A Prediction Divergence Criterion for Model Selection

The problem of model selection is inevitable in an increasingly large number of applications involving partial theoretical knowledge and vast amounts of information, like in medicine, biology or economics. The associated techniques are intended to determine which variables are "important" to "explain a phenomenon under investigation. The terms "important" and "explain" can have very different meanings according to the context and, in fact, model selection can be applied to any situation where one tries to balance variability with complexity. In this paper, we introduce a new class of error measures and of model selection criteria, to which many well know selection criteria belong. Moreover, this class enables us to derive a novel criterion, based on a divergence measure between the predictions produced by two nested models, called the Prediction Divergence Criterion (PDC). Our selection procedure is developed for linear regression models, but has the potential to be extended to other models. We demonstrate that, under some regularity conditions, it is asymptotically loss efficient and can also be consistent. In the linear case, the PDC is a counterpart to Mallow's Cp but with a lower asymptotic probability of overfitting. In a case study and by means of simulations, the PDC is shown to be particularly well suited in "sparse" settings with correlated covariates which we believe to be common in real applications.Comment: 56 page

Humidity-insensitive water evaporation from molecular complex fluids

We investigated theoretically water evaporation from concentrated supramolecular mixtures, such as solutions of polymers or amphiphilic molecules, using numerical resolutions of a one dimensional model based on mass transport equations. Solvent evaporation leads to the formation of a concentrated solute layer at the drying interface, which slows down evaporation in a long-time scale regime. In this regime, often referred to as the falling rate period, evaporation is dominated by diffusive mass transport within the solution, as already known. However, we demonstrate that, in this regime, the rate of evaporation does not also depend on the ambient humidity for many molecular complex fluids. Using analytical solutions in some limiting cases, we first demonstrate that a sharp decrease of the water chemical activity at high solute concentration, leads to evaporation rates which depend weakly on the humidity, as the solute concentration at the drying interface slightly depends on the humidity. However, we also show that a strong decrease of the mutual diffusion coefficient of the solution enhances considerably this effect, leading to nearly independent evaporation rates over a wide range of humidity. The decrease of the mutual diffusion coefficient indeed induces strong concentration gradients at the drying interface, which shield the concentration profiles from humidity variations, except in a very thin region close to the drying interface.Comment: 13 pages, 10 figure

Unusual presentation of acute annular urticaria: A case report

Acute urticarial lesions may display central clearing with ecchymotic or haemorrhagic hue, often misdiagnosed as erythema multiforme, serum-sickness-like reactions, or urticarial vasculitis. We report a case of acute annular urticaria with unusual presentation occurring in a 20-month-old child to emphasize the distinctive morphologic manifestations in a single disease. Clinicians who care for children should be able to differentiate acute urticaria from its clinical mimics. A directed history and physical examination can reliably orientate necessary diagnostic testing and allow for appropriate treatment

A Study of the Allan Variance for Constant-Mean Non-Stationary Processes

The Allan Variance (AV) is a widely used quantity in areas focusing on error measurement as well as in the general analysis of variance for autocorrelated processes in domains such as engineering and, more specifically, metrology. The form of this quantity is widely used to detect noise patterns and indications of stability within signals. However, the properties of this quantity are not known for commonly occurring processes whose covariance structure is non-stationary and, in these cases, an erroneous interpretation of the AV could lead to misleading conclusions. This paper generalizes the theoretical form of the AV to some non-stationary processes while at the same time being valid also for weakly stationary processes. Some simulation examples show how this new form can help to understand the processes for which the AV is able to distinguish these from the stationary cases and hence allow for a better interpretation of this quantity in applied cases