Improved Monte Carlo inference for models with additive error

Some statistical models defined in terms of a generating stochastic mechanism have intractable distribution theory, which renders parameter estimation difficult. However, a Monte Carlo estimate of the log-likelihood surface for such a model can be obtained via computation of nonparametric density estimates from simulated realizations of the model. Unfortunately, the bias inherent in density estimation can cause bias in the resulting log-likelihood estimate that alters the location of its maximizer. In this paper a methodology for radically reducing this bias is developed for models with an additive error component. An illustrative example involving a stochastic model of molecular fragmentation and measurement is given.     

Alternative Methods for Computing the Sensitivity of Complex Surveillance Systems

Stochastic scenario trees are a new and popular method by which surveillance systems can be analyzed to demonstrate freedom from pests and disease. For multiple component systems—such as a combination of a serological survey and systematically collected observations—it can be difficult to represent the complete system in a tree because many branches are required to represent complex conditional relationships. Here we show that many of the branches of some scenario trees have identical outcomes and are therefore redundant. We demonstrate how to prune branches and derive compact representations of scenario trees using matrix algebra and Bayesian belief networks. The Bayesian network representation is particularly useful for calculation and exposition. It therefore provides a firm basis for arguing disease freedom in international forums.     

A hybrid genetic algorithm/mathematical programming approach to the multi-family flowshop scheduling problem with lot streaming

This paper presents a hybrid genetic algorithm/mathematical programming heuristic for the n-job, m-machine flowshop problems with lot streaming. The number of sublots for each job and the size of sublots are directly addressed by the heuristic and setups may be sequence-dependent. A new aspect of the problem, the interleaving of sublots from different jobs in the processing sequence, is developed and addressed. Computational results from 12 randomly generated test sets of 24 problems each are presented.     

Confronting Anxiety in Couple and Family Therapy Supervision: A Developmental Supervisory Model Based on Attachment Theory

Referencing relevant supervisory literature and attachment theory, this article presents a developmental couple and family therapy supervisory model that emphasises the efficacy of the supervisory relationship. Issues concerning anxiety, cognition and learning theory are addressed and phases in the supervisory process are identified and described. Cognitive, emotional and social development are linked to attachment theory and discussed in the supervisory context.     

EFFECTS OF EXPOSURE ON PREVALENCE AND CUMULATIVE RELATIVE RISK: DIRECT AND INDIRECT EFFECTS IN A RECURSIVE HAZARD MODEL

This paper outlines decomposition methods for assessing how exposure affects prevalence and cumulative relative risk. Let     x     denote a vector of exogenous covariates and suppose that a single dimension of time   t   governs two event processes     T ₁  and   T ₂.    If the occurrence of the event     T ₁    determines entry into the risk of the event     T ₂,    then subgroup variation in     T ₁    will affect the prevalence     T ₂,    even if subgroups in the population are otherwise identical. Although researchers often acknowledge this phenomenon, the literature has not provided procedures to assess the magnitude of an exposure effect of     T ₁    on the prevalence of     T ₂.    We derive decompositions that assess how variation in exposure generated by direct and indirect effects of the covariates     x     affect measures of absolute and relative prevalence of     T ₂.    We employ a parametric but highly flexible specification for baseline hazard for the     T ₁  and   T ₂    processes and use the resulting parametric proportional hazard model to illustrate the direct and indirect effects of family structure when     T ₁    is age at first sexual intercourse and     T ₂    is age at a premarital first birth for data on a cohort of non-hispanic white U.S. women.     

Analysis of Regional Scale Risk of Whirling Disease in Populations of Colorado and Rio Grande Cutthroat Trout Using a Bayesian Belief Network Model

Introduction and spread of the parasite Myxobolus cerebralis, the causative agent of whirling disease, has contributed to the collapse of wild trout populations throughout the intermountain west. Of concern is the risk the disease may have on conservation and recovery of native cutthroat trout. We employed a Bayesian belief network to assess probability of whirling disease in Colorado River and Rio Grande cutthroat trout (Oncorhynchus clarkii pleuriticus and Oncorhynchus clarkii virginalis, respectively) within their current ranges in the southwest United States. Available habitat (as defined by gradient and elevation) for intermediate oligochaete worm host, Tubifex tubifex, exerted the greatest influence on the likelihood of infection, yet prevalence of stream barriers also affected the risk outcome. Management areas that had the highest likelihood of infected Colorado River cutthroat trout were in the eastern portion of their range, although the probability of infection was highest for populations in the southern, San Juan subbasin. Rio Grande cutthroat trout had a relatively low likelihood of infection, with populations in the southernmost Pecos management area predicted to be at greatest risk. The Bayesian risk assessment model predicted the likelihood of whirling disease infection from its principal transmission vector, fish movement, and suggested that barriers may be effective in reducing risk of exposure to native trout populations. Data gaps, especially with regard to location of spawning, highlighted the importance in developing monitoring plans that support future risk assessments and adaptive management for subspecies of cutthroat trout.     

A Note on the Large Sample Properties of Estimators Based on Generalized Linear Models for Correlated Pseudo‐observations

Pseudo‐values have proven very useful in censored data analysis in complex settings such as multi‐state models. It was originally suggested by Andersen et al., Biometrika, 90, 2003, 335 who also suggested to estimate standard errors using classical generalized estimating equation results. These results were studied more formally in Graw et al., Lifetime Data Anal., 15, 2009, 241 that derived some key results based on a second‐order von Mises expansion. However, results concerning large sample properties of estimates based on regression models for pseudo‐values still seem unclear. In this paper, we study these large sample properties in the simple setting of survival probabilities and show that the estimating function can be written as a U‐statistic of second order giving rise to an additional term that does not vanish asymptotically. We further show that previously advocated standard error estimates will typically be too large, although in many practical applications the difference will be of minor importance. We show how to estimate correctly the variability of the estimator. This is further studied in some simulation studies.     

Validation of Nonparametric Two-sample Bootstrap in ROC Analysis on Large Datasets

The nonparametric two-sample bootstrap is applied to computing uncertainties of measures in receiver operating characteristic (ROC) analysis on large datasets in areas such as biometrics, speaker recognition, etc. when the analytical method cannot be used. Its validation was studied by computing the standard errors of the area under ROC curve using the well-established analytical Mann–Whitney statistic method and also using the bootstrap. The analytical result is unique. The bootstrap results are expressed as a probability distribution due to its stochastic nature. The comparisons were carried out using relative errors and hypothesis testing. These match very well. This validation provides a sound foundation for such computations.