4.2) about the fact that using a double exponential prior along a Cauchy likelihood was producing a zero MAP (maximum a posteriori) estimate. Isn’t that the essence of the Bayesian lasso?! Of course, as you can still check in the current edition, the example was intended as a counter-example to the use of MAP estimates, not as an argument about the parsimony induced by double exponential priors. (Exercice 4.6 in both editions builds upon this example to notice that, with a small enough scale parameter, the absolute shrinkage to zero vanishes.) I thus lost the opportunity of “inventing” the Bayesian Lasso! To my shame, I must add that in the even earlier 1992 French edition of the book, I made a mistake in the derivation of the MAP and hence completely missed the point!!!**

*The Bayesian Choice*
September 23, 2010 at 8:45 am

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