beyond subjective and objective in Statistics

Posted in Books, Statistics, University life with tags , , , , , , , , , , , , , on August 28, 2015 by xi'an

“At the level of discourse, we would like to move beyond a subjective vs. objective shouting match.” (p.30)

This paper by Andrew Gelman and Christian Henning 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.

“…scientists and the general public celebrate the brilliance and inspiration of greats such as Einstein, Darwin, and the like, recognizing the roles of their personalities and individual experiences in shaping their theories and discoveries” (p.2)

I do not see the relevance of this argument, in that the myriad of factors leading, say, Marie Curie or Rosalind Franklin to their discoveries are more than subjective, as eminently personal and the result of unique circumstance, but the corresponding theories remain within a common and therefore objective corpus of scientific theories. Hence I would not equate the derivation of statistical estimators or even less the computation of statistical estimates to the extension or negation of existing scientific theories by scientists.

“We acknowledge that the “real world” is only accessible to human beings through observation, and that scientific observation and measurement cannot be independent of human preconceptions and theories.” (p.4)

The above quote reminds me very much of Poincaré‘s

“It is often said that experiments should be made without preconceived ideas. That is impossible. Not only would it make every experiment fruitless, but even if we wished to do so, it could not be done. Every man has his own conception of the world, and this he cannot so easily lay aside.” Henri Poincaré, La Science et l’Hypothèse

The central proposal of the paper is to replace `objective’ and `subjective’ with less value-loaded and more descriptive terms. Given that very few categories of statisticians take pride in their subjectivity, apart from a majority of Bayesians, but rather use the term as derogatory for other categories, I fear the proposal stands little chance to see this situation resolved. Even though I agree we should move beyond this distinction that does not reflect the complexity and richness of statistical practice. As the discussion in Section 2 makes it clear, all procedures involve subjective choices and calibration (or tuning), either plainly acknowledged or hidden under the carpet. Which is why I would add (at least) two points to the virtues of subjectivity:

  1. Spelling out unverifiable assumptions about the data production;
  2. Awareness of calibration of tuning parameters.

while I do not see consensus as necessarily a virtue. The following examples in Section 3 are all worth considering as they bring more details, albeit in specific contexts, to the authors’ arguments. Most of them give the impression that the major issue stands with the statistical model itself, which may be both the most acute subjectivity entry in statistical analyses and the least discussed one. Including the current paper, where e.g. Section 3.4 wants us to believe that running a classical significance test is objective and apt to detect an unfit model. And the hasty dismissal of machine learning in Section 6 is disappointing, because one thing machine learning does well is to avoid leaning too much on the model, using predictive performances instead. Furthermore, apart from Section 5.3, I actually see little in the paper about the trial-and-error way of building a statistical model and/or analysis, while subjective inputs from the operator are found at all stages of this construction and should be spelled out rather than ignored (and rejected).

“Yes, Bayesian analysis can be expressed in terms of subjective beliefs, but it can also be applied to other settings that have nothing to do with beliefs.” (p.31)

The survey in Section 4 about what philosophy of sciences says about objectivity and subjectivity is quite thorough, as far as I can judge, but does not expand enough the issue of “default” or all-inclusive statistical solutions, used through “point-and-shoot” software by innumerate practitioners in mostly inappropriate settings, with the impression of conducting “the” statistical analysis. This false feeling of “the” proper statistical analysis and its relevance for this debate also transpire through the treatment of statistical expertises by media and courts. I also think we could avoid the Heisenberg principle to be mentioned in this debate, as it does not really contribute anything useful. More globally, the exposition of a large range of notions of objectivity is as often the case in philosophy not conclusive and I feel nothing substantial comes out of it… And that it is somehow antagonistic with the notion of a discussion paper, since every possible path has already been explored. Even forking ones. As a non-expert in philosophy, I would not feel confident in embarking upon a discussion on what realism is and is not.

“the subjectivist Bayesian point of view (…) can be defended for honestly acknowledging that prior information often does not come in ways that allow a unique formalization” (p.25)

When going through the examination of the objectivity of the major streams of statistical analysis, I get the feeling of exploring small worlds (in Lindley‘s words) rather than the entire spectrum of statistical methodologies. For instance, frequentism seems to be reduced to asymptotics, while completely missing the entire (lost?) continent of non-parametrics. (Which should not be considered to be “more” objective, but has the advantage of loosening the model specification.) While the error-statistical (frequentist) proposal of Mayo (1996) seems to consume a significant portion [longer than the one associated with the objectivist Bayesianism section] of the discussion with respect to its quite limited diffusion within statistical circles. From a Bayesian perspective, the discussions of subjective, objective, and falsificationist Bayes do not really bring a fresh perspective to the debate between those three branches, apart from suggesting we should give up such value loaded categorisations. As an O-Bayes card-carrying member, I find the characterisation of the objectivist branch somehow restrictive, by focussing solely on Jaynesmaxent solution. Hence missing the corpus of work on creating priors with guaranteed frequentist or asymptotic properties. Like matching priors. I also find the defence of the falsificationist perspective, i.e. of Gelman and Shalizi (2013) both much less critical and quite extensive, in that, again, this is not what one could call a standard approach to statistics. Resulting in an implicit (?) message that this may the best way to proceed.

In conclusion, on the positive side [for there is a positive side!], the paper exposes the need to spell out the various inputs (from the operator) leading to a statistical analysis, both for replicability or reproducibility, and for “objectivity” purposes, although solely conscious choices and biases can be uncovered this way. It also reinforces the call for model awareness, by which I mean a critical stance on all modelling inputs, including priors!, a disbelief that any model is true, applying to statistical procedures Popper’s critical rationalism. This has major consequences on Bayesian modelling in that, as advocated in Gelman and Shalizi (2013) , as well as Evans (2015), sampling and prior models should be given the opportunity to be updated when they are inappropriate for the data at hand. On the negative side, I fear the proposal is far too idealistic in that most users (and some makers) of statistics cannot spell out their assumptions and choices, being unaware of those. This is in a way [admitedly, with gross exaggeration!] the central difficulty with statistics that almost anyone anywhere can produce an estimate or a p-value without ever being proven wrong. It is therefore difficult to perceive how the epistemological argument therein [that objective versus subjective is a meaningless opposition] is going to profit statistical methodology, even assuming the list of Section 2.3 was to be made compulsory. The eight deadly sins listed in the final section would require expert reviewers to vanish from publication (and by expert, I mean expert in statistical methodology), while it is almost never the case that journals outside our field make a call to statistics experts when refereeing a paper. Apart from banning all statistics arguments from a journal, I am afraid there is no hope for a major improvement in that corner…

All in all, the authors deserve a big thank for making me reflect upon those issues and (esp.) back their recommendation for reproducibility, meaning not only the production of all conscious choices made in the construction process, but also through the posting of (true or pseudo-) data and of relevant code for all publications involving a statistical analysis.

abcfr 0.9-3

Posted in R, Statistics, University life with tags , , , , , , , , on August 27, 2015 by xi'an

garden tree, Jan. 12, 2012In 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!

abcrfThe 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)

forest fires

Posted in Mountains, pictures, Travel with tags , , , , , , , , , , , , , , on August 26, 2015 by xi'an

fire1Wildfires 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…fire2Washington 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.fire3The 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…)fire5Even 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.fire4And, 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!)fire6

Blue Lake

Posted in Mountains, pictures, Running, Travel with tags , , , , on August 25, 2015 by xi'an

blu

consistency of ABC

Posted in pictures, Statistics, Travel, University life with tags , , , , , , , , , on August 25, 2015 by xi'an

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.

ABC à… Montréal

Posted in pictures, Statistics, Travel, University life with tags , , , , , , , , , on August 24, 2015 by xi'an

Montreal1Like 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…)

congrats!

Posted in Statistics, University life with tags , , , , , , , on August 24, 2015 by xi'an

Two items of news that reached my mailbox at about the same time: my friends and CMU coauthors Rebecca (Beka) Steorts and Steve Fienberg both received a major award in the past few days. Congrats to both of them!!! At JSM 2015, Steve got the 2015 Jerome Sacks Award for Cross-Disciplinary Research “for a remarkable career devoted to the development and application of statistical methodology to solve problems for the benefit of society, including aspects of human rights, privacy and confidentiality, forensics, survey and census-taking, and more; and for exceptional leadership in a variety of professional and governmental organizations, including in the founding of NISS.” The Award is delivered by the National Institute of Statistical Sciences (NISS) in honour of Jerry Sacks. And Beka has been selected as one of the 35 innovators under 35 for 2015, a list published yearly by the MIT Technology Review. In particular for her record-linkage work on estimating the number of casualties in the Syrian civil war. (Which led the Review to classify her as a humanitarian rather than a visionary, which list includes two other machine learners.) Great!

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