Abstract Prognostic risk scores provide individualized risk estimates for an outcome (“event”) based on included covariates. Calibration indicates the extent to which risk estimates are reliable. We review four increasingly stringent definitions of calibration: mean, weak, moderate, and strong calibration. The latter requires that the risk model perfectly corresponds to the observed proportions for every single covariate pattern, and hence can be regarded as impossible to achieve in practice (“utopic”). We present an overview of methods to assess calibration, including goodness‐of‐fit tests, summary measures, and graphical procedures. We show that estimation and visualization of the degree of (mis)calibration is essential, whereas testing is problematic. We illustrate the methods with a case study on the prediction of the histology of retroperitoneal lymph nodes following chemotherapy for testicular cancer.

Abstract Partial order scalogram analysis with base coordinates (POSAC) is a dimensionality reduction technique based on an iterative procedure that projects a set ofm‐dimensional partially ordered elements on a two‐dimensional space, while preserving “as well as possible” their partial ordering relations. POSAC is part of the theory of Partially Ordered Sets and Facet theory, and it is mainly used in evaluation studies seeking a ranking or a prioritization of statistical units using a noncompensatory approach. Being a dimensionality reduction technique, POSAC implies a loss of information that is compensated by an easier interpretation of partial ordering in two rather than inm‐dimensions. This makes POSAC especially useful to discuss policy strategies in front of nontechnical decision‐makers.

Abstract Although the INGARCH models for count time series are said to be an integer‐valued counterpart to the generalized autoregressive conditional heteroskedasticity (GARCH) models, they may also be understood as an adaption of the autoregressive moving‐average (ARMA) models to the count‐data case. The stochastic properties of these models as well as some extensions are discussed. In particular, the INGARCH models that are a type of linear conditional regression model, and also nonlinear regression models have been proposed for count time series.

Abstract Monte Carlo simulation is a numerical method that estimates the means of random variables and multidimensional integrals. This method returns the arithmetic average of function values observed at a finite number,n, of well‐chosen nodes. One may wish to know when a simulation can be stopped while satisfying a user‐specified error criterion. This entry summarizes some algorithms that choosenautomatically.

Abstract The g‐computation formula, where “g” stands for general, is arguably the most fundamental of all the concepts and methods in statistical causal inference, as it responds directly to the question “what would happen if …?.” This directness makes it useful in a wide range of problems and (in conjunction with maximum likelihood estimation) statistically efficient. This article describes the g‐computation formula first in the simple context of estimating the effect of a binary exposure in the presence of measured confounders, before discussing its use in more complex settings, such as longitudinal studies with time‐dependent confounding, the comparison of dynamic regimes, and mediation analysis.

Abstract This article reviews the micro‐randomized trial, an experimental design developed to support mobile intervention development in modern mobile health applications. The article first gives an introduction to mobile health and the motivation for the micro‐randomized trial and then describes the design of micro‐randomized trials, including an overview of the data analysis and an example.

Abstract In this article, we give a brief review of semiparametric theory, using as a running example the common problem of estimating an average causal effect. Semiparametric models allow at least part of the data‐generating process to be unspecified and unrestricted, and can often yield robust estimators that nonetheless behave similarly to those based on parametric likelihood assumptions, for example, fast rates of convergence to normal limiting distributions. We discuss the basics of semiparametric theory, focusing on influence functions.

Abstract This article presents different methodologies used by energy companies to model extreme events, especially natural hazards, a common requirement for these industries with strong social and environmental responsibilities.

Abstract In within‐case designs, individuals are measured repeatedly over time or across multiple experimental conditions. Univariate and multivariate parametric procedures for testing within‐case effects may lose statistical power under departures from a multivariate normal distribution. Nonparametric procedures based on rank scores or bootstrapping are useful alternatives for testing within‐case effects when the data are skewed or have heavy tails. We consider these methods when there are missing observations and for complex designs.

Abstract A partially ordered set is a set endowed with an ordering criterion, which is in general not complete, that is, such that some pairs of elements of the set cannot be ordered or compared. Partially ordered sets are the natural setting for the description and the analysis of multidimensional systems of indicators, particularly, but not exclusively, when they are of an ordinal kind. They can be used in evaluation studies, for the computation of non‐aggregative synthetic indicators, for the definition of rankings, in cluster analysis, and in many other data analysis tasks. As the availability of complex ordinal data sets and multidimensional indicator systems is increasing, partially ordered sets are becoming a key tool for applied statistics, particularly in socio‐economics, environmental and ecological studies, and multicriteria decision‐making. Their use may involve heavy computations, but effective algorithms and software resources exist that make them a very useful tool in many concrete problems.