Prevalence and strength of density-dependent tree recruitment.

Density dependence could maintain diversity in forests, but studies continue to disagree on its role. Part of the disagreement results from the fact that different studies have evaluated different responses (survival, recruitment, or growth) of different stages (seeds, seedlings, or adults) to different inputs (density of seedlings, density or distance to adults). Most studies are conducted on a single site and thus are difficult to generalize. Using USDA Forest Service's Forest Inventory and Analysis data, we analyzed over a million seedling-to-sapling recruitment observations of 50 species from the eastern United States, controlling for the effects of climate. We focused on the per-seedling recruitment rate, because it is most likely to promote diversity and to be identified in observational or experimental data. To understand the prevalence of density dependence, we quantified the number of species with significant positive or negative effects. To understand the strength of density dependence, we determined the magnitude of effects among con- and heterospecifics, and how it changes with overall species abundance. We found that density dependence is pervasive among the 50 species, as the majority of them have significant effects and mostly negative. Density-dependence effects are stronger from conspecific than heterospecfic adult neighbors, consistent with the predictions of the Janzen-Connell hypothesis. Contrary to recent reports, density-dependence effects are more negative for common than rare species, suggesting disproportionately stronger population regulation in common species. We conclude that density dependence is pervasive, and it is strongest from conspecific neighbors of common species. Our analysis provides direct evidence that density dependence reaulates opulation dynamics of tree species in eastern U.S. forests.

Bayesian Modeling for Physical Processes in Industrial Hygiene Using Misaligned Workplace Data.

In industrial hygiene, a worker's exposure to chemical, physical, and biological agents is increasingly being modeled using deterministic physical models that study exposures near and farther away from a contaminant source. However, predicting exposure in the workplace is challenging and simply regressing on a physical model may prove ineffective due to biases and extraneous variability. A further complication is that data from the workplace are usually misaligned. This means that not all timepoints measure concentrations near and far from the source. We recognize these challenges and outline a flexible Bayesian hierarchical framework to synthesize the physical model with the field data. We reckon that the physical model, by itself, is inadequate for enhanced inferential and predictive performance and deploy (multivariate) Gaussian processes to capture uncertainties and associations. We propose rich covariance structures for multiple outcomes using latent stochastic processes. This article has supplementary material available online.

The Polya Tree Sampler: Towards Efficient and Automatic Independent Metropolis-Hastings Proposals.

We present a simple, efficient, and computationally cheap sampling method for exploring an un-normalized multivariate density on ℝ(d), such as a posterior density, called the Polya tree sampler. The algorithm constructs an independent proposal based on an approximation of the target density. The approximation is built from a set of (initial) support points - data that act as parameters for the approximation - and the predictive density of a finite multivariate Polya tree. In an initial "warming-up" phase, the support points are iteratively relocated to regions of higher support under the target distribution to minimize the distance between the target distribution and the Polya tree predictive distribution. In the "sampling" phase, samples from the final approximating mixture of finite Polya trees are used as candidates which are accepted with a standard Metropolis-Hastings acceptance probability. Several illustrations are presented, including comparisons of the proposed approach to Metropolis-within-Gibbs and delayed rejection adaptive Metropolis algorithm.

A misclassification model for the non-disjunction fraction in meiosis I.

In this paper we introduce a misclassification model for the meiosis I non-disjunction fraction in numerical chromosomal anomalies named trisomies. We obtain posteriors, and their moments, for the probability that a non-disjunction occurs in the first division of meiosis and for the misclassification errors. We also extend previous works by providing the exact posterior, and its moments, for the probability that a non-disjunction occurs in the first division of meiosis assuming the model proposed in the literature which does not consider that data are subject to misclassification. We perform Monte Carlo studies in order to compare Bayes estimates obtained by using both models. An application to Down Syndrome data is also presented.

Testing and estimating the non-disjunction fraction in Meiosis I using reference priors.

In this paper we analyze the fraction of non-disjunction in Meiosis I assuming reference (non-informative) priors. We consider Jeffreys's approach to built a non-informative prior (Jeffreys's prior) for the fraction of non-disjunction in Meiosis I. We prove that Jeffreys's prior is a proper distribution. We perform Monte Carlo studies in order to compare Bayes estimates obtained assuming Jeffreys's and uniform priors. We consider full Bayesian significance test (FBST) and Bayes factor (BF) for testing precise hypothesis on the fraction of non-disjunction in Meiosis I. The ultimate goal of this paper is to compare these two test procedures through simulation studies using both prior specifications. An application to Down Syndrome data is also presented.