## simulating Nature

Posted in Books, Statistics with tags , , , , , , , , , , , , , , , on July 25, 2012 by xi'an

This book, Simulating Nature: A Philosophical Study of Computer-Simulation Uncertainties and Their Role in Climate Science and Policy Advice, by Arthur C. Petersen, was sent to me twice by the publisher for reviewing it for CHANCE. As I could not find a nearby “victim” to review the book, I took it with me to Australia and read it by bits and pieces along the trip.

“Models are never perfectly reliable, and we are always faced with ontic uncertainty and epistemic uncertainty, including epistemic uncertainty about ontic uncertainty.” (page 53)

The author, Arthur C. Petersen, was a member of the United Nations’ Intergovernmental Panel on Climate Change (IPCC) and works as chief scientist at the PBL Netherlands Environmental Assessment Agency. He mentions that the first edition of this book, Simulating Nature, has achieved some kind of cult status, while being now out of print,  which is why he wrote this second edition. The book centres on the notion of uncertainty connected with computer simulations in the first part (pages 1-94) and on the same analysis applied to the simulation of climate change, based on the experience of the author, in the second part (pages 95-178). I must warn the reader that, as the second part got too focussed and acronym-filled for my own taste, I did not read it in depth, even though the issues of climate change and of the human role in this change are definitely of interest to me. (Readers of CHANCE must also realise that there is very little connection with Statistics in this book or my review of it!) Note that the final chapter is actually more of a neat summary of the book than a true conclusion, so a reader eager to get an idea about the contents of the book can grasp them through the eight pages of the eighth chapter.

“An example of the latter situation is a zero-dimensional (sic) model that aggregates all surface temperatures into a single zero-dimensional (re-sic) variable of globally averaged surface temperature.” (page 41)

The philosophical questions of interest therein are that a computer simulation of reality is not reproducing reality and that the uncertainty(ies) pertaining to this simulation cannot be assessed in its (their) entirety. (This the inherent meaning of the first quote, epistemic uncertainty relating to our lack of knowledge about the genuine model reproducing Nature or reality…) The author also covers the more practical issue of the interface between scientific reporting and policy making, which reminded me of Christl Donnelly’s talk at the ASC 2012 meeting (about cattle epidemics in England). The book naturally does not bring answers to any of those questions, naturally because a philosophical perspective should consider different sides of the problem, but I find it more interested in typologies and classifications (of types of uncertainties, in crossing those uncertainties with panel attitudes, &tc.) than in the fundamentals of simulation. I am obviously incompetent in the matter, however, as a naïve bystander, it does not seem to me that the book makes any significant progress towards setting epistemological and philosophical foundations for simulation. The part connected with the author’s implication in the IPCC shed more light on the difficulties to operate in committees and panels made of members with heavy political agendas than on the possible assessments of uncertainties within the models adopted by climate scientists…With the same provision as above, the philosophical aspects do not seem very deep: the (obligatory?!) reference to Karl Popper does not bring much to the debate, because what is falsification to simulation? Similarly, Lakatos’ prohibition of “direct[ing] the modus tollens at [the] hard core” (page 40) does not turn into a methodological assessment of simulation praxis.

“I argue that the application of statistical methods is not sufficient for adequately dealing with uncertainty.” (page 18)

“I agree (…) that the theory behind the concepts of random and systematic errors is purely statistical and not related to the locations and other dimensions of uncertainty.” (page 55)

Statistics is mostly absent from the book, apart from the remark that statistical uncertainty (understood as the imprecision induced by a finite amount of data) differs from modelling errors (the model is not reality), which the author considers cannot be handled by statistics (stating that Deborah Mayo‘s theory of statistical error analysis cannot be extended to simulation, see the footnote on page 55). [In other words, this book has no connection with Monte Carlo Statistical Methods! With or without capitals... Except for a mention of real' random number generators on—one of many—footnotes on page 35.]  Mention is made of “subjective probabilities” (page 54), presumably meaning a Bayesian perspective. But the distinction between statistical uncertainty and scenario uncertainty which “cannot be adequately described in terms of chances or probabilities” (page 54) misses the Bayesian perspective altogether, as does the following sentence that “specifying a degree of probability or belief [in such uncertainties] is meaningless since the mechanism that leads to the events are not sufficiently known” (page 54).

“Scientists can also give their subjective probability for a claim, representing their estimated chance that the claim is true. Provided that they indicate that their estimate for the probability is subjective, they are then explicitly allowing for the possibility that their probabilistic claim is dependent on expert judgement and may actually turn out to be false.” (page 57)

In conclusion, I fear the book does not bring enough of a conclusion on the philosophical justifications of using a simulation model instead of the actual reality and on the more pragmatic aspects of validating/invalidating a computer model and of correcting its imperfections with regards to data/reality. I am quite conscious that this is an immensely delicate issue and that, were it to be entirely solved, the current level of fight between climate scientists and climatoskeptics would not persist. As illustrated by the “Sound Science debate” (pages 68-70), politicians and policy-makers are very poorly equipped to deal with uncertainty and even less with decision under uncertainty. I however do not buy the (fuzzy and newspeak) concept of “post-normal science” developed in the last part of Chapter 4, where the scientific analysis of a phenomenon is abandoned for decision-making, “not pretend[ing] to be either value-free or ethically neutral” (page 75).

## David Hume as pre-Bayesian

Posted in Books, Statistics, University life with tags , , , , , on January 11, 2012 by xi'an

Probability is of two kinds: either when the object is itself uncertain, and to be determined by chance: or, when though the object is already certain, yet it is uncertain to our judgment, which finds a number of proofs or presumptions on each side of the question.” A Treatise of Human Nature, by David Hume, 1739.

Jean-Louis Foulley pointed out to me this great citation from the Scottish philosopher David Hume,  more than twenty years prior to Thomas Bayes… Actually, there is an interesting historical question as to whether (and then how) Hume and Bayes could have interacted. (When Bayes studied in Edinburgh in the 1720′s, Hume was less than 12…)

## Error and Inference [on wrong models]

Posted in Books, Statistics, University life with tags , , , , , , on December 6, 2011 by xi'an

In connection with my series of posts on the book Error and Inference, and my recent collation of those into an arXiv document, Deborah Mayo has started a series of informal seminars at the LSE on the philosophy of errors in statistics and the likelihood principle. and has also posted a long comment on my argument about only using wrong models. (The title is inspired from the Rolling Stones’ “You can’t always get what you want“, very cool!) The discussion about the need or not to take into account all possible models (which is the meaning of the “catchall hypothesis” I had missed while reading the book) shows my point was not clear. I obviously do not claim in the review that all possible models should be accounted for at once, this was on the opposite my understanding of Mayo’s criticism of the Bayesian approach (I thought the following sentence was clear enough: “According to Mayo, this alternative hypothesis should “include all possible rivals, including those not even though of” (p.37)”)! So I see the Bayesian approach as a way to put on the table a collection of reasonable (if all wrong) models and give to those models a posterior probability, with the purpose that improbable ones are eliminated. Therefore, I am in agreement with most of the comments in the post, esp. because this has little to do with Bayesian versus frequentist testing! Even rejecting the less likely models from a collection seems compatible with a Bayesian approach, model averaging is not always an appropriate solution, depending on the loss function!

## Error and Inference [arXived]

Posted in Books, Statistics, University life with tags , , , , , , , on November 29, 2011 by xi'an

Following my never-ending series of posts on the book Error and Inference, (edited) by Deborah Mayo and Ari Spanos (and kindly sent to me by Deborah), I decided to edit those posts into a (slightly) more coherent document, now posted on arXiv. And to submit it as a book review to Siam Review, even though I had not high expectations it fits the purpose of the journal: the review was rejected between the submission to arXiv and the publication of this post!

## Error and Inference [end]

Posted in Books, Statistics, University life with tags , , , , , , , , , on October 11, 2011 by xi'an

(This is my sixth and last post on Error and Inference, being as previously a raw and naïve reaction born from a linear and sluggish reading of the book, rather than a deeper and more informed criticism with philosophical bearings. Read at your own risk.)

‘It is refreshing to see Cox and Mayo give a hard-nosed statement of what scientific objectivity demands of an account of statistics, show how it relates to frequentist statistics, and contrast that with the notion of “objectivity” used by O-Bayesians.”—A. Spanos, p.326, Error and Inference, 2010

In order to conclude my pedestrian traverse of Error and Inference, I read the discussion by Aris Spanos of the second part of the seventh chapter by David Cox’s and Deborah Mayo’s, discussed in the previous post. (In the train to the half-marathon to be precise, which may have added a sharper edge to the way I read it!) The first point in the discussion is that the above paper is “a harmonious blend of the Fisherian and N-P perspectives to weave a coherent frequentist inductive reasoning anchored firmly on error probabilities”(p.316). The discussion by Spanos is very much a-critical of the paper, so I will not engage into a criticism of the non-criticism, but rather expose some thoughts of mine that came from reading this apology. (Remarks about Bayesian inference are limited to some piques like the above, which only reiterates those found earlier [and later: "the various examples Bayesians employ to make their case involve some kind of "rigging" of the statistical model", Aris Spanos, p.325; "The Bayesian epistemology literature is filled with shadows and illusions", Clark Glymour, p. 335] in the book.) [I must add I do like the mention of O-Bayesians, as I coined the O'Bayes motto for the objective Bayes bi-annual meetings from 2003 onwards! It also reminds me of the O-rings and of the lack of proper statistical decision-making in the Challenger tragedy...]

The “general frequentist principle for inductive reasoning” (p.319) at the core of Cox and Mayo’s paper is obviously the central role of the p-value in “providing (strong) evidence against the null H0 (for a discrepancy from H0)”. Once again, I fail to see it as the epitome of a working principle in that

1. it depends on the choice of a divergence d(z), which reduces the information brought by the data z;
2. it does not articulate the level for labeling nor the consequences of finding a low p-value;
3. it ignores the role of the alternative hypothesis.

Furthermore, Spanos’ discussion deals with “the fallacy of rejection” (pp.319-320) in a rather artificial (if common) way, namely by setting a buffer of discrepancy γ around the null hypothesis. While the choice of a maximal degree of precision sounds natural to me (in the sense that a given sample size should not allow for the discrimination between two arbitrary close values of the parameter), the fact that γ is in fine set by the data (so that the p-value is high) is fairly puzzling. If I understand correctly, the change from a p-value to a discrepancy γ is a fine device to make the “distance” from the null better understood, but it has an extremely limited range of application. If I do not understand correctly, the discrepancy γ is fixed by the statistician and then this sounds like an extreme form of prior selection.

There is at least one issue I do not understand in this part, namely the meaning of the severity evaluation probability

$P(d(Z) > d(z_0);\,\mu> \mu_1)$

as the conditioning on the event seems impossible in a frequentist setting. This leads me to an idle and unrelated questioning as to whether there is a solution to

$\sup_d \mathbb{P}_{H_0}(d(Z) \ge d(z_0))$

as this would be the ultimate discrepancy. Or whether this does not make any sense… because of the ambiguous role of z0, which needs somehow to be integrated out. (Otherwise, d can be chosen so that the probability is 1.)

“If one renounces the likelihood, the stopping rule, and the coherence principles, marginalizes the use of prior information as largely untrustworthy, and seek procedures with good’ error probabilistic properties (whatever that means), what is left to render the inference Bayesian, apart from a belief (misguided in my view) that the only way to provide an evidential account of inference is to attach probabilities to hypotheses?”—A. Spanos, p.326, Error and Inference, 2010

The role of conditioning ancillary statistics is emphasized both in the paper and the discussion. This conditioning clearly reduces variability, however there is no reservation about the arbitrariness of such ancillary statistics. And the fact that conditioning any further would lead to conditioning upon the whole data, i.e. to a Bayesian solution. I also noted a curious lack of proper logical reasoning in the argument that, when

$f(z|\theta) \propto f(z|s) f(s|\theta),$

using the conditional ancillary distribution is enough, since, while “any departure from f(z|s) implies that the overall model is false” (p.322), but not the reverse. Hence, a poor choice of s may fail to detect a departure. (Besides the fact that  fixed-dimension sufficient statistics do not exist outside exponential families.) Similarly, Spanos expands about the case of a minimal sufficient statistic that is independent from a maximal ancillary statistic, but such cases are quite rare and limited to exponential families [in the iid case]. Still in the conditioning category, he also supports Mayo’s argument against the likelihood principle being a consequence of the sufficiency and weak conditionality principles. A point I discussed in a previous post. However, he does not provide further evidence against Birnbaum’s result, arguing rather in favour of a conditional frequentist inference I have nothing to complain about. (I fail to perceive the appeal of the Welch uniform example in terms of the likelihood principle.)

In an overall conclusion, let me repeat and restate that this series of posts about Error and Inference is far from pretending at bringing a Bayesian reply to the philosophical arguments raised in the volume. The primary goal being of “taking some crucial steps towards legitimating the philosophy of frequentist statistics” (p.328), I should not feel overly concerned. It is only when the debate veered towards a comparison with the Bayesian approach [often too often of the "holier than thou" brand] that I felt allowed to put in my twopennies worth… I do hope I may crystallise this set of notes into a more constructed review of the book, if time allows, although I am pessimistic at the chances of getting it published given our current difficulties with the critical review of Murray Aitkin’s  Statistical Inference. However, as a coincidence, we got back last weekend an encouraging reply from Statistics and Risk Modelling, prompting us towards a revision and the prospect of a reply by Murray.