Rao–Blackwellisation is a notion often occurring in the MCMC literature, with possibly different meanings and connections with the original Rao–Blackwell theorem as established by C.R. Rao in 1945 and D. Blackwell in 1947, including a reduction of the variance of the resulting Monte Carlo approximations. This survey reviews some of the meanings of the term.

In this article, the authors provide a glimpse into the legendary career of centenarian Professor C. Radhakrishna Rao, a career that is inextricably linked to the history of modern statistics from Pearson and Fisher to the age of big data and Artificial Intelligence. A scientist of extraordinary vision, his ground-breaking contributions have influenced not only the field of statistics, but the mathematical

Statistical inference is constructed upon a statistical model consisting of a parameterised family of probability distributions, which forms a manifold. It is important to study the geometry of the manifold. It was Professor C. R. Rao who initiated information geometry in his monumental paper published in 1945. It not only included fundamentals of statistical inference such as the Cramér–Rao theorem

Cyber security is an important concern for all individuals, organisations and governments globally. Cyber attacks have become more sophisticated, frequent and dangerous than ever, and traditional anomaly detection methods have been proved to be less effective when dealing with these new classes of cyber threats. In order to address this, both classical and Bayesian models offer a valid and innovative

The paper aims to develop a universally implementable efficient test for testing homogeneity of mean directions of several independent hyper-spherical populations. Conventional tests are valid only under highly concentrated and/or large-size groups. Focusing on the popular Langevin distribution on a d-hyper-sphere, the present work extends the very recent results for the circular case. The hurdle of

In many applications of two-component mixture models such as the popular zero-inflated model for discrete-valued data, it is customary for the data analyst to evaluate the inherent heterogeneity in view of observed data. To this end, the score test, acclaimed for its simplicity, is routinely performed. It has long been recognised that this test may behave erratically under model misspecification, but

Household surveys provide information on both person-level and household-level characteristics. To ensure consistent estimates between both levels, statistical offices often use integrated weights that are equal for all persons within a household and the household itself. However, these integrated weights ignore the individual patterns of the persons, and the heterogeneity within a household is no

In Ficek et al,1 the ‘element of’ (∈) symbol was mistakenly corrected to the ‘epsilon’ (ε) symbol throughout. The online version has been corrected. We apologize for this error.

The scientific rigor and computational methods of causal inference have had great impacts on many disciplines but have only recently begun to take hold in spatial applications. Spatial causal inference poses analytic challenges due to complex correlation structures and interference between the treatment at one location and the outcomes at others. In this paper, we review the current literature on spatial

This article provides an overview of supervised machine learning (ML) with a focus on applications in banking. The supervised ML techniques covered include bagging (random forest), boosting (gradient boosting machine) and neural networks. We begin with an introduction to ML tasks and techniques. This is followed by a description of tree‐based ensemble algorithms, including bagging with random forest

Mixed‐effects models for repeated measures (MMRMs) with an ‘unstructured’ (UN) covariance structure are frequently used in primary analyses for group comparisons of incomplete continuous longitudinal data from drug development trials. However, MMRM‐UN analysis could lead to convergence problems in numerical optimisation, especially in trials with a small sample size or high dropout rate. Although the

No abstract is available for this article.

As sources of data become more plentiful and massive datasets are easier to acquire, new ethical issues arise involving data quality and privacy, and the analysis, interpretation and dissemination of data‐driven decisions. There are numerous anecdotes involving abuses of complex data analyses and algorithms, and the impact they have had on society. In this paper, we discuss what statisticians can do

This erratum corrects the following article: Modern Strategies for Time Series Regression Stephanie Clark, Rob J. Hyndman, Dan Pagendam, Louise M. Ryan International Statistical Review (2020), 88, S1, S179–S204 doi:10.1111/insr.12432 First published online: 3 December 2020 In Clark et al. (2020), errors in the sizing and resolution resulted in a lack of clarity in some of the figures. The figures have

Several different approaches have been proposed for the calculation of sampling errors in consumer price indices (CPIs), but only one is in regular use providing published estimates. The history of the development of sampling error estimation for CPIs is reviewed, and the development in the USA (where most research has taken place) is summarised. The proposed approaches for sampling error estimation

The objective of spatial sampling is to collect subsets of individuals from a population in the two‐dimensional space, in order to estimate some population characteristics. Traditional sampling techniques are accordingly enriched to keep space into account. We consider sequential techniques that use weights for introducing space in the update of population units' inclusion probabilities and propose

This work gives an overview of an innovative class of methods for the analysis of spatial and of functional data observed over complicated two‐dimensional domains. This class is based on regression with regularising terms involving partial differential equations. The associated estimation problems are solved resorting to advanced numerical analysis techniques. The synergical interplay of approaches

In 1929, Fisher proposed a test for periodicity based on the largest periodogram ordinate. If the true frequency lies between two consecutive Fourier frequencies and the signal to noise ratio is low, the test may conclude that there is no periodicity. This loss of power was noted by Whittle in 1952, as well as the necessary assumption that the noise be white. Whittle and subsequent authors suggested

The expectation–maximization (EM) algorithm is a familiar tool for computing the maximum likelihood estimate of the parameters in hidden Markov and semi‐Markov models. This paper carries out a detailed study on the influence that the initial values of the parameters impose on the results produced by the algorithm. We compare random starts and partitional and model‐based strategies for choosing the

The statistical literature is known to be inconsistent in the use of the terms "permutation test" and "randomization test". Several authors succesfully argue that these terms should be used to refer to two distinct classes of tests and that there are major conceptual differences between these classes. The present paper explains an important difference in mathematical reasoning between these classes:

Building on Yu and Kumbier's PCS framework and for randomized experiments, we introduce a novel methodology for Stable Discovery of Interpretable Subgroups via Calibration (StaDISC), with large heterogeneous treatment effects. StaDISC was developed during our re-analysis of the 1999-2000 VIGOR study, an 8076 patient randomized controlled trial (RCT), that compared the risk of adverse events from a

This paper discusses several modern approaches to regression analysis involving time series data where some of the predictor variables are also indexed by time. We discuss classical statistical approaches as well as methods that have been proposed recently in the machine learning literature. The approaches are compared and contrasted, and it will be seen that there are advantages and disadvantages

The statistical challenges in using big data for making valid statistical inference in the finite population have been well documented in literature. These challenges are due primarily to statistical bias arising from under-coverage in the big data source to represent the population of interest and measurement errors in the variables available in the data set. By stratifying the population into a big

Analysing data from large‐scale, multiexperiment studies requires scientists to both analyse each experiment and to assess the results as a whole. In this article, we develop double empirical Bayes testing (DEBT), an empirical Bayes method for analysing multiexperiment studies when many covariates are gathered per experiment. DEBT is a two‐stage method: in the first stage, it reports which experiments

Sparse generalised additive models (GAMs) are an extension of sparse generalised linear models that allow a model's prediction to vary non‐linearly with an input variable. This enables the data analyst build more accurate models, especially when the linearity assumption is known to be a poor approximation of reality. Motivated by reluctant interaction modelling, we propose a multi‐stage algorithm,

No abstract is available for this article.

We show that the family of asymmetric distributions studied in a recent publication in the International Statistical Review is equivalent to the family of two‐piece distributions. Moreover, we show that the location‐scale asymmetric family proposed in that publication is non‐identifiable (overparameterised), and it coincides with the family of two‐piece distributions after removing the redundant parameters

Rubio (2020) points out an identification problem for the four‐parameter family of two‐piece asymmetric densities introduced by Nassiri & Loris (2013). This implies that statistical inference for that family is problematic. Establishing probabilistic properties for this four‐parameter family however still makes sense. For the three‐parameter family, there is no identification problem. The main contribution

We review some recent work on removing hidden confounding and causal regularization from a unified viewpoint. We describe how simple and user-friendly techniques improve stability, replicability and distributional robustness in heterogeneous data. In this sense, we provide additional thoughts to the issue on concept drift, raised by Efron (2020), when the data generating distribution is changing.

Rank‐based inference methods are applied in various disciplines, typically when procedures relying on standard normal theory are not justifiable. Various specific rank‐based methods have been developed for two and more samples and also for general factorial designs (e.g. Kruskal–Wallis test or Akritas–Arnold–Brunner test). It is the aim of the present paper (1) to demonstrate that traditional rank

Multivariate count data arise naturally in practice. In analysing such data, it is critical to define a model that can accurately capture the underlying dependence structure between the counts. To this end, this paper develops a multivariate model wherein correlated Poisson margins are generated by a comonotonic shock vector. The proposed model allows for greater flexibility in the dependence structure

Paul Embrechts was born in Schoten, Belgium, on 3 February 1953. He holds a Licentiaat in Mathematics from Universiteit Antwerpen (1975) and a DSc from Katholieke Universiteit Leuven (1979), where he was also a Research Assistant from 1975 to 1983. He then held a lectureship in Statistics at Imperial College, London (1983–1985) and was a Docent at Limburgs Universitair Centrum, Belgium (1985–1989)

In Bayesian inference, predictive distributions are typically in the form of samples generated via Markov chain Monte Carlo (MCMC) or related algorithms. In this paper, we conduct a systematic analysis of how to make and evaluate probabilistic forecasts from such simulation output. Based on proper scoring rules, we develop a notion of consistency that allows to assess the adequacy of methods for estimating

Usually, in spatial generalised linear models, covariates that are spatially smooth are collinear with spatial random effects. This affects the bias and precision of the regression coefficients. This is known in the spatial statistics literature as spatial confounding. We discuss the problem of confounding in the case of multilevel spatial models wherein there are multiple observations within clusters

Using social media data for statistical analysis of general population faces commonly two basic obstacles: firstly, social media data are collected for different objects than the population units of interest; secondly, the relevant measures are typically not available directly but need to be extracted by algorithms or machine learning techniques. In this paper we examine and summarise two existing

The concepts of isotropy/anisotropy and separability/non‐separability of a covariance function are strictly related. If a covariance function is separable, it cannot be isotropic or geometrically anisotropic, except for the Gaussian covariance function, which is the only model both separable and isotropic. In this paper, some interesting results concerning the Gaussian covariance model and its properties

One way of evaluating the quality of a simulation study methodology is to estimate the Monte Carlo Error (MCE). The formula for this calculation was incorrectly implemented in Nagaraja & Nagaraja (2020). The correct formula that replaces equation (24) on page 96 of the original paper is as follows. Borrowing the notation from Koehler et al. (2009), let φ ^ r be an indicator of confidence interval r

In the 2ndparagraph of Merikoski (2020), the equal symbol in (1 = k= n– 1) should be corrected to ≤. The correct equation should be as follows: ( 1 ≤ k ≤ n − 1 )

No abstract is available for this article.

Summary A variety of demographic statistical models exist for studying population dynamics when individuals can be tracked over time. In cases where data are missing due to imperfect detection of individuals, the associated measurement error can be accommodated under certain study designs (e.g. those that involve multiple surveys or replication). However, the interaction of the measurement error and

Summary Multi‐compartment models have been playing a central role in modelling infectious disease dynamics since the early 20th century. They are a class of mathematical models widely used for describing the mechanism of an evolving epidemic. Integrated with certain sampling schemes, such mechanistic models can be applied to analyse public health surveillance data, such as assessing the effectiveness

As the coronavirus disease 2019 outbreak evolves, statistical network analysis is playing an essential role in informing policy decisions Therefore, researchers who are new to such studies need to understand the techniques available to them As a field, statistical network analysis aims to develop methods that account for the complex dependencies found in network data Over the last few decades, the

Differential privacy is a framework for data analysis that provides rigorous privacy protections for database participants. It has increasingly been accepted as the gold standard for privacy in the analytics industry, yet there are few techniques suitable for statistical inference in the health sciences. This is notably the case for regression, one of the most widely used modelling tools in clinical

Summary Small area estimation (SAE) entails estimating characteristics of interest for domains, often geographical areas, in which there may be few or no samples available SAE has a long history and a wide variety of methods have been suggested, from a bewildering range of philosophical standpoints We describe design-based and model-based approaches and models that are specified at the area level and

In the last two decades, several methods for estimating Value at Risk have been proposed in the literature. Four of the most successful approaches are conditional autoregressive Value at Risk, extreme value theory, filtered historical simulation and time‐varying higher order conditional moments. In this paper, we compare their performances under both an empirical investigation using 80 assets and a

Appropriate modelling of Likert‐type items should account for the scale level and the specific role of the neutral middle category, which is present in most Likert‐type items that are in common use. Powerful hierarchical models that account for both aspects are proposed. To avoid biased estimates, the models separate the neutral category when modelling the effects of explanatory variables on the outcome

Adrian Smith joined The Alan Turing Institute as Institute Director and Chief Executive in September 2018. In May 2020, he was confirmed as President Elect of the Royal Society. He is also a member of the government's AI Council, which helps boost AI growth in the UK and promote its adoption and ethical use in businesses and organisations across the country. Professor Smith's previous role was Vice-Chancellor

I thoroughly enjoyed reading the article by Bhadra et. al. (2020) and convey my congratulations to the authors for providing a comprehensive and coherent review of horseshoe‐based regularization approaches for machine learning models. I am thankful to the editors for providing this opportunity to write a discussion on this useful article, which I expect will turn out to be a good guide in the future

During the last years, graphical models have become a popular tool to represent dependencies among variables in many scientific areas. Typically, the objective is to discover dependence relationships that can be represented through a directed acyclic graph (DAG). The set of all conditional independencies encoded by a DAG determines its Markov property. In general, DAGs encoding the same conditional

Social and economic studies are often implemented as complex survey designs. For example, multistage, unequal probability sampling designs utilised by federal statistical agencies are typically constructed to maximise the efficiency of the target domain level estimator (e.g. indexed by geographic area) within cost constraints for survey administration. Such designs may induce dependence between the

A brief historical introduction to nine women who were trailblazers in the statistical sciences is presented. During their times, men dominated the profession. Yet we see how these women in their various ways blazed trails and as such became mentors and inspirations for generations of women practitioners who worked with them and followed in their footsteps.

In this paper, we modify small area estimators, based on the unit‐level model, so that they add up to reliable higher‐level estimates of population totals. These modifications result in benchmarked small area estimators. We consider two benchmarking procedures. One is based on augmenting the unit‐level model with a suitable variable. The other one uses the calibrated weights of the direct estimators

Justifying ridge regression from a geometrical perspective is one of the main contributions of this paper. To the best of our knowledge, this question has not been treated previously. This paper shows that ridge regression is a particular case of raising procedures that provide greater flexibility by transforming the matrix X associated with the model. Thus, raising procedures, based on a geometrical

There has been considerable and controversial research over the past two decades into how successfully random effects misspecification in mixed models (i.e. assuming normality for the random effects when the true distribution is non‐normal) can be diagnosed and what its impacts are on estimation and inference. However, much of this research has focused on fixed effects inference in generalised linear

Readership: Graduate students and researchers interested in random matrices. Chapters: 1. Circulants, 2. Symmetric and reverse circulant, 3. LSD: normal approximation, 4. LSD: dependent input, 5. Spectral radius: light tail, 6. Spectral radius: k‐circulant, 7. Maximum of scaled eigenvalues: dependent input, 8. Poisson convergence, 9. Heavy‐tailed input: LSD, 10. Heavy‐tailed input: spectral radius

Readership: Researchers and practitioners in the area of quality control. I have been involved in the field of quality and reliability engineering for more than 40 years. I have taught courses at both undergraduate and graduate levels, taught many short courses for a wide range of industries, conducted research, authored and coauthored books and papers in this field and was a consultant for many companies

Readership: Teachers and students of a first course in probability. Chapters: 1. The Concept of Probability, 2. Finite Sample Spaces – Combinatorial Methods, 3. Conditional Probability – Independent Events, 4. Discrete Random Variables and Distributions, 5. Some Important Discrete Distributions, 6. Continuous Random Variables, 7. Some Important Continuous Distributions. Appendices: A. Sums and Products

Causal Inference in Statistics: A Primer Judea Pearl, Madelyn Glymour and Nicholas P. Jewell John Wiley & Sons, 2019, 156 pages, $46.75, paperback ISBN: 978‐1‐1191‐8684‐7 Readership: Graduate students and researchers interested in causal inference. This book, initially originating from course notes, covers the basics of causal inference in statistics. Often classical statistical methods fail to uncover

Readership: Statistics/machine learning graduate students and researchers. This is an excellent book. It provides a lucid, accessible and in‐depth treatment of non‐asymptotic high‐dimensional statistical theory, which is critical as the underpinning of modern statistics and machine learning. It succeeds brilliantly in providing a self‐contained overview of high‐dimensional statistics, suitable for

Readership: Graduate students, practitioners and researchers interested in calculus, matrices, optimisation problems, statistical models and/or their applications. The book has become the standard reference on matrix differential calculus since first published in 1988. This is the third edition of the book, with seven parts devoted to the theory and application of matrix differential calculus. Matrix