Multiple Systems Estimation has been used as an approach to quantify hard-to-reach or hidden populations and to inform public policy. Motivated by the application to human trafficking and to modern slavery, we review a particular methodological advancement in the frequentist regime, that makes it possible to account for model selection when finding confidence intervals for estimates.

Multiple systems estimation using a Poisson loglinear model is a standard approach to quantifying hidden populations where data sources are based on lists of known cases. Information criteria are often used for selecting between the large number of possible models. Confidence intervals are often reported conditional on the model selected, providing an over-optimistic impression of estimation accuracy. A bootstrap approach is a natural way to account for the model selection. However, because the model selection step has to be carried out for every bootstrap replication, there may be a high or even prohibitive computational burden. We explore the merit of modifying the model selection procedure in the bootstrap to look only among a subset of models, chosen on the basis of their information criterion score on the original data. This provides large computational gains with little apparent effect on inference. We also incorporate rigorous and economical ways of approaching issues of the existence of estimators when applying the method to sparse data tables.

Multiple systems estimation strategies have recently been applied to quantify hard-to-reach populations, particularly when estimating the number of victims of human trafficking and modern slavery. In such contexts, it is not uncommon to see sparse or even no overlap between some of the lists on which the estimates are based. These create difficulties in model fitting and selection, and we develop inference procedures to address these challenges. The approach is based on Poisson log-linear regression modeling. Issues investigated in detail include taking proper account of data sparsity in the estimation procedure, as well as the existence and identifiability of maximum likelihood estimates. A stepwise method for choosing the most suitable parameters is developed, together with a bootstrap approach to finding confidence intervals for the total population size. We apply the strategy to two empirical data sets of trafficking in US regions, and find that the approach results in stable, reasonable estimates. An accompanying R software implementation has been made publicly available.

We describe the vote package in R, which implements the plurality (or first-past-the-post), two-round runoff, score, approval and single transferable vote (STV) electoral systems, as well as methods for selecting the Condorcet winner and loser. We emphasize the STV system, which we have found to work well in practice for multi-winner elections with small electorates, such as committee and council elections, and the selection of multiple job candidates. For single-winner elections, the STV is also called instant runoff voting (IRV), ranked choice voting (RCV), or the alternative vote (AV) system. The package also implements the STV system with equal preferences, for the first time in a software package, to our knowledge. It also implements a new variant of STV, in which a minimum number of candidates from a specified group are required to be elected. We illustrate the package with several real examples.

Combinations of intense non-pharmaceutical interventions (lockdowns) were introduced worldwide to reduce SARS-CoV-2 transmission. Many governments have begun to implement exit strategies that relax restrictions while attempting to control the risk of a surge in cases. Mathematical modelling has played a central role in guiding interventions, but the challenge of designing optimal exit strategies in the face of ongoing transmission is unprecedented. Here, we report discussions from the Isaac Newton Institute ‘Models for an exit strategy’ workshop (11–15 May 2020). A diverse community of modellers who are providing evidence to governments worldwide were asked to identify the main questions that, if answered, would allow for more accurate predictions of the effects of different exit strategies. Based on these questions, we propose a roadmap to facilitate the development of reliable models to guide exit strategies. This roadmap requires a global collaborative effort from the scientific community and policymakers, and has three parts: (i) improve estimation of key epidemiological parameters; (ii) understand sources of heterogeneity in populations; and (iii) focus on requirements for data collection, particularly in low-to-middle-income countries. This will provide important information for planning exit strategies that balance socio-economic benefits with public health.

Summary Multiple-systems estimation is a key approach for quantifying hidden populations such as the number of victims of modern slavery. The UK Government published an estimate of 10000–13000 victims, constructed by the present author, as part of the strategy leading to the Modern Slavery Act 2015. This estimate was obtained by a stepwise multiple-systems method based on six lists. Further investigation shows that a small proportion of the possible models give rather different answers, and that other model fitting approaches may choose one of these. Three data sets collected in the field of modern slavery, together with a data set about the death toll in the Kosovo conflict, are used to investigate the stability and robustness of various multiple-systems-estimate methods. The crucial aspect is the way that interactions between lists are modelled, because these can substantially affect the results. Model selection and Bayesian approaches are considered in detail, in particular to assess their stability and robustness when applied to real modern slavery data. A new Markov chain Monte Carlo Bayesian approach is developed; overall, this gives robust and stable results at least for the examples considered. The software and data sets are freely and publicly available to facilitate wider implementation and further research.

Julian Besag was an outstanding statistical scientist, distinguished for his pioneering work on the statistical theory and analysis of spatial processes, especially conditional lattice systems. His work has been seminal in statistical developments over the last several decades ranging from image analysis to Markov chain Monte Carlo methods. He clarified the role of auto-logistic and auto-normal models as instances of Markov random fields and paved the way for their use in diverse applications. Later work included investigations into the efficacy of nearest neighbour models to accommodate spatial dependence in the analysis of data from agricultural field trials, image restoration from noisy data, and texture generation using lattice models.

Abstract Victims of modern slavery are often hidden from view, making it difficult to estimate how many there are. Multiple systems estimation helped Kevin Bales, Olivia Hesketh and Bernard Silverman provide an answer

Phase variation in functional data obscures the true amplitude variation when a typical cross-sectional analysis of these responses would be performed. Time warping or curve registration aims at eliminating the phase variation, typically by applying transformations, the warping functions ?n, to the function arguments. We propose a warping method that jointly estimates a decomposition of the warping function in warping components, and amplitude components. For the estimation routine, adaptive MCMC calculations are performed and implemented in C rather than R to increase computational speed. The R-C interface makes the program user-friendly, in that no knowledge of C is required and all input and output will be handled through R. The R package MRwarping contains all needed files.

¹H Nuclear Magnetic Resonance spectroscopy (¹H NMR) is increasingly used to measure metabolite concentrations in sets of biological samples for top-down systems biology and molecular epidemiology. For such purposes, knowledge of the sources of human variation in metabolite concentrations is valuable, but currently sparse. We conducted and analysed a study to create such a resource. In our unique design, identical and non-identical twin pairs donated plasma and urine samples longitudinally. We acquired ¹H NMR spectra on the samples, and statistically decomposed variation in metabolite concentration into familial (genetic and common-environmental), individual-environmental, and longitudinally unstable components. We estimate that stable variation, comprising familial and individual-environmental factors, accounts on average for 60% (plasma) and 47% (urine) of biological variation in ¹H NMR-detectable metabolite concentrations. Clinically predictive metabolic variation is likely nested within this stable component, so our results have implications for the effective design of biomarker-discovery studies. We provide a power-calculation method which reveals that sample sizes of a few thousand should offer sufficient statistical precision to detect ¹H NMR-based biomarkers quantifying predisposition to disease.

We consider perfect simulation algorithms for locally stable point processes based on dominated coupling from the past, and apply these methods in two different contexts. A new version of the algorithm is developed which is feasible for processes which are neither purely attractive nor purely repulsive. Such processes include multiscale area-interaction processes, which are capable of modelling point patterns whose clustering structure varies across scales. The other topic considered is nonparametric regression using wavelets, where we use a suitable area-interaction process on the discrete space of indices of wavelet coefficients to model the notion that if one wavelet coefficient is non-zero then it is more likely that neighbouring coefficients will be also. A method based on perfect simulation within this model shows promising results compared to the standard methods which threshold coefficients independently.

The procedure known as warping aims at reducing phase variability in a sample of functional curve observations, by applying a smooth bijection to the argument of each of the functions. We propose a natural representation of warping functions in terms of a new type of elementary function named 'warping component functions' which are combined into the warping function by composition. A sequential Bayesian estimation strategy is introduced, which fits a series of models and transfers the posterior of the previous fit into the prior of the next fit. Model selection is based on a warping analogue to wavelet thresholding, combined with Bayesian inference.

Summary For regularly spaced one-dimensional data, wavelet shrinkage has proven to be a compelling method for non-parametric function estimation. We create three new multiscale methods that provide wavelet-like transforms both for data arising on graphs and for irregularly spaced spatial data in more than one dimension. The concept of scale still exists within these transforms, but as a continuous quantity rather than dyadic levels. Further, we adapt recent empirical Bayesian shrinkage techniques to enable us to perform multiscale shrinkage for function estimation both on graphs and for irregular spatial data. We demonstrate that our methods perform very well when compared with several other methods for spatial regression for both real and simulated data. Although we concentrate on multiscale shrinkage (regression) we present our new ‘wavelet transforms’ as generic tools intended to be the basis of methods that might benefit from a multiscale representation of data either on graphs or for irregular spatial data.

Research funding and reputation in the UK have, for over two decades, been increasingly dependent on a regular peer-review of all UK departments. This is to move to a system more based on bibliometrics. Assessment exercises of this kind influence the behavior of institutions, departments and individuals, and therefore bibliometrics will have effects beyond simple measurement. [arXiv:0910.3529]