the most important statistical ideas of the past 50 years

Aki and Andrew are celebrating the New Year in advance by composing a list of the most important statistics ideas occurring (roughly) since they were born (or since Fisher died)! Like

• substitution of computing for mathematical analysis (incl. bootstrap)
• fitting a model with a large number of parameters, using some regularization procedure to get stable estimates and good predictions (e.g., Gaussian processes, neural networks, generative adversarial networks, variational autoencoders)
• multilevel or hierarchical modelling (incl. Bayesian inference)
• advances in statistical algorithms for efficient computing (with a long list of innovations since 1970, including ABC!), pointing out that a large fraction was of the  divide & conquer flavour (in connection with large—if not necessarily Big—data)
• statistical decision analysis (e.g., Bayesian optimization and reinforcement learning, getting beyond classical experimental design )
• robustness (under partial specification, misspecification or in the M-open world)
• EDA à la Tukey and statistical graphics (and R!)
• causal inference (via counterfactuals)

Now, had I been painfully arm-bent into coming up with such a list, it would have certainly been shorter, for lack of opinion about some of these directions (even the Biometrika deputeditoship has certainly helped in reassessing the popularity of different branches!), and I would have have presumably been biased towards Bayes as well as more mathematical flavours. Hence objecting to the witty comment that “theoretical statistics is the theory of applied statistics”(p.10) and including Ghosal and van der Vaart (2017) as a major reference. Also bemoaning the lack of long-term structure and theoretical support of a branch of the machine-learning literature.

Maybe also more space and analysis could have been spent on “debates remain regarding appropriate use and interpretation of statistical methods” (p.11) in that a major difficulty with the latest in data science is not so much the method(s) as the data on which they are based, which in a large fraction of the cases, is not representative and is poorly if at all corrected for this bias. The “replication crisis” is thus only one (tiny) aspect of the challenge.

postdoc in Bayesian machine learning in Berlin [reposted]

The working group of Statistics at Humboldt University of Berlin invites applications for one Postdoctoral research fellow (full-time employment, 3 years with extension possible) to contribute to the research on mathematical and statistical aspects of (Bayesian) learning approaches. The research positions are associated with the Emmy Noether group Regression Models beyond the Mean – A Bayesian Approach to Machine Learning and working group of Applied Statistics at the School of Business and Economics at Humboldt-Universität Berlin. Opportunities for own scientific qualification (PhD)/career development are provided, see an overview and further links. The positions are to be filled at the earliest possible date and funded by the German Research Foundation (DFG) within the Emmy Noether programme.

Requirements:
– an outstanding PhD in Statistics, Mathematics, or related field with specialisation in Statistics, Data Science or Mathematics;
– a strong background in at least one of the following fields: mathematical statistics, computational methods, Bayesian statistics, statistical learning, advanced regression modelling;
– a thorough mathematical understanding.
– substantial experience in scientific programming with Matlab, Python, C/C++, R or similar;
– strong interest in developing novel statistical methodology and its applications in various fields such as economics or natural and life sciences;
– a very good communication skills and team experience, proficiency of the written and spoken English language (German is not obligatory).

Opportunities:
We offer the unique environment of young researchers and leading international experts in the fields. The vibrant international network includes established collaborations in Singapore and Australia. The positions offer potential to closely work with several applied sciences. Information about the research profile of the research group and further contact details can be found here. The positions are paid according to the Civil Service rates of the German States “TV-L”, E13 (if suitably qualified).

Applications should include:
– a CV with list of publications
– a motivational statement (at most one page) explaining the applicant’s interest in the announced position as well as their relevant skills and experience
– copies of degrees/university transcripts
– names and email addresses of at least two professors that may provide letters of recommendation directly to the hiring committee Applications should be sent as a single PDF file to: Prof. Dr. Nadja Klein (nadja.klein[at]hu-berlin.de), whom you may also contact for questions concerning this job post. Please indicate “Research Position Emmy Noether”.

Application deadline: 31st of January 2020

HU is seeking to increase the proportion of women in research and teaching, and specifically encourages qualified female scholars to apply. Severely disabled applicants with equivalent qualifications will be given preferential consideration. People with an immigration background are specifically encouraged to apply. Since we will not return your documents, please submit copies in the application only.

SADA’16

Big Bayes stories in print [and in force]

The 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 Kerrie L. Mengersen and Christian P. Robert; 1
• Estimating the Distribution of Dietary Consumption Patterns Raymond J. Carroll; 2-8
• Estimation of HIV Burden through Bayesian Evidence Synthesis Daniela De Angelis, Anne M. Presanis, Stefano Conti and A. E. Ades; 9-17
• Bayesian Estimation of Population-Level Trends in Measures of Health Status Mariel M. Finucane, Christopher J. Paciorek, Goodarz Danaei and Majid Ezzati; 18-25
• How Bayesian Analysis Cracked the Red-State, Blue-State Problem Andrew Gelman; 26-35
• From Science to Management: Using Bayesian Networks to Learn about Lyngbya  Sandra Johnson, Eva Abal, Kathleen Ahern and Grant Hamilton; 36-41
• Experiences in Bayesian Inference in Baltic Salmon Management Sakari Kuikka, Jarno Vanhatalo, Henni Pulkkinen, Samu Mäntyniemi and Jukka Corander; 42-49
• Finding the Most Distant Quasars Using Bayesian Selection Methods Daniel Mortlock; 50-57
• Bayesian Population Projections for the United Nations Adrian E. Raftery, Leontine Alkema and Patrick Gerland; 58-68
• Search for the Wreckage of Air France Flight AF 447 Lawrence D. Stone, Colleen M. Keller, Thomas M. Kratzke and Johan P. Strumpfer; 69-80
• Galaxy Formation: Bayesian History Matching for the Observable Universe Ian Vernon, Michael Goldstein and Richard Bower; 81-90
• Discussion of Big Bayes Stories and BayesBag Peter Bühlmann; 91-94
• Discussion of “Estimating the Distribution of Dietary Consumption Patterns” Stephen E. Fienberg and Rebecca C. Steorts; 95-96
• Contribution M. A. Girolami; 97
• Wonderful Examples, but Let’s not Close Our Eyes David J. Hand; 98-100
• Discussion A. H. Welsh; 101-102
• Reply to the Discussion of “Estimating the Distribution of Dietary Consumption Patterns” Raymond J. Carroll; 103
• Response to Discussion by A. H. Welsh on the AF 447 Paper Lawrence D. Stone; 104-105

Principles of Applied Statistics

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.