Consistency of Bayesian Linear Model Selection With a Growing Number of Parameters

Linear models with a growing number of parameters have been widely used in modern statistics. One important problem about this kind of model is the variable selection issue. Bayesian approaches, which provide a stochastic search of informative variables, have gained popularity. In this paper, we will study the asymptotic properties related to Bayesian model selection when the model dimension $p$ is growing with the sample size $n$. We consider $p\le n$ and provide sufficient conditions under which: (1) with large probability, the posterior probability of the true model (from which samples are drawn) uniformly dominates the posterior probability of any incorrect models; and (2) with large probability, the posterior probability of the true model converges to one. Both (1) and (2) guarantee that the true model will be selected under a Bayesian framework. We also demonstrate several situations when (1) holds but (2) fails, which illustrates the difference between these two properties. Simulated examples are provided to illustrate the main results

Analysis of binary spatial data by quasi-likelihood estimating equations

The goal of this paper is to describe the application of quasi-likelihood estimating equations for spatially correlated binary data. In this paper, a logistic function is used to model the marginal probability of binary responses in terms of parameters of interest. With mild assumptions on the correlations, the Leonov-Shiryaev formula combined with a comparison of characteristic functions can be used to establish asymptotic normality for linear combinations of the binary responses. The consistency and asymptotic normality for quasi-likelihood estimates can then be derived. By modeling spatial correlation with a variogram, we apply these asymptotic results to test independence of two spatially correlated binary outcomes and illustrate the concepts with a well-known example based on data from Lansing Woods. The comparison of generalized estimating equations and the proposed approach is also discussed.Comment: Published at http://dx.doi.org/10.1214/009053605000000057 in the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

Two Computer Programs for Predicting Exponential Observables

1 online resource (PDF, 7 pages

Bayesian Nonparametric Bandits

1 online resource (PDF, 28 pages

A Comparison of Several Model Selection Procedures

1 online resource (PDF, 28 pages

Combined effects of heat waves and droughts on avian communities across the conterminous United States

Increasing surface temperatures and climatic variability associated with global climate change are expected to produce more frequent and intense heat waves and droughts in many parts of the world. Our goal was to elucidate the fundamental, but poorly understood, effects of these extreme weather events on avian communities across the conterminous United States. Specifically, we explored: (1) the effects of timing and duration of heat and drought events, (2) the effects of jointly occurring drought and heat waves relative to these events occurring in isolation, and (3) how effects vary among functional groups related to nest location and migratory habit, and among ecoregions with differing precipitation and temperature regimes. Using data from remote sensing, meteorological stations, and the North American Breeding Bird Survey, we used mixed effects models to quantify responses of overall and functional group abundance to heat waves and droughts (occurring alone or in concert) at two key periods in the annual cycle of birds: breeding and post-fledging. We also compared responses among species with different migratory and nesting characteristics, and among 17 ecoregions of the conterminous United States. We found large changes in avian abundances related to 100-year extreme weather events occurring in both breeding and post-fledging periods, but little support for an interaction among time periods. We also found that jointly-, rather than individually-occurring heat waves and droughts were both more common and more predictive of abundance changes. Declining abundance was the only significant response to post-fledging events, while responses to breeding period events were larger but could be positive or negative. Negative responses were especially frequent in the western U.S., and among ground-nesting birds and Neotropical migrants, with the largest single-season declines (36%) occurring among ground-nesting birds in the desert Southwest. These results indicate the importance of functional traits, timing, and geography in determining avian responses to weather extremes. Because dispersal to other regions appears to be an important avian response, it may be essential to maintain habitat refugia in a more climatically variable future

Effects of drought on avian community structure

Droughts are expected to become more frequent under global climate change. Avifauna depend on precipitation for hydration, cover, and food. While there are indications that avian communities respond negatively to drought, little is known about the response of birds with differing functional and behavioral traits, what time periods and indicators of drought are most relevant, or how response varies geographically at broad spatial scales. Our goals were thus to determine (1) how avian abundance and species richness are related to drought, (2) whether community variations are more related to vegetation vigor or precipitation deviations and at what time periods relationships were strongest, (3) how response varies among avian guilds, and (4) how response varies among ecoregions with different precipitation regimes. Using mixed effect models and 1989–2005 North American Breeding Bird Survey data over the central United States, we examined the response to 10 precipitation- and greenness based metrics by abundance and species richness of the avian community overall, and of four behavioral guilds. Drought was associated with the most negative impacts on avifauna in the semiarid Great Plains, while positive responses were observed in montane areas. Our models predict that in the plains, Neotropical migrants respond the most negatively to extreme drought, decreasing by 13.2% and 6.0% in abundance and richness, while permanent resident abundance and richness increase by 11.5% and 3.6%, respectively in montane areas. In most cases, response of abundance was greater than richness and models based on precipitation metrics spanning 32-week time periods were more supported than those covering shorter time periods and those based on greenness. While drought is but one of myriad environmental variations birds encounter, our results indicate that drought is capable of imposing sizable shifts in abundance, richness, and composition on avian communities, an important implication of a more climatically variable future

Lifting the Veil of Dust from NGC 0959: The Importance of a Pixel-Based 2D Extinction Correction

We present the results of a study of the late-type spiral galaxy NGC 0959, before and after application of the pixel-based dust extinction correction described in Tamura et al. 2009 (Paper I). Galaxy Evolution Explorer (GALEX) far-UV (FUV) and near-UV (NUV), ground-based Vatican Advanced Technology Telescope (VATT) UBVR, and Spitzer/Infrared Array Camera (IRAC) 3.6, 4.5, 5.8, and 8.0 micron images are studied through pixel Color-Magnitude Diagrams (pCMDs) and pixel Color-Color Diagrams (pCCDs). We define groups of pixels based on their distribution in a pCCD of (B - 3.6 micron) versus (FUV - U) colors after extinction correction. In the same pCCD, we trace their locations before the extinction correction was applied. This shows that selecting pixel groups is not meaningful when using colors uncorrected for dust. We also trace the distribution of the pixel groups on a pixel coordinate map of the galaxy. We find that the pixel-based (two-dimensional) extinction correction is crucial to reveal the spatial variations in the dominant stellar population, averaged over each resolution element. Different types and mixtures of stellar populations, and galaxy structures such as a previously unrecognized bar, become readily discernible in the extinction-corrected pCCD and as coherent spatial structures in the pixel coordinate map.Comment: 10 pages, LaTeX2e requires 'emulateapj.cls', 'graphicx.sty', and 'natbib.sty' (included), 9 postscript figures, 1 table. Accepted for publication in AJ