## Archive for applied statistics

## SADA’16

Posted in pictures, Statistics, Travel, University life with tags Africa, applied statistics, Bayesian Analysis, Bénin, big data, biostatistics, conference, Cotonou, data analysis, econometrics, Pau, SADA'16, surveys on April 28, 2016 by xi'an## Big Bayes stories in print [and in force]

Posted in Books, Statistics, University life with tags applied statistics, arXiv, Bayes 250, Bayesian statistics, Kerrie Mengersen, Thomas Bayes on May 20, 2014 by xi'an**T**he special issue of Statistical Science Kerrie Mengersen and I edited over the past three (four?) years is now out in print! Even though many ‘Og readers may have already seen the table of contents, here it is once again. We hope you will enjoy this 100 page long excursion in big Bayesiana. The papers are not freely accessible as “current papers” on the journal website but can yet be found in the “future papers” section. ~~(If a sponsor wants to support turning the papers into open access version, he or she is most welcome to contact us or the IMS!)~~ And, thanks to Larry for reminding me!, available on arXiv. Thanks to all authors, discussants, reviewers and special kudos to Jon Wellner for his constant help and support in putting the special issue together!

- Big Bayes Stories—Foreword
- Bayesian Estimation of Population-Level Trends in Measures of Health Status
- Discussion of “Estimating the Distribution of Dietary Consumption Patterns”
- Contribution M. A. Girolam
- Wonderful Examples, but Let’s not Close Our Eyes
- Discussion
- Reply to the Discussion of “Estimating the Distribution of Dietary Consumption Patterns”
- Response to Discussion by A. H. Welsh on the AF 447 Paper

## 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**T**his 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)

**T**o 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)

**A**s 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 wordBayesian, 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)

**M**y 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”

**T**he 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)

**A**part 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 useddirectlyto simulate data.” (p.104)

**T**he 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.