## Archive for normalised maximum likelihood

## baseless!

Posted in Books, Statistics with tags 1922, Bayes theorem, epistemic probability, frequency properties, George Boole, history of statistics, inverse probability, normalised maximum likelihood, Pierre Simon Laplace, R.A. Fisher, Siméon Poisson on July 13, 2021 by xi'an## differences between Bayes factors and normalised maximum likelihood

Posted in Books, Kids, Statistics, University life with tags Bayes factors, binomial distribution, model complexity, normalised maximum likelihood, Rissanen on November 19, 2014 by xi'an**A** recent arXival by Heck, Wagenmaker and Morey attracted my attention: Three Qualitative Differences Between Bayes Factors and Normalized Maximum Likelihood, as it provides an analysis of the differences between Bayesian analysis and Rissanen’s Optimal Estimation of Parameters that I reviewed a while ago. As detailed in this review, I had difficulties with considering the normalised likelihood

as the relevant quantity. One reason being that the distribution does not make experimental sense: for instance, how can one simulate from this distribution? [I mean, when considering only the original distribution.] Working with the simple binomial B(n,θ) model, the authors show the quantity corresponding to the posterior probability may be constant for most of the data values, produces a different upper bound and hence a different penalty of model complexity, and may differ in conclusion for some observations. Which means that the apparent proximity to using a Jeffreys prior and Rissanen’s alternative does not go all the way. While it is a short note and only focussed on producing an illustration in the Binomial case, I find it interesting that researchers investigate the Bayesian nature (vs. artifice!) of this approach…