Stochastic boosting algorithms

In this article we develop a class of stochastic boosting (SB) algorithms, which build upon the work of Holmes and Pintore (Bayesian Stat. 8, Oxford University Press, Oxford, 2007). They introduce boosting algorithms which correspond to standard boosting (e.g. Bühlmann and Hothorn, Stat. Sci. 22:477–505, 2007) except that the optimization algorithms are randomized; this idea is placed within a Bayesian framework. We show that the inferential procedure in Holmes and Pintore (Bayesian Stat. 8, Oxford University Press, Oxford, 2007) is incorrect and further develop interpretational, computational and theoretical results which allow one to assess SB’s potential for classification and regression problems. To use SB, sequential Monte Carlo (SMC) methods are applied. As a result, it is found that SB can provide better predictions for classification problems than the corresponding boosting algorithm. A theoretical result is also given, which shows that the predictions of SB are not significantly worse than boosting, when the latter provides the best prediction. We also investigate the method on a real case study from machine learning.     

“There’s No Crying in Police Work:” Exploring Police Shootings with Feminist Methods

Police shootings are events that result in psychological trauma to all involved, including police officers. Little work explores how officers and their social and professional networks that are involved in deadly police shootings cope with this event. Utilizing one case study, we hear how an officer involved in a deadly shooting, and those close to him, understand this event. We argue that feminist epistemologies and methods allow a better understanding of these events, which is essential if officers and the broader community are to heal.     

Social class variation in risk: a comparative analysis of the dynamics of economic vulnerability1

A joint concern with multidimensionality and dynamics is a defining feature of the pervasive use of the terminology of social exclusion in the European Union. The notion of social exclusion focuses attention on economic vulnerability in the sense of exposure to risk and uncertainty. Sociological concern with these issues has been associated with the thesis that risk and uncertainty have become more pervasive and extend substantially beyond the working class. This paper combines features of recent approaches to statistical modelling of poverty dynamics and multidimensional deprivation in order to develop our understanding of the dynamics of economic vulnerability. An analysis involving nine countries and covering the first five waves of the European Community Household Panel shows that, across nations and time, it is possible to identify an economically vulnerable class. This class is characterized by heightened risk of falling below a critical resource level, exposure to material deprivation and experience of subjective economic stress. Cross‐national differentials in persistence of vulnerability are wider than in the case of income poverty and less affected by measurement error. Economic vulnerability profiles vary across welfare regimes in a manner broadly consistent with our expectations. Variation in the impact of social class within and across countries provides no support for the argument that its role in structuring such risk has become much less important. Our findings suggest that it is possible to accept the importance of the emergence of new forms of social risk and acknowledge the significance of efforts to develop welfare states policies involving a shift of opportunities and decision making on to individuals without accepting the ‘death of social class’ thesis.     

Linear Transformations of Linear Mixed-Effects Models

A number of articles have discussed the way lower order polynomial and interaction terms should be handled in linear regression models. Only if all lower order terms are included in the model will the regression model be invariant with respect to coding transformations of the variables. If lower order terms are omitted, the regression model will not be well formulated. In this paper, we extend this work to examine the implications of the ordering of variables in the linear mixed-effects model. We demonstrate how linear transformations of the variables affect the model and tests of significance of fixed effects in the model. We show how the transformations modify the random effects in the model, as well as their covariance matrix and the value of the restricted log-likelihood. We suggest a variable selection strategy for the linear mixed-effects model.     

Expressions for the distribution and percentiles of the sums and products of chi-squares

Linear combinations of central or non-central chi-squares occur naturally in a variety of contexts. The products of chi-squares occur when a variance has a chi-square prior and in electrical engineering. Here, we give expansions for their distribution and quantiles and also for the products of the powers of chi-squares, including ratios. These provide much more accurate approximations than those based on asymptotic normality. The larger the degrees of freedom or the larger the non-centrality parameters, the better the approximations. We give the first four terms of these expansions. These provide approximations with errors smaller by five magnitudes than those based on asymptotic normality or on Satterthwaite's approximation. His method matched the first two moments of the target and a multiple of a chi-square and is only a first-order approximation like that based on the central limit theorem. We show that it can be made second order by matching the first three moments. The appendices show how to obtain analytical expressions for the distribution of weighted sums of chi-squares.     

Screening designs for model discrimination

We introduce new criteria for model discrimination and use these and existing criteria to evaluate standard orthogonal designs. We show that the capability of orthogonal designs for model discrimination is surprisingly varied. In fact, for specified sample sizes, number of factors, and model spaces, many orthogonal designs are not model discriminating by the definition given in this paper, while others in the same class of orthogonal designs are. We also use these criteria to construct optimal two-level model-discriminating designs for screening experiments. The efficacy of these designs is studied, both in terms of estimation efficiency and discrimination success. Simulation studies indicate that the constructed designs result in substantively higher likelihoods of identifying the correct model.     

Models for longitudinal data with censored changepoints

Summary.  In longitudinal studies of biological markers, different individuals may have different underlying patterns of response. In some applications, a subset of individuals experiences latent events, causing an instantaneous change in the level or slope of the marker trajectory. The paper presents a general mixture of hierarchical longitudinal models for serial biomarkers. Interest centres both on the time of the event and on levels of the biomarker before and after the event. In observational studies where marker series are incomplete, the latent event can be modelled by a survival distribution. Risk factors for the occurrence of the event can be investigated by including covariates in the survival distribution. A combination of Gibbs, Metropolis–Hastings and reversible jump Markov chain Monte Carlo sampling is used to fit the models to serial measurements of forced expiratory volume from lung transplant recipients.     

Modeling multiple‐response categorical data from complex surveys

Although “choose all that apply” questions are common in modern surveys, methods for analyzing associations among responses to such questions have only recently been developed. These methods are generally valid only for simple random sampling, but these types of questions often appear in surveys conducted under more complex sampling plans. The purpose of this article is to provide statistical analysis methods that can be applied to “choose all that apply” questions in complex survey sampling situations. Loglinear models are developed to incorporate the multiple responses inherent in these types of questions. Statistics to compare models and to measure association are proposed and their asymptotic distributions are derived. Monte Carlo simulations show that tests based on adjusted Pearson statistics generally hold their correct size when comparing models. These simulations also show that confidence intervals for odds ratios estimated from loglinear models have good coverage properties, while being shorter than those constructed using empirical estimates. Furthermore, the methods are shown to be applicable to more general problems of modeling associations between elements of two or more binary vectors. The proposed analysis methods are applied to data from the National Health and Nutrition Examination Survey. The Canadian Journal of Statistics © 2009 Statistical Society of Canada     

Bias-reduced estimates for skewness, kurtosis, L-skewness and L-kurtosis

Estimates based on L-moments are less non-robust than estimates based on ordinary moments because the former are linear combinations of order statistics for all orders, whereas the later take increasing powers of deviations from the mean as the order increases. Estimates based on L-moments can also be more efficient than maximum likelihood estimates. Similarly, L-skewness and L-kurtosis are less non-robust and more informative than the traditional measures of skewness and kurtosis. Here, we give nonparametric bias-reduced estimates of both types of skewness and kurtosis. Their asymptotic computational efficiency is infinitely better than that of corresponding bootstrapped estimates.