Nonidentifiability and Bayes

A third paper from The American Statistician compares nonidentifiability in the context of Bayesian inference and Maximum Likelihood Inference.

More than the comparison, I found the paper does an interesting job on explaining nonidentifiability with a simple example, even without getting rid of all the mathematics.

For those folks working with Structural Equation Models, identification of the model is something routinely present. A model will not fit under Maximum Likelihood estimation if the maximum of the likelihood is not unique. One cannot find X and Y that maximizes X + Y = 10, to give a common place example. In a SEM things are much more complicated because no easy rule exists to prove identification, and your only clue is the software yelling at you that it cannot fit the model.

Under Bayesian statistics one does not maximizes things but rather calculates posterior distribution and uses it for confidence intervals, median, means. I am not expert on this, but after reading the paper I would think that it would be a problem also for the Bayesians if they (we?) were often interested in the mode of the posteriori.

So it is worth reading, it was for me. ON the curiosity side, the paper is co-written by some folks from University of Sao Paulo, where I had the privilege of studying a while ago. Maybe a little more than a while ago. The example in the paper is a modification of one found in a book by Sheldon Ross, a book that I used in my first probability course and caused a lot of sweating: we had to solve most of the exercises of the book, and there are so many...