Bayesian prediction of waiting times in stochastic models

The authors show how saddlepoint techniques lead to highly accurate approximations for Bayesian predictive densities and cumulative distribution functions in stochastic model settings where the prior is tractable, but not necessarily the likelihood or the predictand distribution. They consider more specifically models involving predictions associated with waiting times for semi‐Markov processes whose distributions are indexed by an unknown parameter θ. Bayesian prediction for such processes when they are not stationary is also addressed and the inverse‐Gaussian based saddlepoint approximation of Wood, Booth & Butler (1993) is shown to accurately deal with the nonstationarity whereas the normal‐based Lugannani & Rice (1980) approximation cannot, Their methods are illustrated by predicting various waiting times associated with M/M/q and M/G/1 queues. They also discuss modifications to the matrix renewal theory needed for computing the moment generating functions that are used in the saddlepoint methods.     

On predictive distributions and Bayesian networks

In this paper we are interested in discrete prediction problems for a decision-theoretic setting, where the task is to compute the predictive distribution for a finite set of possible alternatives. This question is first addressed in a general Bayesian framework, where we consider a set of probability distributions defined by some parametric model class. Given a prior distribution on the model parameters and a set of sample data, one possible approach for determining a predictive distribution is to fix the parameters to the instantiation with the maximum a posteriori probability. A more accurate predictive distribution can be obtained by computing the evidence (marginal likelihood), i.e., the integral over all the individual parameter instantiations. As an alternative to these two approaches, we demonstrate how to use Rissanen's new definition of stochastic complexity for determining predictive distributions, and show how the evidence predictive distribution with Jeffrey's prior approaches the new stochastic complexity predictive distribution in the limit with increasing amount of sample data. To compare the alternative approaches in practice, each of the predictive distributions discussed is instantiated in the Bayesian network model family case. In particular, to determine Jeffrey's prior for this model family, we show how to compute the (expected) Fisher information matrix for a fixed but arbitrary Bayesian network structure. In the empirical part of the paper the predictive distributions are compared by using the simple tree-structured Naive Bayes model, which is used in the experiments for computational reasons. The experimentation with several public domain classification datasets suggest that the evidence approach produces the most accurate predictions in the log-score sense. The evidence-based methods are also quite robust in the sense that they predict surprisingly well even when only a small fraction of the full training set is used.     

Confidence intervals for secondary parameters following a sequential test

In sequential studies, formal interim analyses are usually restricted to a consideration of a single null hypothesis concerning a single parameter of interest. Valid frequentist methods of hypothesis testing and of point and interval estimation for the primary parameter have already been devised for use at the end of such a study. However, the completed data set may warrant a more detailed analysis, involving the estimation of parameters corresponding to effects that were not used to determine when to stop, and yet correlated with those that were. This paper describes methods for setting confidence intervals for secondary parameters in a way which provides the correct coverage probability in repeated frequentist realizations of the sequential design used. The method assumes that information accumulates on the primary and secondary parameters at proportional rates. This requirement will be valid in many potential applications, but only in limited situations in survival analysis.     

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.     

Confidence intervals based on the deviance statistic for the hyperparameters in state space models

The main objective of this work is to evaluate the performance of confidence intervals, built using the deviance statistic, for the hyperparameters of state space models. The first procedure is a marginal approximation to confidence regions, based on the likelihood test, and the second one is based on the signed root deviance profile. Those methods are computationally efficient and are not affected by problems such as intervals with limits outside the parameter space, which can be the case when the focus is on the variances of the errors. The procedures are compared to the usual approaches existing in the literature, which includes the method based on the asymptotic distribution of the maximum likelihood estimator, as well as bootstrap confidence intervals. The comparison is performed via a Monte Carlo study, in order to establish empirically the advantages and disadvantages of each method. The results show that the methods based on the deviance statistic possess a better coverage rate than the asymptotic and bootstrap procedures.     

Maternal Postpartum Depression Increases Vulnerability for Toddler Behavior Problems through Infant Cortisol Reactivity

The current study examined the role of hypothalamic‐pituitary‐adrenal reactivity (a physiological indicator of stress) in early infancy as a mediator of the relationship between maternal postpartum depression and toddler behavior problems. Participants were 137 at‐risk mothers and their children participating in a longitudinal study of intergenerational transmission of risk. Mothers’ depression was measured five times during the infants’ first 18 months. Infant cortisol was collected during a social stressor (the still‐face paradigm) when infants were 6 months old, and mothers reported on toddlers’ internalizing and externalizing symptoms at 18 months. Among this sample of high‐risk mother–infant dyads, early postpartum depression predicted atypical infant cortisol reactivity at 6 months, which mediated the effect of maternal depression on increased toddler behavior problems. Clinical implications are discussed.     

The Importance of Racial Socialization: School‐Based Racial Discrimination and Racial Identity Among African American Adolescent Boys and Girls

This study examined various parental racial socialization messages as mediators between school‐based racial discrimination and racial identity formation over 4 years for African American boys (N = 639) and African American girls (N = 711). Findings indicated that school‐based racial discrimination was associated with racial identity beliefs. For African American boys, behavioral racial socialization messages mediated the relation between school‐based racial discrimination and racial centrality over time. Mediation also resulted for African American girls, but for a different set of race‐related messages (negative messages and racial barriers) and racial identity beliefs. The developmental significance of the findings and implications for future research are discussed.     

Interplay Between Sensation Seeking and Parental Rules in the Emergence of Heavy Episodic Drinking

This study examined the parallel mediational processes between sensation seeking and parental rules on alcohol, in the emergence of heavy episodic drinking (HED) in adolescents. Data were drawn from a U.K. clustered randomized control trial (control arm only, N ≈ 6,300, M_age at baseline = 12.5). Using parallel process latent growth curve analysis, stricter parental rules at baseline were found to be associated with greater declines in sensation seeking over time and a lower risk of HED at follow‐up (+33 months). Higher initial levels of sensation seeking predicted a faster relaxation of parental rules and a greater risk of HED. By maintaining strict rules about alcohol, parents may promote a positive reduction in sensation seeking and a lower risk of HED.     

Association between sexually explicit messages and sleep health among French sexual minority men

It has been demonstrated that sexual minority men (SMM) participate in sexting. While research has shown that engagement in the exchange of sexually explicit media is associated with poor health outcomes, no previous research has investigated its association with sleep health outcomes. This study sought to examine the association between sexually explicit media and sleep health among SMM, a population that suffers from poor sleep health. A popular geosocial networking application was used to recruit SMM individuals (N?=?580) in the Paris, France, metropolitan area. Multivariate analyses, adjusting for sociodemographics, were used to test the association between the frequency of sexually explicit messaging and three dimensions of sleep health: (1) sleep quality, (2) sleep duration, and (3) two aspects of sleep problems. In multivariate analyses, those who reported engaging in sexually explicit messaging more were more likely to report getting less than seven?hours of sleep (aRR = 1.24; 95% CI = 1.08, 1.43) compared with those who reported engaging in sexually explicit messaging less. No significant associations were found between sexting and sleep quality or reporting sleep problems. Sexually explicit messaging was associated with shorter sleep duration. Intervention targeted at individuals who sext could potentially improve sleep health outcomes.     

Downsizing for downtown: limb lengths,toe lengths,and scale counts decrease with urbanization in western fence lizards (Sceloporus occidentalis)

Urban Ecosystems - Urbanization-induced habitat loss and alteration causes significant challenges for the survival of many species. Identifying how species respond to urbanization can yield...