A Multi-objective Exploratory Procedure for Regression Model Selection

Variable selection is recognized as one of the most critical steps in statistical modeling. The problems encountered in engineering and social sciences are commonly characterized by over-abundance of explanatory variables, non-linearities and unknown interdependencies between the regressors. An added difficulty is that the analysts may have little or no prior knowledge on the relative importance of the variables. To provide a robust method for model selection, this paper introduces the Multi-objective Genetic Algorithm for Variable Selection (MOGA-VS) that provides the user with an optimal set of regression models for a given data-set. The algorithm considers the regression problem as a two objective task, and explores the Pareto-optimal (best subset) models by preferring those models over the other which have less number of regression coefficients and better goodness of fit. The model exploration can be performed based on in-sample or generalization error minimization. The model selection is proposed to be performed in two steps. First, we generate the frontier of Pareto-optimal regression models by eliminating the dominated models without any user intervention. Second, a decision making process is executed which allows the user to choose the most preferred model using visualisations and simple metrics. The method has been evaluated on a recently published real dataset on Communities and Crime within United States.Comment: in Journal of Computational and Graphical Statistics, Vol. 24, Iss. 1, 201

Tidal Evolution of Close Binary Asteroid Systems

We provide a generalized discussion of tidal evolution to arbitrary order in the expansion of the gravitational potential between two spherical bodies of any mass ratio. To accurately reproduce the tidal evolution of a system at separations less than five times the radius of the larger primary component, the tidal potential due to the presence of a smaller secondary component is expanded in terms of Legendre polynomials to arbitrary order rather than truncated at leading order as is typically done in studies of well-separated system like the Earth and Moon. The equations of tidal evolution including tidal torques, the changes in spin rates of the components, and the change in semimajor axis (orbital separation) are then derived for binary asteroid systems with circular and equatorial mutual orbits. Accounting for higher-order terms in the tidal potential serves to speed up the tidal evolution of the system leading to underestimates in the time rates of change of the spin rates, semimajor axis, and mean motion in the mutual orbit if such corrections are ignored. Special attention is given to the effect of close orbits on the calculation of material properties of the components, in terms of the rigidity and tidal dissipation function, based on the tidal evolution of the system. It is found that accurate determinations of the physical parameters of the system, e.g., densities, sizes, and current separation, are typically more important than accounting for higher-order terms in the potential when calculating material properties. In the scope of the long-term tidal evolution of the semimajor axis and the component spin rates, correcting for close orbits is a small effect, but for an instantaneous rate of change in spin rate, semimajor axis, or mean motion, the close-orbit correction can be on the order of tens of percent.Comment: 40 pages, 2 tables, 8 figure

Forest and woodland replacement patterns following drought-related mortality

Forest vulnerability to drought is expected to increase under anthropogenic climate change, and drought-induced mortality and community dynamics following drought have major ecological and societal impacts. Here, we show that tree mortality concomitant with drought has led to short-term (mean 5 y, range 1 to 23 y after mortality) vegetation-type conversion in multiple biomes across the world (131 sites). Self-replacement of the dominant tree species was only prevalent in 21% of the examined cases and forests and woodlands shifted to nonwoody vegetation in 10% of them. The ultimate temporal persistence of such changes remains unknown but, given the key role of biological legacies in long-term ecological succession, this emerging picture of postdrought ecological trajectories highlights the potential for major ecosystem reorganization in the coming decades. Community changes were less pronounced under wetter postmortality conditions. Replacement was also influenced by management intensity, and postdrought shrub dominance was higher when pathogens acted as codrivers of tree mortality. Early change in community composition indicates that forests dominated by mesic species generally shifted toward more xeric communities, with replacing tree and shrub species exhibiting drier bioclimatic optima and distribution ranges. However, shifts toward more mesic communities also occurred and multiple pathways of forest replacement were observed for some species. Drought characteristics, species-specific environmental preferences, plant traits, and ecosystem legacies govern postdrought species turnover and subsequent ecological trajectories, with potential far-reaching implications for forest biodiversity and ecosystem services