The idea to generate synthetic data as a tool for broadening access to sensitive microdata has been proposed for the first time three decades ago. While first applications of the idea emerged around the turn of the century, the approach really gained momentum over the last ten years, stimulated at least in parts by some recent developments in computer science. We consider the 30th jubilee of Rubin’s seminal paper on synthetic data (J. Off. Stat. 9 (1993) 462–468) as an opportunity to look back at the historical developments but also to offer a review of the diverse approaches and methodological underpinnings proposed over the years. We will also discuss the various strategies that have been suggested to measure the utility and remaining risk of disclosure of the generated data.

In oncology dose-finding trials, due to staggered enrollment, it might be desirable to make dose-assignment decisions in real time in the presence of pending toxicity outcomes, for example, when the dose-limiting toxicity is late onset. Patients’ time-to-event information may be utilized to facilitate such decisions. We review statistical frameworks for time-to-event modeling in dose-finding trials and summarize existing designs into two classes: TITE designs and POD designs. TITE designs are based on inference about toxicity probabilities, while POD designs are based on probabilities of dose-assignment decisions. These two classes of designs contain existing individual designs as special cases and also give rise to new designs. We discuss and study the theoretical properties of these designs, including large-sample convergence properties, coherence principles and the underlying decision rules. To facilitate the use of these designs in practice, we introduce efficient computational algorithms and review common practical considerations, such as safety rules and suspension rules. Finally, the operating characteristics of several designs are evaluated and compared through computer simulations.

We give a review of some recent ANOVA-like procedures for testing group differences based on data in a metric space and present a new such procedure. Our statistic is derived from the classic Levene’s test for detecting differences in dispersion. It uses only pairwise distances of data points and can be computed quickly and precisely in situations where the computation of barycenters (“generalized means”) in the data space is slow, only by approximation or even infeasible. It also satisfies asymptotic normality.

We discuss the relative merits of the various procedures based on simulation studies for spatial point patterns and image data in a 1-way ANOVA setting. As applications, we perform 1- and 2-way ANOVAs on a data set of bubbles in a mineral flotation process and a data set of local pest counts in Madrid.

Variable selection is an important statistical problem. This problem becomes more challenging when the candidate predictors are of mixed type (e.g., continuous and binary) and impact the response variable in nonlinear and/or nonadditive ways. In this paper, we review existing variable selection approaches for the Bayesian additive regression trees (BART) model, a nonparametric regression model, which is flexible enough to capture the interactions between predictors and nonlinear relationships with the response. An emphasis of this review is on the ability to identify relevant predictors. We also propose two variable importance measures, which can be used in a permutation-based variable selection approach, and a backward variable selection procedure for BART. We introduce these variations as a way of illustrating limitations and opportunities for improving current approaches and assess these via simulations.

Graphical models based on Directed Acyclic Graphs (DAGs) are widely used to answer causal questions across a variety of scientific and social disciplines. However, observational data alone cannot distinguish in general between DAGs representing the same conditional independence assertions (Markov equivalent DAGs); as a consequence, the orientation of some edges in the graph remains indeterminate. Interventional data, produced by exogenous manipulations of variables in the network, enhance the process of structure learning because they allow to distinguish among equivalent DAGs, thus sharpening causal inference. Starting from an equivalence class of DAGs, a few procedures have been devised to produce a collection of variables to be manipulated in order to identify a causal DAG. Yet, these algorithmic approaches do not determine the sample size of the interventional data required to obtain a desired level of statistical accuracy. We tackle this problem from a Bayesian experimental design perspective, taking as input a sequence of target variables to be manipulated to identify edge orientation. We then propose a method to determine, at each intervention, the optimal sample size to produce an experiment which, with high assurance, will deliver an overall probability of decisive and correct evidence.

This paper reviews the most common situations in which the regularity conditions that underlie classical likelihood-based parametric inference fail, focusing on the large-sample properties of the likelihood ratio statistic. We identify three main classes of problems: boundary problems, indeterminate parameter problems—which include nonidentifiable parameters and singular information matrices—and change-point problems. We emphasise analytical solutions, consider software implementations where available, and summarise how the key results are derived.

After Bayes, the oldest Bayesian account of enumerative induction is given by Laplace’s so-called rule of succession: if all n observed instances of a phenomenon to date exhibit a given character, the probability that the next instance of that phenomenon will also exhibit the character is $\frac{\mathit{n}\mathbf{+}1}{\mathit{n}\mathbf{+}2}$. Laplace’s rule however has the apparently counterintuitive mathematical consequence that the corresponding “universal generalization” (every future observation of this type will also exhibit that character) has zero probability. In 1932, the British scientist J. B. S. Haldane proposed an alternative rule giving a universal generalization the positive probability $\frac{\mathit{n}\mathbf{+}1}{\mathit{n}\mathbf{+}2}\times \frac{\mathit{n}\mathbf{+}3}{\mathit{n}\mathbf{+}2}$. A year later, Harold Jeffreys proposed essentially the same rule in the case of a finite population. A related variant rule results in a predictive probability of $\frac{\mathit{n}\mathbf{+}1}{\mathit{n}\mathbf{+}2}\times \frac{\mathit{n}\mathbf{+}4}{\mathit{n}\mathbf{+}3}$. These arguably elegant adjustments of the original Laplacean form have the advantage that they give predictions better aligned with intuition and common sense. In this paper, we discuss J. B. S. Haldane’s rule and its variants, placing them in their historical context, and relating them to subsequent philosophical discussions.

In the context of the binomial distribution, the potential need for a prior point mass on $\mathit{\theta }=0(1)$, given $\mathit{x}=0(\mathit{n})$, was identified more than 100 years ago by Jeffreys. Given previous proposals to implement such a point mass, a slightly different approach is proposed, followed by the corresponding posterior probability of “homogeneity” and posterior predictive distribution.

Guido Wilhelmus Imbens is the Applied Econometrics Professor and Professor of Economics with a joint appointment at the Graduate School of Business and the Department of Economics at Stanford University. He has made fundamental contributions to econometric and statistical methods for drawing causal inferences in experimental and observational studies, and applications to a wide range of disciplines beyond economics, including psychology, education, policy, law, epidemiology, public health and other social and biomedical sciences. Together with his longtime collaborator, Joshua Angrist, Guido was awarded half the 2021 Sveriges Riksbank Prize in Economic Sciences in Memory of Alfred Nobel for their methodological contributions to the analysis of causal relationships, with the other half going to David Card.