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.     

The Impact of Neighboring on Changes in Sense of Community Over Time: A Latent Transition Analysis

Sense of community (SOC) is associated with the quality of community life and the building of social capital. While its linkage to informal social behavior, such as neighboring, is inherent in discussions regarding theory, empirical evidence remains scarce. Moreover, the degree to which neighboring behavior influences SOC over time is largely unknown. Using a latent transition analysis, the effect of neighboring on SOC was investigated over a 5-year span from 2006 to 2011 among a sample of adults (n?=?165) in Arizona. Initially, a latent class analysis identified two SOC subgroups: Low SOC and High SOC. The likelihood of shifts in SOC class membership over 5 years was generally stable, with most individuals staying in the same group (82.3% Low SOC; 92.4% High SOC). Neighboring behavior and socio-demographic covariates impacted the likelihood that individuals changed classes, with 25.3% of Low SOC individuals transitioning to High SOC in 2011 and 55.4% of High SOC individuals moving to Low SOC in 2011. Specifically, having an income greater than $60,000 and visiting with neighbors lessened the likelihood of being in the Low SOC class in 2006; and length of residence and exchanging favors with neighbors lessened the likelihood of being in the Low SOC class in 2011. These findings have implications for both community design and community development practice. Design and development interventions that promote greater social interaction may help build and sustain SOC over time.

     

Foreign-born and native-born migration in the U.S.: evidence from linked IRS administrative and census survey records

Journal of Population Research - This paper details efforts to link administrative records from the Internal Revenue Service (IRS) to American Community Survey (ACS) and 2010 Census microdata for...     

Still-births among the offspring of male radiation workers at the Sellafield nuclear reprocessing plant: detailed results and statistical aspects

Summary. This study investigates whether there was evidence of increasing risk of still-birth with increasing paternal exposure to ionizing radiation received during employment at the Sellafield nuclear installation before the child was conceived. A significant positive association is found between the total paternal preconceptional exposure to external ionizing radiation and the risk of still-birth (after adjustment for year of birth, social class, birth order and paternal age, odds ratio at 100 mSv 1.24 (95% confidence interval 1.04–1.45)). A summary of the principal scientific findings of this study has been published in the Lancet . This paper describes in detail the statistical methods that were used in the investigation and presents the results in full.     

Estimation of location extremes within general families of scale mixtures

In this paper, we study the estimation of the minimum and maximum location parameters, respectively, representing the minimum guaranteed lifetime of series and parallel systems of components, within a general class of scale mixtures. The conditional or underlying distribution has only the primary restriction of being a location-scale family with positive support. The mixing distribution is also quite general in that we only assume that it has positive support and finite second moment. For demonstrative purposes several special cases are highlighted such as the gamma, inverse-Gaussian, and discrete mixture. Various estimators, including bootstrap bias corrected estimators, are compared with respect to both mean-squared-error and Pitman's measure of closeness.     

Bayesian modelling of catch in a north-west Atlantic fishery

Summary. We model daily catches of fishing boats in the Grand Bank fishing grounds. We use data on catches per species for a number of vessels collected by the European Union in the context of the Northwest Atlantic Fisheries Organization. Many variables can be thought to influence the amount caught: a number of ship characteristics (such as the size of the ship, the fishing technique used and the mesh size of the nets) are obvious candidates, but one can also consider the season or the actual location of the catch. Our database leads to 28 possible regressors (arising from six continuous variables and four categorical variables, whose 22 levels are treated separately), resulting in a set of 177 million possible linear regression models for the log-catch. Zero observations are modelled separately through a probit model. Inference is based on Bayesian model averaging, using a Markov chain Monte Carlo approach. Particular attention is paid to the prediction of catches for single and aggregated ships.     

Does parents’ valuation of children’s health mimic their valuation of own health?

A single latent variable model of health status and therapeutic health care utilization is estimated for parents and own children of 6,557 US households. The equation system that identifies latent health status simultaneously determines a number of indicators of general health, including presence of morbidity symptoms, mobility limitations, medication needs, and utilization of therapeutic health care services. The main goal of the paper was to obtain an unbiased estimate of parents’ marginal substitution rate between own and child health. Results indicate that parents’ valuation of their children’s health exceeds their valuation of own health by almost twofold on average.