Eliciting density ratio classes

AbstractThe probability distributions of uncertain quantities needed for predictive modelling and decision support are frequently elicited from subject matter experts. However, experts are often uncertain about quantifying their beliefs using precise probability distributions. Therefore, it seems natural to describe their uncertain beliefs using sets of probability distributions. There are various possible structures, or classes, for defining set membership of continuous random variables. The Density Ratio Class has desirable properties, but there is no established procedure for eliciting this class. Thus, we propose a method for constructing Density Ratio Classes that builds on conventional quantile or probability elicitation, but allows the expert to state intervals for these quantities. Parametric shape functions, ideally also suggested by the expert, are then used to bound the nonparametric set of shapes of densities that belong to the class and are compatible with the stated intervals. This leads to a natural metric for the size of the class based on the ratio of the total areas under upper and lower bounding shape functions. This ratio will be determined by the characteristics of the shape functions, the scatter of the elicited values, and the explicit expert imprecision, as characterized by the width of the stated intervals. We provide some examples, both didactic and real, and conclude with recommendations for the further development and application of the Density Ratio Class

Endocrine regulation of human fetal growth: The role of the mother placenta and fetus

© 2006 by The Endocrine SocietyThe environment in which the fetus develops is critical for its survival and long-term health. The regulation of normal human fetal growth involves many multidirectional interactions between the mother, placenta, and fetus. The mother supplies nutrients and oxygen to the fetus via the placenta. The fetus influences the provision of maternal nutrients via the placental production of hormones that regulate maternal metabolism. The placenta is the site of exchange between mother and fetus and regulates fetal growth via the production and metabolism of growth-regulating hormones such as IGFs and glucocorticoids. Adequate trophoblast invasion in early pregnancy and increased uteroplacental blood flow ensure sufficient growth of the uterus, placenta, and fetus. The placenta may respond to fetal endocrine signals to increase transport of maternal nutrients by growth of the placenta, by activation of transport systems, and by production of placental hormones to influence maternal physiology and even behavior. There are consequences of poor fetal growth both in the short term and long term, in the form of increased mortality and morbidity. Endocrine regulation of fetal growth involves interactions between the mother, placenta, and fetus, and these effects may program long-term physiology.Vanessa E. Murphy, Roger Smith, Warwick B. Giles and Vicki L. Clifto