Batch means and spectral variance estimators in Markov chain Monte Carlo

Calculating a Monte Carlo standard error (MCSE) is an important step in the statistical analysis of the simulation output obtained from a Markov chain Monte Carlo experiment. An MCSE is usually based on an estimate of the variance of the asymptotic normal distribution. We consider spectral and batch means methods for estimating this variance. In particular, we establish conditions which guarantee that these estimators are strongly consistent as the simulation effort increases. In addition, for the batch means and overlapping batch means methods we establish conditions ensuring consistency in the mean-square sense which in turn allows us to calculate the optimal batch size up to a constant of proportionality. Finally, we examine the empirical finite-sample properties of spectral variance and batch means estimators and provide recommendations for practitioners.Comment: Published in at http://dx.doi.org/10.1214/09-AOS735 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

Impacts of stratospheric aerosol geoengineering strategy on Caribbean coral reefs

Purpose: Currently, negotiation on global carbon emissions reduction is very difficult due to lack of international willingness. In response, geoengineering (climate engineering) strategy is proposed to artificially cool the planet. Meanwhile, as the harbor around one-third of all described marine species, coral reefs are the most sensitive ecosystem on the planet to climate change. However, until now, there is no any quantitative assessment on impacts of geoengineering on coral reefs. In this study, we model impacts of stratospheric aerosol geoengineering on coral reefs. Design/methodology/approach: We will use the HadGEM2-ES climate model to model and evaluate impacts of stratospheric aerosol geoengineering on coral reefs. Findings: This study shows that a) stratospheric aerosol geoengineering could significantly mitigate future coral bleaching throughout the Caribbean Sea; b) Changes in downward solar irradiation, sea level rise and sea surface temperature caused by geoengineering implementation should have very little impacts on coral reefs; c) although geoengineering would prolong the return period of future hurricanes, this may still be too short to ensure coral recruitment and survival after hurricane damage

Tachyon Defect Formation and Reheating in Brane-Antibrane Inflation

We study analytically the dynamical formation of lower dimensional branes at the endpoint of brane-antibrane inflation through the condensation of topological defects of the tachyon field which describes the instability of the initial state. We then use this information to quantify the efficiency of the reheating which is due to the coupling of time dependent tachyon background to massless gauge fields which will be localized on the final state branes. We improve upon previous estimates indicating that this can be an efficient reheating mechanism for observers on the brane.Comment: 9 pages. Talk given at the 26th annual Montreal-Rochester-Syracuse-Toronto Conference on High-Energy Physics: MRST 200

Illinois Forest Game Investigations W-87-R-9, Quarterly Federal Aid Performance Report 1 July - 30 September 1987

Quarterly Federal Aid Performance Report W-87-R-9, 1 July - 30 September 1987; Study No. VII-D Harvest Strategies for Illinois Deer Herds, Urban Deer StudyReport issued on: September 30, 1987INHS Technical Report prepared for unspecified recipien