Guiana impressions [#1]

As our daughter Rachel has started her (five year) medical residency with a semester round in a French Guiana hospital, we took the opportunity of the Xmas break and of acceptable travel restrictions to visit her and the largest (and sole American) French departement for a week! This was a most unexpected trip that we enjoyed considerably.

While hot and humid is not my favourite type of weather (!) the weather remained quite tolerable that week, esp. when considering this was the start of the rain season (guiana means land of plentiful water in Arawak!) This made hiking on the (well-traced) paths in the local equatorial rain forest rather interesting, as the red soil is definitely muddy or worse. I however faced much less insects than I feared and mosquito bites were rare beyond the dawn and dusk periods. Plenty of birds, albeit mostly invisible. Except for the fantastic marshes of Kaw, where the variety of birds is amazing, including aras and toucans. Very muddy trails, did I mention it, but beautiful explosion of trees. Green everywhere.My first sight of a sloth was quite the treat, but I regret not spotting anteaters. Or a tapir. Swimming in the marshes of Kaw was great as well, with no worry from local caimans! Which we went spotting after nightfall. The place reminded me in several ways of Tonlé Sap lake, near Angkor.

Ate there an atipa bosco fish from the same place. Which has samurai armor. And two front legs to move outside water! As we had no say in what was served, we also ate paca meat in this restaurant, the agouti paca being a local rodent. Unfortunately because bush meat should not be served to tourists for fear of reducing the animal populations.

Visited several remains of former penal colonies, the whole country being a French penal colony at a not-so-distant-time, from the era when Louisiana was sold to the U.S. to the abolition in 1938, only implemented in 1953… Appalling to think that political and criminal prisoners were sent there to slowly rot to death, with no economical purpose on top of it! To the point of dead prisoners being immersed at sea rather than buried on island gallows, the local cemetery being reserved to guardians and their families….

priors without likelihoods are like sloths without…

“The idea of building priors that generate reasonable data may seem like an unusual idea…”

Andrew, Dan, and Michael arXived a opinion piece last week entitled “The prior can generally only be understood in the context of the likelihood”. Which connects to the earlier Read Paper of Gelman and Hennig I discussed last year. I cannot state strong disagreement with the positions taken in this piece, actually, in that I do not think prior distributions ever occur as a given but are rather chosen as a reference measure to probabilise the parameter space and eventually prioritise regions over others. If anything I find myself even further on the prior agnosticism gradation.  (Of course, this lack of disagreement applies to the likelihood understood as a function of both the data and the parameter, rather than of the parameter only, conditional on the data. Priors cannot be depending on the data without incurring disastrous consequences!)

“…it contradicts the conceptual principle that the prior distribution should convey only information that is available before the data have been collected.”

The first example is somewhat disappointing in that it revolves as so many Bayesian textbooks (since Laplace!) around the [sex ratio] Binomial probability parameter and concludes at the strong or long-lasting impact of the Uniform prior. I do not see much of a contradiction between the use of a Uniform prior and the collection of prior information, if only because there is not standardised way to transfer prior information into prior construction. And more fundamentally because a parameter rarely makes sense by itself, alone, without a model that relates it to potential data. As for instance in a regression model. More, following my epiphany of last semester, about the relativity of the prior, I see no damage in the prior being relevant, as I only attach a relative meaning to statements based on the posterior. Rather than trying to limit the impact of a prior, we should rather build assessment tools to measure this impact, for instance by prior predictive simulations. And this is where I come to quite agree with the authors.

“…non-identifiabilities, and near nonidentifiabilites, of complex models can lead to unexpected amounts of weight being given to certain aspects of the prior.”

Another rather straightforward remark is that non-identifiable models see the impact of a prior remain as the sample size grows. And I still see no issue with this fact in a relative approach. When the authors mention (p.7) that purely mathematical priors perform more poorly than weakly informative priors it is hard to see what they mean by this “performance”.

“…judge a prior by examining the data generating processes it favors and disfavors.”

Besides those points, I completely agree with them about the fundamental relevance of the prior as a generative process, only when the likelihood becomes available. And simulatable. (This point is found in many references, including our response to the American Statistician paper Hidden dangers of specifying noninformative priors, with Kaniav Kamary. With the same illustration on a logistic regression.) I also agree to their criticism of the marginal likelihood and Bayes factors as being so strongly impacted by the choice of a prior, if treated as absolute quantities. I also if more reluctantly and somewhat heretically see a point in using the posterior predictive for assessing whether a prior is relevant for the data at hand. At least at a conceptual level. I am however less certain about how to handle improper priors based on their recommendations. In conclusion, it would be great to see one [or more] of the authors at O-Bayes 2017 in Austin as I am sure it would stem nice discussions there! (And by the way I have no prior idea on how to conclude the comparison in the title!)