## how can a posterior be uniform?

Posted in Books, Statistics with tags , , , , , , on September 1, 2020 by xi'an

How can we have a posterior distribution that is a uniform distribution?

With the underlying message that a uniform distribution does not depend on the data, since it is uniform! While it is always possible to pick the parameterisation a posteriori so that the posterior is uniform, by simply using the inverse cdf transform, or to pick the prior a posteriori so that the prior cancels the likelihood function, there exist more authentic discrete examples of a data realisation leading to a uniform distribution, as eg in the Multinomial model. I deem the confusion to stem from the impression either that uniform means non-informative (what we could dub Laplace’s daemon!) or that it could remain uniform for all realisations of the sampled rv.

## objectivity in prior distributions for the multinomial model

Posted in Statistics, University life with tags , , , , , on March 17, 2016 by xi'an

Today, Danilo Alvares visiting from the Universitat de Valencià gave a talk at CREST about choosing a prior for the Multinomial distribution. Comparing different Dirichlet priors. In a sense this is an hopeless task, first because there is no reason to pick a particular prior unless one picks a very specific and a-Bayesian criterion to discriminate between priors, second because the multinomial is a weird distribution, hardly a distribution at all in that it results from grouping observations into classes, often based on the observations themselves. A construction that should be included within the choice of the prior maybe? But there lurks a danger of ending up with a data-dependent prior. My other remark about this problem is that, among the token priors, Perk’s prior using 1/k as its hyper-parameter [where k is the number of categories] is rather difficult to justify compared with 1/k² or 1/k³, except for aggregation consistency to some extent. And Laplace’s prior gets highly concentrated as the number of categories grows.