Dual systems estimation is a capture–recapture approach to population estimation restricted to two captures of the population. When applied to human populations, the population captures may be existing incomplete listings of the population, as provided by census and administrative datasets. In contrast to much capture-recapture analysis, dual systems applications in official statistics are usually concerned with estimating the distribution of a human population, over combinations of covariates, such as age, sex, ethnic group and small geographic area, rather than focussing primarily on the total population count. We synthesise theory and methods for Bayesian dual systems estimation for this problem, which we refer to as small domain population estimation. We primarily work within a model framework that combines a general model for the covariate distribution, such as an unrestricted multinomial in the case of categorical covariates, with hierarchical logistic models for the probability of inclusion on the lists. We explore the issue of dependence between the two lists which leads to a well-known identifiability problem. We illustrate the use of informative priors for the degree of dependence expressed as an odds ratio, or for certain aggregate level population totals. Although progress can be made using informative priors, the underlying identifiability problem means that inferences are sensitive to prior choices. We relate our approach to the popular log-linear modelling approach to capture-recapture analysis and note that the latter is primarily a re-parameterisation of our model set-up, though with a specific implied prior for the total population in the case of Poisson log-linear models.

The mixture cure model in survival analysis has received large and growing attention in the last few decades. Restricting ourselves mainly to the one-sample case, we present here an overview drawing together some recent significant advances and earlier results, and pointing out areas where further work is needed. New results presented include a discussion of testing for the presence of long term survivors in the null case (when there are no cures present), the probability that an individual is cured (when cures are present), and further analysis of the idea of sufficient followup. Extreme value methods play a key role. We draw attention to some challenging open problems.

The maximum likelihood estimator (MLE) for the unknown parameter vector in logistic regression is well known to be biased. There are many different approaches to reduce this bias including bias correction, adjustment of the score function or of the data itself, jackknifing, penalizing the likelihood, exact logistic regression, and the discriminant function approach. These approaches, as well as many different simulation studies comparing them, are reviewed here. Since the studies use very different parameter settings and sometimes contradict each other, no general recommendations can be given. However, most studies find that the bias of the MLE is substantial for small to medium samples, that the bias-corrected estimators tend to overcorrect in very small samples, and that Firth’s estimator, when considered, is the best choice.

Quantifying the similarity between datasets has widespread applications in statistics and machine learning. The performance of a predictive model on novel datasets, referred to as generalizability, depends on how similar the training and evaluation datasets are. Exploiting or transferring insights between similar datasets is a key aspect of meta-learning and transfer-learning. In simulation studies, the similarity between distributions of simulated datasets and real datasets, for which the performance of methods is assessed, is crucial. In two- or k-sample testing, it is checked, whether the underlying distributions of two or more datasets coincide.

Extremely many approaches for quantifying dataset similarity have been proposed in the literature. We examine more than 100 methods and provide a taxonomy, classifying them into ten classes. In an extensive review of these methods the main underlying ideas, formal definitions, and important properties are introduced.

We compare the 118 methods in terms of their applicability, interpretability, and theoretical properties, in order to provide recommendations for selecting an appropriate dataset similarity measure based on the specific goal of the dataset comparison and on the properties of the datasets at hand. An online tool facilitates the choice of the appropriate dataset similarity measure.

This review article focuses on regularised estimation procedures applicable to geostatistical and spatial econometric models and suitable cross-validation techniques for spatiotemporal data. These methods are particularly relevant in the case of big geospatial data for dimension reduction or model selection. To structure the review, we initially consider the most general case of multivariate spatiotemporal processes (i.e., $g>1$ dimensions of the spatial domain, a one-dimensional temporal domain, and $q\ge 1$ random variables). Then, the idea of regularised/penalised estimation procedures and different choices of shrinkage targets are discussed. Guided by the elements of a mixed-effects model setup, which allows for a variety of spatiotemporal models, we show different regularisation procedures and how they can be used for the analysis of geo-referenced data, e.g. for selection of relevant regressors, dimension reduction of the covariance matrices, detection of conditionally independent locations, or the estimation of a full spatial interaction matrix. The second part is dedicated to cross-validation strategies, which are important for evaluating the model performance and selecting regularisation parameters. We outline the three key assumptions a cross-validation partitioning needs to fulfil and discuss how this can be achieved for time series, spatial data and spatiotemporal data. Additionally, software implementations for these techniques are discussed.