A fundamental problem in Bayesian nonparametrics consists of selecting a prior distribution by assuming that the corresponding predictive probabilities obey certain properties. An early discussion of such a problem, although in a parametric framework, dates back to the seminal work by English philosopher W. E. Johnson, who introduced a noteworthy characterization for the predictive probabilities of the symmetric Dirichlet prior distribution. This is typically referred to as Johnson’s “sufficientness” postulate. In this paper, we review some nonparametric generalizations of Johnson’s postulate for a class of nonparametric priors known as species sampling models. In particular, we revisit and discuss the “sufficientness” postulate for the two parameter Poisson–Dirichlet prior within the more general framework of Gibbs-type priors and their hierarchical generalizations.

Although both Fisher’s and Neyman’s tests are for testing “no treatment effects,” they both test fundamentally different null hypotheses. While Neyman’s null concerns the average casual effect, Fisher’s null focuses on the individual causal effect. When conducting a test, researchers need to understand what is really being tested and what underlying assumptions are being made. If these fundamental issues are not fully appreciated, dubious conclusions regarding causal effects can be made.

Weighting is one of the central steps in surveys. The typical weighting process involves three major stages. At the first stage, each unit is assigned a base weight, which is defined as the inverse of its inclusion probability. The base weights are then modified to account for unit nonresponse. At the last stage, the nonresponse-adjusted weights are further modified to ensure consistency between survey estimates and known population totals. When needed, the weights undergo a last modification through weight trimming or weight smoothing methods in order to improve the efficiency of survey estimates. This article provides an overview of the various stages involved in the typical weighting process used by national statistical offices.

<i>INTRODUCTION</i>: The point of departure for our paper is that most modern statistical models are built to be flexible enough to model diverse data generating mechanisms. Good statistical practice requires us to limit this flexibility, which is typically controlled by a small number of parameters, to the amount “needed” to model the data at hand. The Bayesian framework provides a natural method for doing this although, as DD points out, this trend for penalising model complexity casts a broad shadow over all of modern statistics and data science.The PC prior framework argues for setting priors on these flexibility parameters that are specifically built to penalise a certain type of complexity and avoid overfitting. The discussants raised various points about this core idea. First, DD pointed out that while over-fitting a model is a bad thing, under-fitting is not better: we do not want Occam’s razor to slit our throat. We saw this behaviour when using a half-Normal prior on the distance, while the exponential prior does not lead to obvious attenuation of the estimates. This is confirmed experimentally by Klein and Kneib (2016).

Abstract. Whenever a new approach to perform Bayesian computation is introduced, a common practice is to showcase this approach on a binary regression model and datasets of moderate size. This paper discusses to which extent this practice is sound. It also reviews the current state of the art of Bayesian computation, using binary regression as a running example. Both sampling-based algorithms (importance sampling, MCMC and SMC) and fast approximations (Laplace and EP) are covered. Extensive numerical results are provided, some of which might go against conventional wisdom regarding the effectiveness of certain algorithms. Implications for other problems (variable selection) and other models are also discussed.

Decisions based partly or solely on predictions from probabilistic models may be sensitive to model misspecification. Statisticians are taught from an early stage that "all models are wrong", but little formal guidance exists on how to assess the impact of model approximation on decision making, or how to proceed when optimal actions appear sensitive to model fidelity. This article presents an overview of recent developments across different disciplines to address this. We review diagnostic techniques, including graphical approaches and summary statistics, to help highlight decisions made through minimised expected loss that are sensitive to model misspecification. We then consider formal methods for decision making under model misspecification by quantifying stability of optimal actions to perturbations to the model within a neighbourhood of model space. This neighbourhood is defined in either one of two ways. Firstly, in a strong sense via an information (Kullback-Leibler) divergence around the approximating model. Or using a nonparametric model extension, again centred at the approximating model, in order to `average out' over possible misspecifications. This is presented in the context of recent work in the robust control, macroeconomics and financial mathematics literature. We adopt a Bayesian approach throughout although the methods are agnostic to this position.

espanolExact tests, fuzzy p-values, Gibbs sampling, iterval censoring, linear extensions, linear rank statistics, perfect MCMC, proportional hazard model, topological sorting EnglishWe discuss distribution-free exact rank tests from partially ordered data that arise in various biological and other applications where the primary objective is to conduct testing of significance to assess the linear dependence or to compare different groups. The tests here are obtained by treating the usual rank statistics, based on the completely ordered data as “latent” or missing, and conceptualizing the “latent” p-value as the random probability under the null hypothesis of a test statistic that is as extreme, or more extreme, than the latent test statistics based on the completely ordered data. The latent p-value is then predicted by sampling linear extensions or the complete orderings that are consistent with the observed partially ordered data. The sampling methods explored here include importance sampling methods based on randomized topological sorting algorithms, Gibbs sampling methods, random-walk based Metropolis–Hasting sampling methods and random-walk based modern perfect Markov chain Monte Carlo sampling methods. We discuss running times of these sampling methods and their strength and weaknesses. A simulation experiment and three data examples are given. The simulation experiment illustrates how the exact rank tests from partially ordered data work when the desired result is known. The first data example concerns the light preference behavior of fruit flies and tests whether heterogeneity observed in average light-preference behavior can be explained by manipulations in serotonin signaling. The second one is a reanalysis of the lead absorption data in children of employees who worked in a lead battery factory and consolidates the results reported in Rosenbaum [Ann. Statist. 19 (1991) 1091–1097]. The third one reexamines the breast cosmesis data from Finkelstein [Biometrics 42 (1986) 845–854].

State-based Cormack–Jolly–Seber (CJS) models have become an often used method for assessing states or conditions of free-ranging animals through time. Although originally envisioned to account for differences in survival and observation processes when animals are moving though various geographical strata, the model has evolved to model vital rates in different life-history or diseased states. We further extend this useful class of models to the case of multivariate state data. Researchers can record values of several different states of interest, for example, geographic location and reproductive state. Traditionally, these would be aggregated into one state with a single probability of state uncertainty. However, by modeling states as a multivariate vector, one can account for partial knowledge of the vector as well as dependence between the state variables in a parsimonious way. A hidden Markov model (HMM) formulation allows straightforward maximum likelihood inference. The proposed HMM models are demonstrated with a case study using data from a California sea lion vital rates study.

Peter Gavin Hall was born in Sydney, Australia, on 20th November, 1951, and grew up in the Sydney suburb of Oatley. He received a Bachelor of Science with first class honours from the University of Sydney in 1974, a Master of Science from the Australian National University in 1976 and a Doctor of Philosophy from the University of Oxford in 1976. In 1976– 1978, he was Lecturer in Statistics at the University of Melbourne. During 1978–2006, he served as Lecturer, Senior Lecturer, Reader and Professor of Statistics at the Australian National University. He became Professor of Statistics at the University of Melbourne in 2006, Australian Laureate Fellow in 2012 and was Director of the Australian Research Council Centre of Excellence for Mathematical and Statistical Frontiers in 2014–2015. In 2005, he commenced a one-quarter professorial position at the University of California, Davis. Peter has published 4 books and more than 600 research articles. He has made seminal contributions concerning the bootstrap, rates of convergence, functional data analysis, martingale theory, measurement error models, nonparametric function estimation and smoothing parameter selection. Honours include the following: Officer of the Order of Australia; Fellow of the Australian Academy of Science, Fellow of the Academy of the Social Sciences in Australia, Fellow of the Royal Society of London, Fellow of the Institute of Mathematical Statistics and Fellow of the American Statistical Association; Corresponding Fellow of the Royal Society of Edinburgh, and Foreign Associate of the U.S. National Academy of Sciences; honorary doctorates from the Universite catholique de Louvain, the Universidad de Cantabria, the University of Glasgow and the University of Sydney; the Committee of Presidents of Statistical Societies Award and the Guy Medal in Silver from the Royal Statistical Society. He married Jeannie Jean Chien Lo on 15th April, 1977. His mother, Ruby Payne-Scott, had a distinguished scientific career as the first woman in radio astronomy and her story is published as Under the Radar. The First Woman in Radio Astronomy: Ruby Payne-Scott (2009) Springer. In 2015, Peter was diagnosed with acute leukaemia. He passed away on 9 January, 2016, in Melbourne, Australia. This conversation took place in Melbourne, Australia, on 11 March and 1 April, 2015.

Ewens’s sampling formula exemplifies the harmony of mathematical theory, statistical application, and scientific discovery. The formula not only contributes to the foundations of evolutionary molecular genetics, the neutral theory of biodiversity, Bayesian nonparametrics, combinatorial stochastic processes, and inductive inference but also emerges from fundamental concepts in probability theory, algebra, and number theory. With an emphasis on its far-reaching influence throughout statistics and probability, we highlight these and many other consequences of Ewens’s seminal discovery.