Simulating interventions in graphical chain models for longitudinal data

Simulating the outcome of an intervention is a central problem in many fields as this allows decision-makers to quantify the effect of any given strategy and, hence, to evaluate different schemes of actions. Simulation is particularly relevant in very large systems where the statistical model involves many variables that, possibly, interact with each other. In this case one usually has a large number of parameters whose interpretation becomes extremely difficult. Furthermore, in a real system, although one may have a unique target variable, there may be a number of variables which might, and often should, be logically considered predictors of the target outcome and, at the same time, responses of other variables of the system. An intervention taking place on a given variable, therefore, may affect the outcome either directly and indirectly though the way in which it affects other variables within the system. Graphical chain models are particularly helpful in depicting all of the paths through which an intervention may affect the final outcome. Furthermore, they identify all of the relevant conditional distributions and therefore they are particularly useful in driving the simulation process. Focussing on binary variables, we propose a method to simulate the effect of an intervention. Our approach, however, can be easily extended to continuous and mixed responses variables. We apply the proposed methodology to assess the effect that a policy intervention may have on poorer health in early adulthood using prospective data provided by the 1970 British Birth Cohort Study (BCS70).chain graph, conditional approach, Gibbs Sampling, Simulation of interventions, age at motherhood, mental health

The manifest association structure of the single-factor model: insights from partial correlations

The association structure between manifest variables arising from the single-factor model is investigated using partial correlations. The additional insights to the practitioner provided by partial correlations for detecting a single-factor model are discussed. The parameter space for the partial correlations is presented, as are the patterns of signs in a matrix containing the partial correlations that are not compatible with a single-factor model

Renormalized Vacuum Polarization and Stress Tensor on the Horizon of a Schwarzschild Black Hole Threaded by a Cosmic String

We calculate the renormalized vacuum polarization and stress tensor for a massless, arbitrarily coupled scalar field in the Hartle-Hawking vacuum state on the horizon of a Schwarzschild black hole threaded by an infinte straight cosmic string. This calculation relies on a generalized Heine identity for non-integer Legendre functions which we derive without using specific properties of the Legendre functions themselves.Comment: This is an expanded version of a previous submission, we have added the calculation of the stress tensor. 28 pages, 7 figure

Non-equilibrium dynamics and floral trait interactions shape extant angiosperm diversity.

Why are some traits and trait combinations exceptionally common across the tree of life, whereas others are vanishingly rare? The distribution of trait diversity across a clade at any time depends on the ancestral state of the clade, the rate at which new phenotypes evolve, the differences in speciation and extinction rates across lineages, and whether an equilibrium has been reached. Here we examine the role of transition rates, differential diversification (speciation minus extinction) and non-equilibrium dynamics on the evolutionary history of angiosperms, a clade well known for the abundance of some trait combinations and the rarity of others. Our analysis reveals that three character states (corolla present, bilateral symmetry, reduced stamen number) act synergistically as a key innovation, doubling diversification rates for lineages in which this combination occurs. However, this combination is currently less common than predicted at equilibrium because the individual characters evolve infrequently. Simulations suggest that angiosperms will remain far from the equilibrium frequencies of character states well into the future. Such non-equilibrium dynamics may be common when major innovations evolve rarely, allowing lineages with ancestral forms to persist, and even outnumber those with diversification-enhancing states, for tens of millions of years

The Role of Polycyclic Aromatic Hydrocarbons in Ultraviolet Extinction. I. Probing small molecular PAHs

We have obtained new STIS/HST spectra to search for structure in the ultraviolet interstellar extinction curve, with particular emphasis on a search for absorption features produced by polycyclic aromatic hydrocarbons (PAHs). The presence of these molecules in the interstellar medium has been postulated to explain the infrared emission features seen in the 3-13 $\mu$m spectra of numerous sources. UV spectra are uniquely capable of identifying specific PAH molecules. We obtained high S/N UV spectra of stars which are significantly more reddened than those observed in previous studies. These data put limits on the role of small (30-50 carbon atoms) PAHs in UV extinction and call for further observations to probe the role of larger PAHs. PAHs are of importance because of their ubiquity and high abundance inferred from the infrared data and also because they may link the molecular and dust phases of the interstellar medium. A presence or absence of ultraviolet absorption bands due to PAHs could be a definitive test of this hypothesis. We should be able to detect a 20 \AA wide feature down to a 3$\sigma$ limit of $\sim$0.02 A$_V$. No such absorption features are seen other than the well-known 2175 \AA bump.Comment: 16 pages, 3 figure, ApJ in pres

Model-based inference from microvascular measurements: Combining experimental measurements and model predictions using a Bayesian probabilistic approach

Objective: In vivo imaging of the microcirculation and network-oriented modeling have emerged as powerful means of studying microvascular function and understanding its physiological significance. Network-oriented modeling may provide the means of summarizing vast amounts of data produced by high-throughput imaging techniques in terms of key, physiological indices. To estimate such indices with sufficient certainty, however, network-oriented analysis must be robust to the inevitable presence of uncertainty due to measurement errors as well as model errors. Methods: We propose the Bayesian probabilistic data analysis framework as a means of integrating experimental measurements and network model simulations into a combined and statistically coherent analysis. The framework naturally handles noisy measurements and provides posterior distributions of model parameters as well as physiological indices associated with uncertainty. Results: We applied the analysis framework to experimental data from three rat mesentery networks and one mouse brain cortex network. We inferred distributions for more than 500 unknown pressure and hematocrit boundary conditions. Model predictions were consistent with previous analyses, and remained robust when measurements were omitted from model calibration. Conclusion: Our Bayesian probabilistic approach may be suitable for optimizing data acquisition and for analyzing and reporting large data sets acquired as part of microvascular imaging studies