Archive for hierarchical models

a day for comments

Posted in Mountains, Statistics, Travel, University life with tags , , , , , , , , , , , , , , , , , , , , , , , , , on April 21, 2014 by xi'an

As I was flying over Skye (with [maybe] a first if hazy perspective on the Cuillin ridge!) to Iceland, three long sets of replies to some of my posts appeared on the ‘Og:

Thanks to them for taking the time to answer my musings…

 

Dan Simpson’s seminar at CREST

Posted in Kids, Mountains, Statistics, Travel, University life with tags , , , , , , , , , on April 18, 2014 by xi'an

Daniel Simpson gave a seminar at CREST yesterday on his recently arXived paper, “Penalising model component complexity: A principled, practical  approach to constructing priors” written with Thiago Martins, Andrea Riebler, Håvard Rue, and Sigrunn Sørbye. Paper that he should also have given in Banff last month had he not lost his passport in København airport…  I have already commented at length on this exciting paper, hopefully to become a discussion paper in a top journal!, so I am just pointing out two things that came to my mind during the energetic talk delivered by Dan to our group. The first thing is that those penalised complexity (PC) priors of theirs rely on some choices in the ordering of the relevance, complexity, nuisance level, &tc. of the parameters, just like reference priors. While Dan already wrote a paper on Russian roulette, there is also a Russian doll principle at work behind (or within) PC priors. Each shell of the Russian doll corresponds to a further level of complexity whose order need be decided by the modeller… Not very realistic in a hierarchical model with several types of parameters having only local meaning.

My second point is that the construction of those “politically correct” (PC) priors reflects another Russian doll structure, namely one of embedded models, hence would and should lead to a natural multiple testing methodology. Except that Dan rejected this notion during his talk, by being opposed to testing per se. (A good topic for one of my summer projects, if nothing more, then!)

Hierarchical vs. graphical models

Posted in Books, Statistics, University life with tags , , , on November 21, 2010 by xi'an

An email from a reader:

I’m studying your book  The Bayesian Choice (2007). I know that you mentioned graphics models in the Notes of Section 10. But I’m still confused on what is Hierarchical Bayesian Models and Graphical Models. It seems to me that Hierarchical models are just special cases of graphical models. The Bayesian network that corresponds to a graphical model is a DAG in general and the Bayesian network that corresponds to a hierarchical model is just a chain of directed edges.

Would you please take a few seconds to point me some references or discussions so that I can understand their differences better?

To which I can only reply that hierarchical models are indeed special cases of graphical models for which the edges have some kind of causal interpretation and where some conditional independence relations are imposed by the hierarchy, which is not always the case for graphical models. As probabilistic objects and as distributions, both structures belong to the same family. Inference on those objects may be different though, in that [presence or absence of] edges may be examined individually in graphical models, less so in hierarchical models where they come [and go] in batches respecting the hierarchy (see e.g. random effect models).