Learning from a lot: Empirical Bayes for high‐dimensional model‐based prediction

Empirical Bayes is a versatile approach to “learn from a lot” in two ways: first, from a large number of variables and, second, from a potentially large amount of prior information, for example, stored in public repositories. We review applications of a variety of empirical Bayes methods to several well‐known model‐based prediction methods, including penalized regression, linear discriminant analysis, and Bayesian models with sparse or dense priors. We discuss “formal” empirical Bayes methods that maximize the marginal likelihood but also more informal approaches based on other data summaries. We contrast empirical Bayes to cross‐validation and full Bayes and discuss hybrid approaches. To study the relation between the quality of an empirical Bayes estimator and p, the number of variables, we consider a simple empirical Bayes estimator in a linear model setting. We argue that empirical Bayes is particularly useful when the prior contains multiple parameters, which model a priori information on variables termed “co‐data”. In particular, we present two novel examples that allow for co‐data: first, a Bayesian spike‐and‐slab setting that facilitates inclusion of multiple co‐data sources and types and, second, a hybrid empirical Bayes–full Bayes ridge regression approach for estimation of the posterior predictive interval.     

A general central limit theorem and a subsampling variance estimator for α‐mixing point processes

We establish a central limit theorem for multivariate summary statistics of nonstationary α‐mixing spatial point processes and a subsampling estimator of the covariance matrix of such statistics. The central limit theorem is crucial for establishing asymptotic properties of estimators in statistics for spatial point processes. The covariance matrix subsampling estimator is flexible and model free. It is needed, for example, to construct confidence intervals and ellipsoids based on asymptotic normality of estimators. We also provide a simulation study investigating an application of our results to estimating functions.     

Cox regression of clustered event times with covariates missing not at random

Motivated by a recent tuberculosis (TB) study, this paper is concerned with covariates missing not at random (MNAR) and models the potential intracluster correlation by a frailty. We consider the regression analysis of right‐censored event times from clustered subjects under a Cox proportional hazards frailty model and present the semiparametric maximum likelihood estimator (SPMLE) of the model parameters. An easy‐to‐implement pseudo‐SPMLE is then proposed to accommodate more realistic situations using readily available supplementary information on the missing covariates. Algorithms are provided to compute the estimators and their consistent variance estimators. We demonstrate that both the SPMLE and the pseudo‐SPMLE are consistent and asymptotically normal by the arguments based on the theory of modern empirical processes. The proposed approach is examined numerically via simulation and illustrated with an analysis of the motivating TB study data.     

Bayesian inference for stable Lévy–driven stochastic differential equations with high‐frequency data

In this paper, we consider parametric Bayesian inference for stochastic differential equations driven by a pure‐jump stable Lévy process, which is observed at high frequency. In most cases of practical interest, the likelihood function is not available; hence, we use a quasi‐likelihood and place an associated prior on the unknown parameters. It is shown under regularity conditions that there is a Bernstein–von Mises theorem associated to the posterior. We then develop a Markov chain Monte Carlo algorithm for Bayesian inference, and assisted with theoretical results, we show how to scale Metropolis–Hastings proposals when the frequency of the data grows, in order to prevent the acceptance ratio from going to zero in the large data limit. Our algorithm is presented on numerical examples that help verify our theoretical findings.     

Bayesian density regression for discrete outcomes

We develop Bayesian models for density regression with emphasis on discrete outcomes. The problem of density regression is approached by considering methods for multivariate density estimation of mixed scale variables, and obtaining conditional densities from the multivariate ones. The approach to multivariate mixed scale outcome density estimation that we describe represents discrete variables, either responses or covariates, as discretised versions of continuous latent variables. We present and compare several models for obtaining these thresholds in the challenging context of count data analysis where the response may be over‐ and/or under‐dispersed in some of the regions of the covariate space. We utilise a nonparametric mixture of multivariate Gaussians to model the directly observed and the latent continuous variables. The paper presents a Markov chain Monte Carlo algorithm for posterior sampling, sufficient conditions for weak consistency, and illustrations on density, mean and quantile regression utilising simulated and real datasets.     

A reflected feature space for CART

We present an algorithm for learning oblique decision trees, called HHCART(G). Our decision tree combines learning concepts from two classification trees, HHCART and Geometric Decision Tree (GDT). HHCART(G) is a simplified HHCART algorithm that uses linear structure in the training examples, captured by a modified GDT angle bisector, to define splitting directions. At each node, we reflect the training examples with respect to the modified angle bisector to align this linear structure with the coordinate axes. Searching axis parallel splits in this reflected feature space provides an efficient and effective way of finding oblique splits in the original feature space. Our method is much simpler than HHCART because it only considers one reflected feature space for node splitting. HHCART considers multiple reflected feature spaces for node splitting making it more computationally intensive to build. Experimental results show that HHCART(G) is an effective classifier, producing compact trees with similar or better results than several other decision trees, including GDT and HHCART trees.     

A comparative study of confidence intervals to assess biosimilarity from analytical data

Assessment of analytical similarity of tier 1 quality attributes is based on a set of hypotheses that tests the mean difference of reference and test products against a margin adjusted for standard deviation of the reference product. Thus, proper assessment of the biosimilarity hypothesis requires statistical tests that account for the uncertainty associated with the estimations of the mean differences and the standard deviation of the reference product. Recently, a linear reformulation of the biosimilarity hypothesis has been proposed, which facilitates development and implementation of statistical tests. These statistical tests account for the uncertainty in the estimation process of all the unknown parameters. In this paper, we survey methods for constructing confidence intervals for testing the linearized reformulation of the biosimilarity hypothesis and also compare the performance of the methods. We discuss test procedures using confidence intervals to make possible comparison among recently developed methods as well as other previously developed methods that have not been applied for demonstrating analytical similarity. A computer simulation study was conducted to compare the performance of the methods based on the ability to maintain the test size and power, as well as computational complexity. We demonstrate the methods using two example applications. At the end, we make recommendations concerning the use of the methods.     

Transnational queer sociological analysis of sexual identity and civic‐political activism in Hong Kong,Taiwan and mainland China

The sociology of homosexuality lacks engagement with queer theory and postcolonialism and focuses primarily on the global metropoles, thus failing to provide a plausible account of non‐Western non‐normative sexual identities. This research adopts the author’s newly proposed transnational queer sociology to address these deficiencies. First, it critiques the Western model of sexual identity predominantly employed to elucidate non‐Western, non‐normative sexualities. It does so by examining not only the queer flows between West and non‐West but also those among and within non‐Western contexts to produce translocally shared and mutually referenced experiences. Second, the proposed approach combines sociology with queer theory by emphasizing the significant role of material, as well as discursive, analyses in shaping queer identities, desires and practices. This article employs the approach to examine young gay male identities, as revealed in 90 in‐depth interviews conducted in Hong Kong (n = 30), Taiwan (Taipei, n = 30) and mainland China (Shanghai, n = 30) between 2017 and 2019. More specifically, it highlights the interplay between the state and identity by investigating the intersection and intertwining effects of these young men’s sexual and cultural/national identities, revealing three different forms of civic‐political activism. The article both demonstrates the way in which sexuality and the state are mutually constituted and provides nuanced analysis of the heterogeneity of contemporary homosexualities in Hong Kong, Taiwan and mainland China. In applying a new sociological approach to understanding sexuality, this research joins the growing body of scholarship within sociology that is decentring the Western formation of universal knowledge.     

Making space for ‘the social’: connecting sociology and professional practices in urban lighting design

Lighting is increasingly recognized as a significant social intervention by both lighting professionals and academic social scientists. However, what counts as ‘the social’ is diverse and contested, with consequences for what kind of ‘social’ is performed or invented. Based on a long‐term research programme, we argue that collaboration between sociologists and lighting professionals requires negotiating discourses and practices of ‘the social’. This paper explores the quality and kinds of spaces made for ‘the social’ in professional practices and academic collaborations, focusing on two case studies of urban lighting that demonstrate how the space of ‘the social’ is constrained and impoverished by an institutionalized division between technical and aesthetic lighting. We consider the potential role of sociologists in making more productive spaces for ‘the social’ in urban design, as part of the central sociological task of ‘inventing the social’ (Marres, Guggenheim and Wilkie 2018) in the process of studying it.     

Conjugal intimacy,gender and modernity in contemporary China

The new generation of modernity theorists have forecast the democratization of gender relations within intimate relationships in late‐modern times. Chinese society has undergone rapid and dramatic changes in its unique trajectory of political, social and economic reform. Using China as an example of a region which has been largely ignored in contemporary social theory, this article enters the debate to contest the extent to which conjugal relationships are democratized in line with modernity. We further test the assertion that modern marriages are characterized by increased self‐disclosure and communication between partners. Data from a national survey on Chinese families is analysed in relation to the level of self‐disclosure between husbands and wives; gender division of housework; household decision‐making; and home ownership. We highlight the impact of gender, cohort and location (urban, rural or migrant) on experiences of modernity and draw attention to the material, social and cultural factors which continue to shape conjugal relations in contemporary Chinese society. Based on our findings, we contest the argument that disclosing intimacy between intimate partners is a defining characteristic of modern relationships, and suggest that other social factors may condition degrees of self‐disclosure in marriage. Similarly, we question the extent to which heterosexual conjugal equality is attained: the cultural practices and values of patrilineal family organization, together with material circumstances, continue to influence marital relations in China.