This paper by Andrew Gelman and Christian Hennig calls for the abandonment of the terms objective and subjective in (not solely Bayesian) statistics. And argue that there is more than mere prior information and data to the construction of a statistical analysis. The paper is articulated as the authors’ proposal, followed by four application examples, then a survey of the philosophy of science perspectives on objectivity and subjectivity in statistics and other sciences, next to a study of the subjective and objective aspects of the mainstream statistical streams, concluding with a discussion on the implementation of the proposed move. Continue reading
In conjunction with our reliable ABC model choice via random forest paper, about to be resubmitted to Bioinformatics, we have contributed an R package called abcrf that produces a most likely model and its posterior probability out of an ABC reference table. In conjunction with the realisation that we could devise an approximation to the (ABC) posterior probability using a secondary random forest. “We” meaning Jean-Michel Marin and Pierre Pudlo, as I only acted as a beta tester!
The package abcrf consists of three functions:
- abcrf, which constructs a random forest from a reference table and returns an object of class `abc-rf’;
- plot.abcrf, which gives both variable importance plot of a model choice abc-rf object and the projection of the reference table on the LDA axes;
- predict.abcrf, which predict the model for new data and evaluate the posterior probability of the MAP.
An illustration from the manual:
data(snp) data(snp.obs) mc.rf <- abcrf(snp[1:1e3, 1], snp[1:1e3, -1]) predict(mc.rf, snp[1:1e3, -1], snp.obs)
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!)
Along with David Frazier and Gael Martin from Monash University, Melbourne, we have just completed (and arXived) a paper on the (Bayesian) consistency of ABC methods, producing sufficient conditions on the summary statistics to ensure consistency of the ABC posterior. Consistency in the sense of the prior concentrating at the true value of the parameter when the sample size and the inverse tolerance (intolerance?!) go to infinity. The conditions are essentially that the summary statistics concentrates around its mean and that this mean identifies the parameter. They are thus weaker conditions than those found earlier consistency results where the authors considered convergence to the genuine posterior distribution (given the summary), as for instance in Biau et al. (2014) or Li and Fearnhead (2015). We do not require here a specific rate of decrease to zero for the tolerance ε. But still they do not hold all the time, as shown for the MA(2) example and its first two autocorrelation summaries, example we started using in the Marin et al. (2011) survey. We further propose a consistency assessment based on the main consistency theorem, namely that the ABC-based estimates of the marginal posterior densities for the parameters should vary little when adding extra components to the summary statistic, densities estimated from simulated data. And that the mean of the resulting summary statistic is indeed one-to-one. This may sound somewhat similar to the stepwise search algorithm of Joyce and Marjoram (2008), but those authors aim at obtaining a vector of summary statistics that is as informative as possible. We also examine the consistency conditions when using an auxiliary model as in indirect inference. For instance, when using an AR(2) auxiliary model for estimating an MA(2) model. And ODEs.
Like last year, NIPS will be hosted in Montréal, Québec, Canada, and like last year there will be an ACB NIPS workshop. With a wide variety of speakers and poster presenters. There will also be a probabilistic integration NIPS workshop, to which I have been invited to give a talk, following my blog on the topic! Workshops are on December 11 and 12, and I hope those two won’t overlap so that I can enjoy both at length (before flying back to London for CFE 2015…)
Update: they do overlap, both being on December 11…