Approximate Bayesian inference for latent Gaussian models by using integrated nested Laplace approximations

Summary.  Structured additive regression models are perhaps the most commonly used class of models in statistical applications. It includes, among others, (generalized) linear models, (generalized) additive models, smoothing spline models, state space models, semiparametric regression, spatial and spatiotemporal models, log-Gaussian Cox processes and geostatistical and geoadditive models. We consider approximate Bayesian inference in a popular subset of structured additive regression models, latent Gaussian models , where the latent field is Gaussian, controlled by a few hyperparameters and with non-Gaussian response variables. The posterior marginals are not available in closed form owing to the non-Gaussian response variables. For such models, Markov chain Monte Carlo methods can be implemented, but they are not without problems, in terms of both convergence and computational time. In some practical applications, the extent of these problems is such that Markov chain Monte Carlo sampling is simply not an appropriate tool for routine analysis. We show that, by using an integrated nested Laplace approximation and its simplified version, we can directly compute very accurate approximations to the posterior marginals. The main benefit of these approximations is computational: where Markov chain Monte Carlo algorithms need hours or days to run, our approximations provide more precise estimates in seconds or minutes. Another advantage with our approach is its generality, which makes it possible to perform Bayesian analysis in an automatic, streamlined way, and to compute model comparison criteria and various predictive measures so that models can be compared and the model under study can be challenged.     

Layered adaptive importance sampling

Monte Carlo methods represent the de facto standard for approximating complicated integrals involving multidimensional target distributions. In order to generate random realizations from the target distribution, Monte Carlo techniques use simpler proposal probability densities to draw candidate samples. The performance of any such method is strictly related to the specification of the proposal distribution, such that unfortunate choices easily wreak havoc on the resulting estimators. In this work, we introduce a layered (i.e., hierarchical) procedure to generate samples employed within a Monte Carlo scheme. This approach ensures that an appropriate equivalent proposal density is always obtained automatically (thus eliminating the risk of a catastrophic performance), although at the expense of a moderate increase in the complexity. Furthermore, we provide a general unified importance sampling (IS) framework, where multiple proposal densities are employed and several IS schemes are introduced by applying the so-called deterministic mixture approach. Finally, given these schemes, we also propose a novel class of adaptive importance samplers using a population of proposals, where the adaptation is driven by independent parallel or interacting Markov chain Monte Carlo (MCMC) chains. The resulting algorithms efficiently combine the benefits of both IS and MCMC methods.     

Substance use and vulnerability to sexual and physical aggression: a longitudinal study of young adults

Using data from 2,170 individuals who participated in Waves 8 (age 23) and 9 (age 29) of a multiyear panel study, this study examined whether alcohol and marijuana use in young adulthood increase one's risk for experiencing subsequent sexual or physical assault victimization, whether victims' own violent behavior or involvement in the sale of drugs explain any effects of substance use on victimization, and whether these associations differ by gender. Controlling for prior victimization, we found that marijuana use, but not alcohol use, predicted women's and men's subsequent sexual victimization and men's subsequent physical assault victimization, and that heavy alcohol use, but not marijuana use, predicted women's subsequent physical assault victimization. Whereas the links from marijuana use to victimization were explained by users' own violent behavior, the link from alcohol use to women's physical assault victimization was not.     

A generalization of the adaptive rejection sampling algorithm

Rejection sampling is a well-known method to generate random samples from arbitrary target probability distributions. It demands the design of a suitable proposal probability density function (pdf) from which candidate samples can be drawn. These samples are either accepted or rejected depending on a test involving the ratio of the target and proposal densities. The adaptive rejection sampling method is an efficient algorithm to sample from a log-concave target density, that attains high acceptance rates by improving the proposal density whenever a sample is rejected. In this paper we introduce a generalized adaptive rejection sampling procedure that can be applied with a broad class of target probability distributions, possibly non-log-concave and exhibiting multiple modes. The proposed technique yields a sequence of proposal densities that converge toward the target pdf, thus achieving very high acceptance rates. We provide a simple numerical example to illustrate the basic use of the proposed technique, together with a more elaborate positioning application using real data.     

Locating social service centres using interactive graphics

The paper explores the feasibility of using interactive graphic based solution procedures in location problems with discrete choices. It compares solutions generated through interactive graphics with those generated through optimization for a problem context where service centres had to be located in rural India. The comparison demonstrates the feasibility of generating near optimal solutions for problems with a certain dimensionality. Broad features of the graphic software are described. The paper also highlights other advantages and limitations of the interactive graphic procedure.     

A model for national planning policies

This paper attempts to develop a multiobjective model to help policy-makers choose the most appropriate mix of economic policies concurrent with the elimination of serious gaps. Each individual policy attempts to achieve a specific goal or a set of subgoals; but it may hinder the achievement of some other subgoals. To differentiate between the importance of different objectives, the analyst assigns different priorities to each of the given set of subgoals. Three sets of results are provided by three separate computer runs of this model. Each set of results corresponds to one of the three priority structures, and each run indicates quite differing underachievements or over-achievements of individual subgoals. A detailed explanation for each of these deviations (gaps) from the targeted subgoals is attempted in an overall framework and some interactions between various gaps (savings gaps, foreign exchange gap, domestic growth gap, GNP gap, etc.) are also identified.     

Substance Use and Early Marriage

Prior work indicates that substance use is related to adolescent marriage. We describe two different processes that may account for this relationship and hypothesize patterns of association that would be consistent or inconsistent with each. Using data from a study that followed west coast youth from 7th grade to young adulthood (N = 3,324), we assessed the effects of cigarette, alcohol, and marijuana use in 7th and 10th grade on the probability of marriage prior to age 20. When gender, race, and SES were controlled, cigarette use in adolescence, but not other substance use, was associated with early marriage. Low educational attainment and early unwed parenthood each uniquely mediated this association. These results suggest that the link between substance use and early marriage reflects a disposition toward risky or unconventional behavior, not the judgment‐impairing effects of drug and alcohol use.     

Trends in the participatory process of changing shiftwork arrangements

Abstract

A recent survey by the International Labour Office on changing shiftwork arrangements showed that there were three essential steps commonly taken in the change process in different countries. They could be identified as: (1) group study of operational requirements and workers' needs; (2) establishing feasible options; and (3) consensus building while acting on conflicting interests. The change process was more successful when it was provided with concrete support. Attention is drawn to three major aspects of such support: (a) gathering data about operational requirements of the enterprise and workers' needs and preferences (by applying practical methods such as questionnaire surveys, interviews, group discussion and workshops); (b) support for the participatory development of plans for new arrangements (by organizing a group involving workers' representatives); and (c) training support for facilitating the group work and bargaining required for consensus building. Locally adapted training support is necessary particularly about: (1) understanding shiftwork effects and generally accepted guidelines; (2) how to find feasible options based on gathered data and these guidelines; and (3) how to cope with shiftwork. Thus support from people experienced in facilitating the well-informed, participatory process of change will need to be developed for promoting the improvement of shiftworking conditions.