It was supported by IXXI, Rhône Alpes Complex Systems Institute, a light structure that favors interdisciplinary research to model complex sytems such as biological or social systems, technological networks… This was an opportunity to recycle my Budapest overview from Bayes 250th to Bayes 2.5.0. (As I have changed my email signature initial from X to IX, I further enjoyed the name IXXI!) More seriously, I appreciated (despite the too short time spent there!) the mix of perspectives and disciplines represented in this introduction, from Bayesian networks and causality in computer science and medical expert systems, to neurosciences and the Bayesian theory of mind, to Bayesian population genetics. And hence the mix of audiences. The part about neurosciences and social representations on others’ mind reminded me of the discussion with Pierre Bessières we had a year ago on France Culture. Again, I am quite sorry and apologetic for having missed part of the day and opportunities for discussions, simply because of a tight schedule this week…
Archive for causality
Bayesian introductions at IXXI
Posted in Mountains, Statistics, Travel, University life with tags ABC, Bayesian statistics, causality, Grenoble, history of statistics, neurosciences, population genetics on October 28, 2013 by xi'an10 Little’s simple ideas
Posted in Books, Statistics, University life with tags ASA, causality, Fisher lecture, IMS, JSM, mathematical statistics, missing values, Roderick Little, Ronald Fisher on July 17, 2013 by xi'an“I still feel that too much of academic statistics values complex mathematics over elegant simplicity — it is necessary for a research paper to be complicated in order to be published.” Roderick Little, JASA, p.359
Roderick Little wrote his Fisher lecture, recently published in JASA, around ten simple ideas for statistics. Its title is “In praise of simplicity not mathematistry! Ten simple powerful ideas for the statistical scientist”. While this title is rather antagonistic, blaming mathematical statistics for the rise of mathematistry in the field (a term borrowed from Fisher, who also invented the adjective ‘Bayesian’), the paper focus on those 10 ideas and very little on why there is (would be) too much mathematics in statistics:
- Make outcomes univariate
- Bayes rule, for inference under an assumed model
- Calibrated Bayes, to keep inference honest
- Embrace well-designed simulation experiments
- Distinguish the model/estimand, the principles of estimation, and computational methods
- Parsimony — seek a good simple model, not the “right” model
- Model the Inclusion/Assignment and try to make it ignorable
- Consider dropping parts of the likelihood to reduce the modeling part
- Potential outcomes and principal stratification for causal inferenc
- Statistics is basically a missing data problem
“The mathematics of problems with infinite parameters is interesting, but with finite sample sizes, I would rather have a parametric model. “Mathematistry” may eschew parametric models because the asymptotic theory is too simple, but they often work well in practice.” Roderick Little, JASA, p.365
Both those rules and the illustrations that abund in the paper are reflecting upon Little’s research focus and obviously apply to his model in a fairly coherent way. However, while a mostly parametric model user myself, I fear the rejection of non-parametric techniques is far too radical. It is more and more my convinction that we cannot handle the full complexity of a realistic structure in a standard Bayesian manner and that we have to give up on the coherence and completeness goals at some point… Using non-parametrics and/or machine learning on some bits and pieces then makes sense, even though it hurts elegance and simplicity.
“However, fully Bayes inference requires detailed probability modeling, which is often a daunting task. It seems worth sacrifycing some Bayesian inferential purity if the task can be simplified.” Roderick Little, JASA, p.366
I will not discuss those ideas in detail, as some of them make complete sense to me (like Bayesian statistics laying its assumptions in the open) and others remain obscure (e.g., causality) or with limited applicability. It is overall a commendable Fisher lecture that focus on methodology and the practice of statistical science, rather than on theory. I however do not see the reason why maths should be blamed for this state of the field. Nor why mathematical statistics journals like AoS would carry some responsibility in the lack of further applicability in other fields. Students of statistics do need a strong background in mathematics and I fear we are losing ground in this respect, at least judging by the growing difficulty in finding measure theory courses abroad for our exchange undergradutes from Paris-Dauphine. (I also find the model misspecification aspects mostly missing from this list.)
epidemiology in Le Monde
Posted in Books, Statistics, University life with tags Académie de Médecine, causality, epidemiology, impact factor, INSERM, John Maynard Keynes, Le Monde, R.A. Fisher, Science, Statistics on February 19, 2012 by xi'anQuite an interesting weekend Le Monde issue: a fourth (2 pages!) of the science folder is devoted to epidemiology… In the statistical sense. (The subtitle is actually Strengths and limitations of Statistics.) The paper does not delve into technical statistical issues but points out the logical divergence between a case-by-case study and an epidemiological study. The impression that the higher the conditioning (i.e. the more covariates), the better the explanation is a statistical fallacy some of the opponents interviewed in the paper do not grasp. (Which reminded me of Keynes seemingly going the same way.) The short paragraph written on causality and Hill’s criteria is vague enough to concur to the overall remark that causality can never been proved or disproved… The fourth examples illustrating the strengths and limitations are tobacco vs. lung cancer, a clear case except for R.A. Fisher!, mobile phones vs. brain tumors, a not yet conclusive setting, hepatitis B vaccine vs. sclerosis, lacking data (the pre-2006 records were destroyed for legal reasons), and leukemia vs. nuclear plants, with a significant [?!] correlation between the number of cases and the distance to a nuclear plant. (The paper was inspired by a report recently published by the French Académie de Médecine on epidemiology in France.) The science folder also includes a review of a recent Science paper by Wilhite and Fong on the coercive strategies used by some journals/editors to increase their impact factor, e.g., “you cite Leukemia [once in 42 references]. Consequently, we kindly ask you to add references of articles published in Leukemia to your present article”.
Principles of Applied Statistics
Posted in Books, Statistics, University life with tags applied statistics, capture-recapture, causality, Christl Donnelly, data analysis, David Cox, design, foundations, frogs, lizards, Principles of Applied Statistics, Statistics on February 13, 2012 by xi'an
This book by David Cox and Christl Donnelly, Principles of Applied Statistics, is an extensive coverage of all the necessary steps and precautions one must go through when contemplating applied (i.e. real!) statistics. As the authors write in the very first sentence of the book, “applied statistics is more than data analysis” (p.i); the title could indeed have been “Principled Data Analysis”! Indeed, Principles of Applied Statistics reminded me of how much we (at least I) take “the model” and “the data” for granted when doing statistical analyses, by going through all the pre-data and post-data steps that lead to the “idealized” (p.188) data analysis. The contents of the book are intentionally simple, with hardly any mathematical aspect, but with a clinical attention to exhaustivity and clarity. For instance, even though I would have enjoyed more stress on probabilistic models as the basis for statistical inference, they only appear in the fourth chapter (out of ten) with error in variable models. The painstakingly careful coverage of the myriad of tiny but essential steps involved in a statistical analysis and the highlight of the numerous corresponding pitfalls was certainly illuminating to me. Just as the book refrains from mathematical digressions (“our emphasis is on the subject-matter, not on the statistical techniques as such p.12), it falls short from engaging into detail and complex data stories. Instead, it uses little grey boxes to convey the pertinent aspects of a given data analysis, referring to a paper for the full story. (I acknowledge this may be frustrating at times, as one would like to read more…) The book reads very nicely and smoothly, and I must acknowledge I read most of it in trains, métros, and planes over the past week. (This remark is not intended as a criticism against a lack of depth or interest, by all means [and medians]!)
“A general principle, sounding superficial but difficult to implement, is that analyses should be as simple as possible, but not simpler.” (p.9)
To get into more details, Principles of Applied Statistics covers the (most!) purposes of statistical analyses (Chap. 1), design with some special emphasis (Chap. 2-3), which is not surprising given the record of the authors (and “not a moribund art form”, p.51), measurement (Chap. 4), including the special case of latent variables and their role in model formulation, preliminary analysis (Chap. 5) by which the authors mean data screening and graphical pre-analysis, [at last!] models (Chap. 6-7), separated in model formulation [debating the nature of probability] and model choice, the later being somehow separated from the standard meaning of the term (done in §8.4.5 and §8.4.6), formal [mathematical] inference (Chap. 8), covering in particular testing and multiple testing, interpretation (Chap. 9), i.e. post-processing, and a final epilogue (Chap. 10). The readership of the book is rather broad, from practitioners to students, although both categories do require a good dose of maturity, to teachers, to scientists designing experiments with a statistical mind. It may be deemed too philosophical by some, too allusive by others, but I think it constitutes a magnificent testimony to the depth and to the spectrum of our field.
“Of course, all choices are to some extent provisional.“(p.130)
As a personal aside, I appreciated the illustration through capture-recapture models (p.36) with a remark of the impact of toe-clipping on frogs, as it reminded me of a similar way of marking lizards when my (then) student Jérôme Dupuis was working on a corresponding capture-recapture dataset in the 90’s. On the opposite, while John Snow‘s story [of using maps to explain the cause of cholera] is alluring, and his map makes for a great cover, I am less convinced it is particularly relevant within this book.
“The word Bayesian, however, became more widely used, sometimes representing a regression to the older usage of flat prior distributions supposedly representing initial ignorance, sometimes meaning models in which the parameters of interest are regarded as random variables and occasionaly meaning little more than that the laws of probability are somewhere invoked.” (p.144)
My main quibble with the book goes, most unsurprisingly!, with the processing of Bayesian analysis found in Principles of Applied Statistics (pp.143-144). Indeed, on the one hand, the method is mostly criticised over those two pages. On the other hand, it is the only method presented with this level of details, including historical background, which seems a bit superfluous for a treatise on applied statistics. The drawbacks mentioned are (p.144)
- the weight of prior information or modelling as “evidence”;
- the impact of “indifference or ignorance or reference priors”;
- whether or not empirical Bayes modelling has been used to construct the prior;
- whether or not the Bayesian approach is anything more than a “computationally convenient way of obtaining confidence intervals”
The empirical Bayes perspective is the original one found in Robbins (1956) and seems to find grace in the authors’ eyes (“the most satisfactory formulation”, p.156). Contrary to MCMC methods, “a black box in that typically it is unclear which features of the data are driving the conclusions” (p.149)…
“If an issue can be addressed nonparametrically then it will often be better to tackle it parametrically; however, if it cannot be resolved nonparametrically then it is usually dangerous to resolve it parametrically.” (p.96)
Apart from a more philosophical paragraph on the distinction between machine learning and statistical analysis in the final chapter, with the drawback of using neural nets and such as black-box methods (p.185), there is relatively little coverage of non-parametric models, the choice of “parametric formulations” (p.96) being openly chosen. I can somehow understand this perspective for simpler settings, namely that nonparametric models offer little explanation of the production of the data. However, in more complex models, nonparametric components often are a convenient way to evacuate burdensome nuisance parameters…. Again, technical aspects are not the focus of Principles of Applied Statistics so this also explains why it does not dwell intently on nonparametric models.
“A test of meaningfulness of a possible model for a data-generating process is whether it can be used directly to simulate data.” (p.104)
The above remark is quite interesting, especially when accounting for David Cox’ current appreciation of ABC techniques. The impossibility to generate from a posited model as some found in econometrics precludes using ABC, but this does not necessarily mean the model should be excluded as unrealistic…
“The overriding general principle is that there should be a seamless flow between statistical and subject-matter considerations.” (p.188)
As mentioned earlier, the last chapter brings a philosophical conclusion on what is (applied) statistics. It is stresses the need for a careful and principled use of black-box methods so that they preserve a general framework and lead to explicit interpretations.
Anathem
Posted in Books, University life with tags Anathem, book review, causality, Cryptonomicon, cyberpunk literature, DAG, monastic orders, Nature, Neal Stephenson, quantum mechanics, Snow Crash, The Baroque Cycle on November 20, 2010 by xi'an
One colleague of mine in Dauphine gave me Anathem to read a few weeks ago. I had seen it in a bookstore once and planned to read it, so this was a perfect opportunity. I read through it slowly at first and then with more and more eagerness as the story built on, spending a fair chunk of the past evenings (and Metro rides) into finishing it. Anathem is a wonderful book, especially for mathematicians, and while it could still qualify as a science-fiction book, it blurs the frontiers between the genres of science-fiction, speculative fiction, documentary writings and epistemology… Just imagine any other sci’fi’ book being reviewed in Nature! Still, the book was awarded the 2009 Locus SF Award. So it has true sci’fi’ characteristics, including Clarke-ian bouts of space opera with a Rama-like vessel popping out of nowhere. But this is not the main feature that makes Anathem so unique and fascinating.
“The Adrakhonic theorem, which stated that the square of a right triangle hypotenuse was equal to the sum of the squares of the other two sides…” (p. 128)
