The shuffle estimator for explainable variance in fMRI experiments

In computational neuroscience, it is important to estimate well the proportion of signal variance in the total variance of neural activity measurements. This explainable variance measure helps neuroscientists assess the adequacy of predictive models that describe how images are encoded in the brain. Complicating the estimation problem are strong noise correlations, which may confound the neural responses corresponding to the stimuli. If not properly taken into account, the correlations could inflate the explainable variance estimates and suggest false possible prediction accuracies. We propose a novel method to estimate the explainable variance in functional MRI (fMRI) brain activity measurements when there are strong correlations in the noise. Our shuffle estimator is nonparametric, unbiased, and built upon the random effect model reflecting the randomization in the fMRI data collection process. Leveraging symmetries in the measurements, our estimator is obtained by appropriately permuting the measurement vector in such a way that the noise covariance structure is intact but the explainable variance is changed after the permutation. This difference is then used to estimate the explainable variance. We validate the properties of the proposed method in simulation experiments. For the image-fMRI data, we show that the shuffle estimates can explain the variation in prediction accuracy for voxels within the primary visual cortex (V1) better than alternative parametric methods.Comment: Published in at http://dx.doi.org/10.1214/13-AOAS681 the Annals of Applied Statistics (http://www.imstat.org/aoas/) by the Institute of Mathematical Statistics (http://www.imstat.org

Geoadditive Regression Modeling of Stream Biological Condition

Indices of biotic integrity (IBI) have become an established tool to quantify the condition of small non-tidal streams and their watersheds. To investigate the effects of watershed characteristics on stream biological condition, we present a new technique for regressing IBIs on watershed-specific explanatory variables. Since IBIs are typically evaluated on anordinal scale, our method is based on the proportional odds model for ordinal outcomes. To avoid overfitting, we do not use classical maximum likelihood estimation but a component-wise functional gradient boosting approach. Because component-wise gradient boosting has an intrinsic mechanism for variable selection and model choice, determinants of biotic integrity can be identified. In addition, the method offers a relatively simple way to account for spatial correlation in ecological data. An analysis of the Maryland Biological Streams Survey shows that nonlinear effects of predictor variables on stream condition can be quantified while, in addition, accurate predictions of biological condition at unsurveyed locations are obtained

Density-dependent, central-place foraging in a grazing herbivore: competition and tradeoffs in time allocation near water

Optimal foraging theory addresses one of the core challenges of ecology: predicting the distribution and abundance of species. Tests of hypotheses of optimal foraging, however, often focus on a single conceptual model rather than drawing upon the collective body of theory, precluding generalization. Here we demonstrate links between two established theoretical frameworks predicting animal movements and resource use: central-place foraging and density-dependent habitat selection. Our goal is to better understand how the nature of critical, centrally placed resources like water (or minerals, breathing holes, breeding sites, etc.) might govern selection for food (energy) resources obtained elsewhere - a common situation for animals living in natural conditions. We empirically test our predictions using movement data from a large herbivore distributed along a gradient of water availability (feral horses, Sable Island, Canada, 2008–2013). Horses occupying western Sable Island obtain freshwater at ponds while in the east horses must drink at self-excavated wells (holes). We studied the implications of differential access to water (time needed for a horse to obtain water) on selection for vegetation associations. Consistent with predictions of density-dependent habitat selection, horses were reduced to using poorer-quality habitat (heathland) more than expected close to water (where densities were relatively high), but were free to select for higher-quality grasslands farther from water. Importantly, central-place foraging was clearly influenced by the type of water-source used (ponds vs. holes, the latter with greater time constraints on access). Horses with more freedom to travel (those using ponds) selected for grasslands at greater distances and continued to select grasslands at higher densities, whereas horses using water holes showed very strong density-dependence in how habitat could be selected. Knowledge of more than one theoretical framework may be required to explain observed variation in foraging behavior of animals where multiple constraints simultaneously influence resource selection