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.     

Linear scalar-on-surface random effects regression models

Many research fields increasingly involve analyzing data of a complex structure. Models investigating the dependence of a response on a predictor have moved beyond the ordinary scalar-on-vector regression. We propose a regression model for a scalar response and a surface (or a bivariate function) predictor. The predictor has a random component and the regression model falls in the framework of linear random effects models. We estimate the model parameters via maximizing the log-likelihood with the ECME (Expectation/Conditional Maximization Either) algorithm. We use the approach to analyze a data set where the response is the neuroticism score and the predictor is the resting-state brain function image. In the simulations we tried, the approach has better performance than two other approaches, a functional principal component regression approach and a smooth scalar-on-image regression approach.     

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.     

Integrated nested Laplace approximation for the analysis of count data via the combined model: A simulation study

The combined model accounts for different forms of extra-variability and has traditionally been applied in the likelihood framework, or in the Bayesian setting via Markov chain Monte Carlo. In this article, integrated nested Laplace approximation is investigated as an alternative estimation method for the combined model for count data, and compared with the former estimation techniques. Longitudinal, spatial, and multi-hierarchical data scenarios are investigated in three case studies as well as a simulation study. As a conclusion, integrated nested Laplace approximation provides fast and precise estimation, while avoiding convergence problems often seen when using Markov chain Monte Carlo.     

A Factor-Adjusted Multiple Testing Procedure With Application to Mutual Fund Selection

In this article, we propose a factor-adjusted multiple testing (FAT) procedure based on factor-adjusted p-values in a linear factor model involving some observable and unobservable factors, for the purpose of selecting skilled funds in empirical finance. The factor-adjusted p-values were obtained after extracting the latent common factors by the principal component method. Under some mild conditions, the false discovery proportion can be consistently estimated even if the idiosyncratic errors are allowed to be weakly correlated across units. Furthermore, by appropriately setting a sequence of threshold values approaching zero, the proposed FAT procedure enjoys model selection consistency. Extensive simulation studies and a real data analysis for selecting skilled funds in the U.S. financial market are presented to illustrate the practical utility of the proposed method. Supplementary materials for this article are available online.     

Uniform consistency rate of kNN regression estimation for functional time series data

In this paper, we investigate the k-nearest neighbours (kNN) estimation of nonparametric regression model for strong mixing functional time series data. More precisely, we establish the uniform almost complete convergence rate of the kNN estimator under some mild conditions. Furthermore, a simulation study and an empirical application to the real data analysis of sea surface temperature (SST) are carried out to illustrate the finite sample performances and the usefulness of the kNN approach.     

Empirical evaluation of the implementation of the EMA guideline on missing data in confirmatory clinical trials: Specification of mixed models for longitudinal data in study protocols

In confirmatory clinical trials, the prespecification of the primary analysis model is a universally accepted scientific principle to allow strict control of the type I error. Consequently, both the ICH E9 guideline and the European Medicines Agency (EMA) guideline on missing data in confirmatory clinical trials require that the primary analysis model is defined unambiguously. This requirement applies to mixed models for longitudinal data handling missing data implicitly. To evaluate the compliance with the EMA guideline, we evaluated the model specifications in those clinical study protocols from development phases II and III submitted between 2015 and 2018 to the Ethics Committee at Hannover Medical School under the German Medicinal Products Act, which planned to use a mixed model for longitudinal data in the confirmatory testing strategy. Overall, 39 trials from different types of sponsors and a wide range of therapeutic areas were evaluated. While nearly all protocols specify the fixed and random effects of the analysis model (95%), only 77% give the structure of the covariance matrix used for modeling the repeated measurements. Moreover, the testing method (36%), the estimation method (28%), the computation method (3%), and the fallback strategy (18%) are given by less than half the study protocols. Subgroup analyses indicate that these findings are universal and not specific to clinical trial phases or size of company. Altogether, our results show that guideline compliance is to various degrees poor and consequently, strict type I error rate control at the intended level is not guaranteed.     

Intimacy,rapport, and exceptional disclosure: a comparison of in-person and mediated interview contexts

While qualitative researchers increasingly accept online video interviews as a reliable method, many maintain concerns about rapport and data quality. Drawing on two separate interview projects conducted in private in-person settings, public in-person settings, and privately via Skype, we compare interview contexts with regard to rapport, suitability to sensitive topics, interview duration, and scheduling concerns raised by prior research. Analytical comparison of these two corpuses of data suggest, largely in contrast to previous literature, that (1) interviews conducted in private settings (either in-person or via Skype) result in more sharing of deeply personal experiences, and there is little difference in this exceptional disclosure between Skype and in-person private interviews; (2) interviewing via Skype produces neither reduction nor inappropriate excesses of rapport; and (3) Skype interviews are a popular choice among participants, did not result in shorter interview duration, and were not subject to greater rescheduling or cancellation.     

Indigenous data,indigenous methodologies and indigenous data sovereignty

The field of Indigenous methodologies has grown strongly since Tuhiwai Smith’s 1999 groundbreaking book Decolonizing Indigenous Methodologies. For the most part however, there has been a marked absence of quantitative methodologies with the methods aligned with Indigenous methodologies predominantly qualitative. This article proposes that the absence of an Indigenous presence from Indigenous data production has resulted in an overwhelming statistical narrative of deficit for dispossessed Indigenous peoples around the globe. Using the theoretical concept of Indigenous Lifeworlds this article builds on the core premises of Walter and Andersen’s 2013 book Indigenous quantitative methodologies. Arguing for a fundamental disturbance of the Western logics of statistical data the article details recent developments in the field including the emergence of the Indigenous Data Sovereignty movement. The article also explores Indigenous quantitative methodologies in practice using the case study of a Tribal Epidemiology Centre in New Mexico.     

What influences the size of child maintenance payments? A register‐based study of maintenance payments in Finland

The aim of this study was to explore how particular economic and demographic factors contribute to the level of the child maintenance payment (CMP) paid by the non‐resident parent. For this study, we used 5‐year longitudinal panel data from years 2009 to 2013 consisting of over 80,000 non‐resident parents from the Finnish Tax Administration and The Finnish Population Register Centre. Results from regression models indicate that the single biggest factor affecting the size of CMPs is the number of dependent children. We found that the non‐resident parent's higher income is associated with higher CMPs and that non‐resident fathers pay on average larger CMPs than non‐resident mothers, even after accounting for differences in income. Unexpectedly, we found that the age of the dependent child did not predict changes in CMPs. This suggests that once formal CMP‐contracts are determined between the parents, they are seldom changed. Our results suggest that some degree of mandatory periodic review for maintenance contracts is worth considering.