In this paper, we introduce a new concept for constructing prior distributions. We exploit the natural nested structure inherent to many model components, which defines the model component to be a flexible extension of a base model. Proper priors are defined to penalise the complexity induced by deviating from the simpler base model and are formulated after the input of a user-defined scaling parameter for that model component, both in the univariate and the multivariate case. These priors are invariant to reparameterisations, have a natural connection to Jeffreys’ priors, are designed to support Occam’s razor and seem to have excellent robustness properties, all which are highly desirable and allow us to use this approach to define default prior distributions. Through examples and theoretical results, we demonstrate the appropriateness of this approach and how it can be applied in various situations.

The large-sample properties of likelihood-based statistical inference under mixture models have received much attention from statisticians. Although the consistency of the nonparametric MLE is regarded as a standard conclusion, many researchers ignore the precise conditions required on the mixture model. An incorrect claim of consistency can lead to false conclusions even if the mixture model under investigation seems well behaved. Under a finite normal mixture model, for instance, the consistency of the plain MLE is often erroneously assumed in spite of recent research breakthroughs. This paper streamlines the consistency results for the nonparametric MLE in general, and in particular for the penalized MLE under finite normal mixture models.

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, VB and EP) are covered. Extensive numerical results are provided, and are used to make recommendations to both end users and Bayesian computation experts. Implications for other problems (variable selection) and other models are also discussed.

The Lasso is a computationally efficient regression regularization procedure that can produce sparse estimators when the number of predictors $(p)$ is large. Oracle inequalities provide probability loss bounds for the Lasso estimator at a deterministic choice of the regularization parameter. These bounds tend to zero if $p$ is appropriately controlled, and are thus commonly cited as theoretical justification for the Lasso and its ability to handle high-dimensional settings. Unfortunately, in practice the regularization parameter is not selected to be a deterministic quantity, but is instead chosen using a random, data-dependent procedure. To address this shortcoming of previous theoretical work, we study the loss of the Lasso estimator when tuned optimally for prediction. Assuming orthonormal predictors and a sparse true model, we prove that the probability that the best possible predictive performance of the Lasso deteriorates as $p$ increases is positive and can be arbitrarily close to one given a sufficiently high signal to noise ratio and sufficiently large $p$. We further demonstrate empirically that the amount of deterioration in performance can be far worse than the oracle inequalities suggest and provide a real data example where deterioration is observed.

In public discussions of the quality of forecasts, attention typically focuses on the predictive performance in cases of extreme events. However, the restriction of conventional forecast evaluation methods to subsets of extreme observations has unexpected and undesired effects, and is bound to discredit skillful forecasts when the signal-to-noise ratio in the data generating process is low. Conditioning on outcomes is incompatible with the theoretical assumptions of established forecast evaluation methods, thereby confronting forecasters with what we refer to as the forecaster’s dilemma. For probabilistic forecasts, proper weighted scoring rules have been proposed as decision-theoretically justifiable alternatives for forecast evaluation with an emphasis on extreme events. Using theoretical arguments, simulation experiments and a real data study on probabilistic forecasts of U.S. inflation and gross domestic product (GDP) growth, we illustrate and discuss the forecaster’s dilemma along with potential remedies.

Professor Robert M. Groves is among the world leaders in survey methodology and survey statistics over the last four decades. Groves’ research—particularly on survey nonresponse, survey errors and costs, and responsive design—helped to provide intellectual footing for a new academic discipline. In addition, Groves has had remarkable success building academic programs that integrate the social sciences with statistics and computer science. He was instrumental in the development of degree programs in survey methodology at the University of Michigan and the University of Maryland. Recently, as Provost of Georgetown University, he has championed the use of big data sets to increase understanding of society and human behavior. Between his academic tenures, Groves served as Director of the US Census Bureau. Professor Groves is an elected fellow of the American Statistical Association, elected member of the International Statistical Institute, elected member of the American Academy of Arts and Sciences, elected member of the US National Academy of Sciences, elected member of the Institute of Medicine of the US National Academies and presidential appointed member of the National Science Board. The interview was conducted in early 2016 at Georgetown University.

Lynne Billard was born in Toowomba, Australia. She earned her B.Sc. (Honors I) in 1966, and a Ph.D. degree in 1969, both from the University of New South Wales, Australia. She is perhaps best known for her ground breaking research in the areas of HIV/AIDS and Symbolic Data Analysis. Broadly put, Professor Billard’s research interests include epidemic theory, stochastic processes, sequential analysis, time series analysis and symbolic data. She has written extensively in all these areas and more through numerous fundamental contributions. She has published more than 200 research papers in some of the leading international journals including Australian Journal of Statistics, Biometrika, Journal of American Statistical Association, Journal of Applied Probability, Journal of Royal Statistical Society, Journal of Time Series Analysis, Nature, Sequential Analysis, Statistical Science, Statistics in Medicine and Stochastic Processes and Their Applications, plus book chapters in a number of acclaimed edited volumes.

Professor Billard has (co-)edited or (co-)authored eight prestigious books including her authoritative text (co-authored with E. Diday), Symbolic Data Analysis: Conceptual Statistics and Data Mining (2006) published by Wiley. During the period 1969 through 1980, the career path took her to travel to University of Birmingham (U.K., 1969–1970), State University of New York at Buffalo (1971, 1974–1975), University of Waterloo (Canada, 1971–1974), Stanford University (California, 1974), Florida State University at Tallahassee (1975–1980), Naval Postgraduate School (U.S.A., 1979), University of California (Berkeley, 1979), Imperial College (1986), Isaac Newton Institute, Cambridge (1993), and other prestigious places.

She had joined the Department of Statistics at Florida State University as an Associate Professor in 1975 and during 1976–1978 she served as the Associate Head there. She became a Professor at Florida State in 1980 but went on leave to visit the Department of Computer Science and Statistics at University of Georgia, Athens. She joined the same department in Georgia permanently as Professor of Statistics and Head in 1980. When the Department of Statistics was formed in Georgia under Professor Billard’s leadership, she became its Professor and Head (1984–1989). Since 1992, she has held the most prestigious and coveted position, the University Professor, in the University of Georgia.

She served as an Associate Editor for numerous journals including the Journal of American Statistical Association and Statistical Analysis and Data Mining. All her life, she has served extensively by holding high-level offices as well as memberships of both national and international committees at several scholarly international societies including the American Statistical Association (ASA), the Institute of Mathematical Statistics (IMS), International Biometrics Society (IBS) and Eastern North American Region (ENAR), Bernoulli Society and the International Statistical Institute (ISI). For example, Professor Billard was elected President of ENAR (1985), International Vice President (1993, 1996) and International President (1994, 1995) of IBS and President of ASA (1996).

She has earned many honors and awards, including Fellow of the IMS (1988), Fellow of the ASA (1980), Fellow of the American Association for the Advancement of Science (2001) and elected membership in the ISI (1980). Professor Billard received several prestigious awards including the S. S. Wilks Medal (1999) of the ASA. Its citation read, “For significant contributions to the theory and methodology of statistics and the advancement of scientific knowledge in a variety of fields, especially in the area of HIV/AIDS; for effective leadership on issues of public interest, particularly with respect to the decennial census; for energetic professional service nationally and internationally; and for influential dedication to the statistical education of both statisticians and the public at large.”

She was honored by the Founders Award (2003) from the ASA. She received the Committee of Presidents of Statistical Societies (COPSS) Elizabeth Scott Award (2008) and FN David Award (2013), as well as the Janet L Norwood Award (2011). In 2015, she was installed as an Honorary Member of the Statistical Society of Slovenia.

Professor Billard travels extensively to scientific conferences as an invited participant, works harder than many half her age, and continues to inspire through her writings and uniquely affectionate presence.

The following conversation began August 1, 2011, at the Joint Statistical Meetings held in Miami, Florida.