Bernard Walter Silverman

University of Oxford | OX · Department of Statistics

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...

Multiple systems estimation is a standard approach to quantifying hidden populations where data sources are based on lists of known cases. A typical modelling approach is to fit a Poisson loglinear model to the numbers of cases observed in each possible combination of the lists. It is necessary to decide which interaction parameters to include in t...

In March 2020, the UK was placed in lockdown following the spread of the Covid-19 virus. Just as legitimate workplaces made changes to enable their employees to work from home, the illicit drugs trade also made alternative arrangements, adapting its supply models to ensure continuity of operations. Based upon qualitative interviews with 46 practiti...

In March 2020, the UK was placed in lockdown following the spread of the Covid-19 virus. Just as legitimate workplaces made changes to enable their employees to work from home, the illicit drugs trade also made alternative arrangements, adapting its supply models to ensure continuity of operations. Based upon qualitative interviews with 46 practiti...

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...

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 th...

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 th...

Combinations of intense non-pharmaceutical interventions (lockdowns) were introduced in countries worldwide to reduce SARS-CoV-2 transmission. Many governments have begun to implement lockdown exit strategies that allow restrictions to be relaxed while attempting to control the risk of a surge in cases. Mathematical modelling has played a central r...

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...

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 difficulti...

This article presents a cross-national comparative analysis of the relationship between different dimensions of globalization and modern slavery. It argues that both the economic and political dimensions of globalization are strongly associated with lower levels of slavery prevalence. Recent estimates suggest there are more than 40 million people i...

In an effort to develop a model for estimating prevalence in a city or region of the United States, this study employed Multiple Systems Estimation, a statistical approach that uses data on known cases collected from individual agencies to estimate the number not known, with the ultimate aim of estimating the prevalence of trafficking in a region....

Multiple Systems Estimation is a key estimation approach for hidden populations such as the number of victims of Modern Slavery. The UK Government estimate of 10,000 to 13,000 victims was obtained by a multiple systems estimate based on six lists. A stepwise method was used to choose the terms in the model. Further investigation shows that a small...

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 difficulti...

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 clar...

Julian Besag's contributions to the discipline of statistics are profound. They have been, and continue to be, of far-reaching consequence. Julian's research work had authority and great originality. He seldom wrote the last word on a subject, but was there at the start of many of the key developments in modern stochastic modelling. His record of p...

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

Most statistical analyses involve one or more observations taken on each of a number of individuals in a sample, with the aim of making inferences about the general population from which the sample is drawn. In an increasing number of fields, these observations are curves or images. Curves and images are examples of functions, since an observed int...

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 th...

H 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...

Details of statistical association between each mQTL-driven metabolite and the SNPs within 200 kb of its hit region. Genomic locations are given in NCBI build 37 coordinates. Columns labelled ‘Beta,’ ‘S.E. Beta’ (S.E. = standard error) and ‘p-value’ (for the test of the null hypothesis that ) give details of the fit of the non-Bayesian mixed-effect...

(A) Non-synonymous SNPs in LD with mQTL SNPs. (B) Corresponding residue changes and predicted functional effects of non-synonymous SNPs. (DOC)

Focussing on the work of Sir John Kingman, one of the world's leading researchers in probability and mathematical genetics, this book touches on the important areas of these subjects in the last 50 years. Leading authorities give a unique insight into a wide range of currently topical problems. Papers in probability concentrate on combinatorial and...

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-intera...

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 a transformation, the warping function, to the function argument. We propose a warping method that j...

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 effect...

We consider perfect simulation algorithms for locally stable point processes based on dominated coupling from the past. A 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 p...

We introduce a new method of Bayesian wavelet shrinkage for reconstructing a signal when we observe a noisy version. Rather than making the common assumption that the wavelet coefficients of the signal are independent, we allow for the possibility that they are locally correlated in both location (time) and scale (frequency). This leads us to a pri...

Because we can perceive the pitch, timbre, and spatial location of a sound source independently, it seems natural to suppose that cortical processing of sounds might separate out spatial from nonspatial attributes. Indeed, recent studies support the existence of anatomically segregated "what" and "where" cortical processing streams. However, few at...

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 wi...

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 th...

The paper proposes a new approach to imputation using the expected sparse representation of a surface in a wavelet or lifting scheme basis. Our method incorporates a Bayesian mixture prior for these wavelet coefficients into a Gibbs sampler to generate a complete posterior distribution for the variable of interest. Intuitively, the estimator operat...

Most statistical analyses involve one or more observations taken on each of a number of individuals in a sample, with the aim of making inferences about the general population from which the sample is drawn. In an increasing number of fields, these observations are curves or images. Curves and images are examples of functions, since an observed int...

Suppose one is trying to estimate a high dimensional vector of parameters from a series of one observation per parameter. Often, it is possible to take advantage of sparsity in the parameters by thresholding the data in an appropriate way. A marginal maximum likelihood approach, within a suitable Bayesian structure, has excellent properties. For ve...

In humans, the rate of recombination, as measured on the megabase scale, is positively associated with the level of genetic variation, as measured at the genic scale. Despite considerable debate, it is not clear whether these factors are causally linked or, if they are, whether this is driven by the repeated action of adaptive evolution or molecula...

Maximum Likelihood Estimates of the Strength of Gene Conversion (G = 4Nect) from SNPs in the African-American Population Sample for Each Quintile of the Recombination Rate In this analysis we assume that GAT→GC = −GGC→AT. Estimates are shown both including (A) and excluding (B) potential CpG mutations. Also shown are estimates of G for SNPs in quin...

Note on the Relationship between Correlation Coefficients for Raw and Wavelet-Transformed Signals (48 KB DOC)

Data Used in the Wavelet Analysis A gzipped, comma-delimited file containing details of SNP discovery and other chromosomal features in 1-kb windows along human Chromosome 20 in build 34 coordinates (hg16). Columns are window start (bp), window end (bp), number of SNPs called across window (NB, this includes redundant calls), total bases sequenced...

R-scripts for Performing Wavelet Analyses Presented in the Paper The scripts can be used to generate some of the figures in the paper by saving both the unzipped Dataset S1 file (saved as “Chr20_1kb.csv”) and the Dataset S2 file (saved as “PLoS_code.r”) in the same folder. After starting the R program, change directory to that in which the files we...

Power Spectra and Pairwise Correlations of Smoothed Wavelet Coefficients Diagonal plots show the power spectrum of the wavelet decomposition of each factor on the long (red) and short (blue) arms of Chromosome 20. Off-diagonal plots show the rank correlation coefficient between pairs of smoothed wavelet coefficients at each scale on the long (top r...

Estimates of the Strength of Gene Conversion from Allele Frequency Distributions Mutations were classified into four categories (GC→GC, GC→AT, AT→AT, and AT→GC on the basis of comparison of the human alleles with that of the Chimpanzee reference sequence). For each class we calculated the likelihood for a grid of values of the strength of gene conv...

SNP Discovery and Estimation of Diversity (32 KB DOC)

This paper explores a class of empirical Bayes methods for level-dependent threshold selection in wavelet shrinkage. The prior considered for each wavelet coefficient is a mixture of an atom of probability at zero and a heavy-tailed density. The mixing weight, or sparsity parameter, for each level of the transform is chosen by marginal maximum like...

Bacterial communities provide important services. They break down pollutants, municipal waste and ingested food, and they are the primary means by which organic matter is recycled to plants and other autotrophs. However, the processes that determine the rate at which these services are supplied are only starting to be identified. Biodiversity influ...

Suppose that a sequence of unknown parameters is observed sub ject to independent Gaussian noise. The EbayesThresh package in the S language implements a class of Empirical Bayes thresholding methods that can take advantage of possible sparsity in the sequence, to improve the quality of estimation. The prior for each parameter in the sequence is...

Suppose that a sequence of unknown parameters is observed subject to independent Gaussian noise. The EbayesThresh package in the S language implements a class of Empirical Bayes thresholding methods that can take advantage of possible sparsity in the sequence, to improve the quality of estimation. The prior for each parameter in the sequence is a m...

In humans, the rate of recombination, as measured on the megabase scale, is positively associated with the level of genetic variation, as measured at the genic scale. Despite considerable debate, it is not clear whether these factors are causally linked or, if they are, whether this is driven by the repeated action of adaptive evolution or molecula...

In this article we are interested in modeling the relationship between a scalar, Y , and a functional predictor, X(t). We introduce a highly flexible approach called "Functional Adaptive Model Estimation" (FAME) which extends generalized linear models (GLM), generalized additive models (GAM) and projection pursuit regression (PPR) to handle functio...

There are standard modifications of certain compactly supported wavelets that yield orthonormal bases on a bounded interval. We extend one such construction to those wavelets, such as ‘coiflets', that may have fewer vanishing moments than had to be assumed previously. Our motivation lies in function estimation in statistics. We use these boundary-m...

There are standard modifications of certain compactly supported wavelets that yield orthonormal bases on a bounded interval. We extend one such construction to those wavelets, such as `coiflets', that may have fewer vanishing moments than had to be assumed previously. Our motivation lies in function estimation in statistics. We use these boundary-m...

An empirical Bayes approach to the estimation of possibly sparse sequences observed in Gaussian white noise is set out and investigated. The prior considered is a mixture of an atom of probability at zero and a heavy-tailed density, with the mixing weight chosen by marginal maximum likelihood, in the hope of adapting between sparse and dense sequen...

Introduction.- Life Course Data in Criminology.- The Nondurable Goods Index.- Bone Shapes from a Paleopathology Study.- Modeling Reaction Time Distributions.- Zooming in on Human Growth.- Time Warping Handwriting and Weather Records.- How do Bone Shapes Indicate Arthritis?- Functional Models for Test Items.- Predicting Lip Acceleration from Electro...

To compare objectively the shape of the intercondylar notch in human osteoarthritic and non-osteoarthritic femora. A sample of 96 human femora from a large skeletal population were selected for study. These femora included subjects with evidence of late stage osteoarthritis (that is, with eburnation present) and subjects with no such evidence. The...

We use cumulants to derive Bayesian credible intervals for wavelet regression estimates. The first four cumulants of the posterior distribution of the estimates are expressed in terms of the observed data and integer powers of the mother wavelet functions. These powers are closely approximated by linear combinations of wavelet scaling functions at...

A long record of atmospheric 14C concentration, from 45 to 11 thousand years ago (ka), was obtained from a stalagmite with thermal-ionization mass-spectrometric 230Th and accelerator mass-spectrometric 14C measurements. This record reveals highly elevated Delta14C between 45 and 33 ka, portions of which may correlate with peaks in cosmogenic 36Cl a...

In standard wavelet methods, the empirical wavelet coefficients are thresholded term by term, on the basis of their individual magnitudes. Information on other coefficients has no influence on the treatment of particular coefficients. We propose and investigate a wavelet shrinkage method that incorporates information on neighbouring coefficients in...

This article proposes some non-linear, thresholded wavelet density estimators, and investigates the practical problems involved in their implementation. Our proposed thresholding method exploits the non-stationary variance structure of the wavelet coefficients. One proposed method of estimating the variances of the raw coefficients uses the scaling...

To examine objectively spatial patterns of osteophytes around the distal end of the femur and to identify distinct subgroups. A sample of 107 human femora from a large skeletal population were selected for study. These femora included subjects with evidence of late stage osteoarthritis (that is, with eburnation present) and those with no such evide...

In recent years there has been an explosion of interest in wavelets, in a wide range of fields in science and engineering and beyond. This book brings together contributions from researchers from disparate fields, both in order to demonstrate to a wide readership the current breadth of work in wavelets, and to encourage cross-fertilization of ideas...

We consider random functions defined by atomic decompositions in a wavelet dictionary. The scale and dilation of the wavelet atoms are not dyadic constraints, but the function is modelled as a sum of wavelet functions at arbitrary positions and scales. The locations of the wavelet atoms and the magnitudes of their coefficients are chosen with respe...

In standard wavelet methods, the empirical wavelet coe#cients are thresholded term by term, on the basis of their individual magnitudes. Information on other coe#- cients has no in#uence on the treatment of particular coe#cients. We propose and investigate a wavelet shrinkage method that incorporates information on neighboring coe#cients into the d...

In recent years there has been an explosion of interest in wavelets, in a wide range of fields in science and engineering and beyond. This book brings together contributions from researchers from disparate fields, both in order to demonstrate to a wide readership the current breadth of work in wavelets, and to encourage cross-fertilization of ideas...

We consider random functions defined in terms of members of an overcomplete wavelet dictionary. The function is modelled as a sum of wavelet components at arbitrary positions and scales where the locations of the wavelet components and the magnitudes of their coefficients are chosen with respect to a marked Poisson process model. The relationships...

Introduction A common method of analyzing images is to model them as deformed versions of a "standard image," called a template. The method is often applied to medical images and can be used to analyze shape variation, particularly that due to some pathology. Our methodology was developed with reference to a particular data set of human femora aris...

In standard wavelet methods, the empirical wavelet coefficients are thresholded term by term, on the basis of their individual magnitudes. Information on other coefficients has no influence on the treatment of particular coefficients. We propose a wavelet shrinkage method that incorporates information on neighboring coefficients into the decision m...

. Various aspects of the wavelet approach to nonparametric regression are considered, with the overall aim of extending the scope of wavelet techniques, to irregularly-spaced data, to regularly-spaced data sets of arbitrary size, to heteroscedastic and correlated data, and to data that contain outliers. The core of the methodology is an algorithm f...

this paper. To demonstrate the method, results from these algorithms are presented and discussed in Section 7. 2

In recent years there has been an explosion of interest in wavelets, in a wide range of fields in science and engineering and beyond. This book brings together contributions from researchers from disparate fields, both in order to demonstrate to a wide readership the current breadth of work in wavelets, and to encourage cross-fertilization of ideas...

In recent years there has been an explosion of interest in wavelets, in a wide range of fields in science and engineering and beyond. This book brings together contributions from researchers from disparate fields, both in order to demonstrate to a wide readership the current breadth of work in wavelets, and to encourage cross-fertilization of ideas...

The original application of wavelets in statistics was to the estimation of a curve given observations of the curve plus white noise at 2 J regularly spaced points. The rationale for the use of wavelet methods in this context is reviewed briefly. Various extensions of the standard statistical methodology are discussed. These include curve estimatio...

We discuss a Bayesian formalism which gives rise to a type of wavelet threshold estimation in non-parametric regression. A prior distribution is imposed on the wavelet coe#cients of the unknown response function, designed to capture the sparseness of wavelet expansion common to most applications. For the prior speci#ed, the posterior median yields...

To assess the force plate as a diagnostic aid in equine locomotor abnormalities, particularly for abnormalities such as navicular disease that do not have specific diagnostic criteria. 17 Thoroughbreds without observable locomotor abnormalities (group A), 6 Thoroughbreds with superficial digital flexor tendon injury (group B), and 8 Thoroughbreds w...

To determine the difference in shape of the distal femur, viewed axially in two dimensions, between eburnated and non-eburnated femora. A comparison of 52 non-eburnated and 16 eburnated femora drawn from a large archeological skeletal population. Eburnation was taken to indicate late stage osteoarthritis. Shape variability, based on landmarks, was...