a third way of probability?

Because the title intrigued me (who would dream of claiming connection with Tony Blair’s “new” Labour move to centre-right?!) , I downloaded William Briggs‘ paper the Third Way of Probability & Statistics from arXiv and read it while secluded away, with no connection to the outside world, at Longmire, Mount Rainier National Park. Early morning at Paradise Inn. The subtitle of the document is “Beyond Testing and Estimation To Importance, Relevance, and Skill“. Actually, Longmire may have been the only place where I would read through the entire paper and its 14 pages, as the document somewhat sounds like a practical (?) joke. And almost made me wonder whether Mr Briggs was a pseudonym… And where the filter behind arXiv publishing principles was that day.

The notion behind Briggs’ third way is that parameters do not exist and that only conditional probability exists. Not exactly a novel perspective then. The first five pages go on repeating this principle in various ways, without ever embarking into the implementation of the idea, at best referring to a future book in search of a friendly publisher… The remainder of the paper proceeds to analyse a college GPA dataset without ever explaining how the predictive distribution was constructed. The only discussion is about devising a tool to compare predictors, which is chosen as the continuous rank probability score of Gneiting and Raftery (2007). Looking at those scores seems to encompass this third way advocated by the author, then, which sounds to me to be an awfully short lane into statistics. With no foray whatsoever into probability.

forest fires

Wildfires rage through the US West, with currently 33 going in the Pacific Northwest, 29 in Northern California, and 18 in the northern Rockies, with more surface burned so far this year than in any of the past ten years. Drought, hot weather, high lightning frequency, and a shortage of firefighters across the US all are contributing factors…Washington State is particularly stricken and when we drove to the North Cascades from Mt. Rainier, we came across at least two fires, one near Twisp and the other one around Chelan… The visibility was quite poor, due to the amount of smoke, and, while the road was open, we saw many burned areas with residual fumaroles and even a minor bush fire that was apparently let to die out by itself. The numerous orchards around had been spared, presumably thanks to their irrigation system.The owner of a small café and fruit stand on Highway 20 told us about her employee, who had taken the day off to protect her home, near Chelane, that had already burned down last year. Among 300 or so houses. Later on our drive north, the air cleared up, but we saw many instances of past fires, like the one below near Hart’s Pass, which occurred in 2003 and has not yet reached regeneration. Wildfires have always been a reality in this area, witness the first US smokejumpers being based (in 1939) at Winthrop, in the Methow valley, but this does not make it less of an objective danger. (Which made me somewhat worried as we were staying in a remote wooden area with no Internet or phone coverage to hear about evacuation orders. And a single evacuation route through a forest…)Even when crossing the fabulous North Cascades Highway to the West and Seattle-Tacoma airport, we saw further smoke clouds, like this one near Goodall, after Lake Ross, with closed side roads and campgrounds.And, when flying back on Wednesday, along the Canadian border, more fire fronts and smoke clouds were visible from the plane. Little did we know then that the town of Winthrop, near which we stayed, was being evacuated at the time, that the North Cascades Highway was about to be closed, and that three firefighters had died in nearby Twisp… Kudos to all firefighters involved in those wildfires! (And close call for us as we would still be “stuck” there!)

a glimpse of Mt. Rainier

JSM 2015 [day #3]

My first morning session was about inference for philogenies. While I was expecting some developments around Kingman’s  coalescent models my coauthors needed and developped ABC for, I was surprised to see models that were producing closed form (or close enough to) likelihoods. Due to strong restrictions on the population sizes and migration possibilities, as explained later to me by Vladimir Minin. No need for ABC there since MCMC was working on the species trees, with Vladimir Minin making use of [the Savage Award winner] Vinayak Rao’s approach on trees that differ from the coalescent. And enough structure to even consider and demonstrate tree identifiability in Laura Kubatko’s case.

I then stopped by the astrostatistics session as the first talk by Gwendolin Eddie was about galaxy mass estimation, a problem I may actually be working on in the Fall, but it ended up being a completely different problem and I was further surprised that the issue of whether or not the data was missing at random was not considered by the authors.

Christening a session Unifying foundation(s) may be calling for trouble, at least from me! In this spirit, Xiao Li Meng gave a talk attempting at a sort of unification of the frequentist, Bayesian, and fiducial paradigms by introducing the notion of personalized inference, which is a notion I had vaguely thought of in the past. How much or how far do you condition upon? However, I have never thought of this justifying fiducial inference in any way and Xiao Li’s lively arguments during and after the session not enough to convince me of the opposite: Prior-free does not translate into (arbitrary) choice-free. In the earlier talk about confidence distributions by Regina Liu and Minge Xie, that I partly missed for Galactic reasons, I just entered into the room at the very time when ABC was briefly described as a confidence distribution because it was not producing a convergent approximation to the exact posterior, a logic that escapes me (unless those confidence distributions are described in such a loose way as to include about any method f inference). Dongchu Sun also gave us a crash course on reference priors, with a notion of random posteriors I had not heard of before… As well as constructive posteriors… (They seemed to mean constructible matching priors as far as I understood.)

The final talk in this session by Chuanhei Liu on a new approach (modestly!) called inferential model was incomprehensible, with the speaker repeatedly stating that the principles were too hard to explain in five minutes and needed an incoming book… I later took a brief look at an associated paper, which relates to fiducial inference and to Dempster’s belief functions. For me, it has the same Münchhausen feeling of creating a probability out of nothing, creating a distribution on the parameter by ignoring the fact that the fiducial equation x=a(θ,u) modifies the distribution of u once x is observed.