Asymptotic unbiased density estimator

International audienceThis paper introduces a computationally tractable density estimator that has the same asymptotic variance as the classical Nadaraya-Watson density estimator but whose asymptotic bias is zero. We achieve this result using a two stage estimator that applies a multiplicative bias correction to an oversmooth pilot estimator. Simulations show that our asymptotic results are available for samples as low as n = 50, where we see an improvement of as much as 20% over the traditionnal estimator. Mathematics Subject Classification. 62G07, 62G20

Inequity Measures for Evaluations of Environmental Justice: A Case Study of Close Proximity to Highways in NYC

Assessments of environmental and territorial justice are similar in that both assess whether empirical relations between the spatial arrangement of undesirable hazards (or desirable public goods and services) and socio-demographic groups are consistent with notions of social justice, evaluating the spatial distribution of benefits and burdens (outcome equity) and the process that produces observed differences (process equity. Using proximity to major highways in NYC as a case study, we review methodological issues pertinent to both fields and discuss choice and computation of exposure measures, but focus primarily on measures of inequity. We present inequity measures computed from the empirically estimated joint distribution of exposure and demographics and compare them to traditional measures such as linear regression, logistic regression and Theil’s entropy index. We find that measures computed from the full joint distribution provide more unified, transparent and intuitive operational definitions of inequity and show how the approach can be used to structure siting and decommissioning decisions

Stochastic Event Reconstruction of Atmospheric Contaminant Dispersion Using Bayesian Inference

Environmental sensors have been deployed in various cities for early detection of contaminant releases into the atmosphere. Event reconstruction and improved dispersion modeling capabilities are needed to estimate the extent of contamination, which is required to implement effective strategies in emergency management. To this end, a stochastic event reconstruction capability that can process information from an environmental sensor network is developed. A probability model is proposed to take into account both zero and non-zero concentration measurements that can be available from a sensor network because of a sensor’s specified limit of detection. The inference is based on the Bayesian paradigm with Markov chain Monte Carlo (MCMC) sampling. Fast-running Gaussian plume dispersion models are adopted as the forward model in the Bayesian inference approach to achieve rapid-response event reconstructions. The Gaussian plume model is substantially enhanced by introducing stochastic parameters in its turbulent diffusion parameterizations and estimating them within the Bayesian inference framework. Additionally, parameters of the likelihood function are estimated in a principled way using data and prior probabilities to avoid tuning in the overall method, The event reconstruction method is successfully validated for both real and synthetic dispersion problems, and posterior distributions of the model parameters are used to generate probabilistic plume envelopes with specified confidence levels to aid emergency decisions

Computationally Efficient and Error Aware Surrogate Construction for Numerical Solutions of Subsurface Flow Through Porous Media

Limiting the injection rate to restrict the pressure below a threshold at a critical location can be an important goal of simulations that model the subsurface pressure between injection and extraction wells. The pressure is approximated by the solution of Darcy's partial differential equation (PDE) for a given permeability field. The subsurface permeability is modeled as a random field since it is known only up to statistical properties. This induces uncertainty in the computed pressure. Solving the PDE for an ensemble of random permeability simulations enables estimating a probability distribution for the pressure at the critical location. These simulations are computationally expensive, and practitioners often need rapid online guidance for real-time pressure management. An ensemble of numerical PDE solutions is used to construct a Gaussian process regression model that can quickly predict the pressure at the critical location as a function of the extraction rate and permeability realization. Our first novel contribution is to identify a sampling methodology for the random environment and matching kernel technology for which fitting the Gaussian process regression model scales as O(n log n) instead of the typical O(n^3) rate in the number of samples n used to fit the surrogate. The surrogate model allows almost instantaneous predictions for the pressure at the critical location as a function of the extraction rate and permeability realization. Our second contribution is a novel algorithm to calibrate the uncertainty in the surrogate model to the discrepancy between the true pressure solution of Darcy's equation and the numerical solution. Although our method is derived for building a surrogate for the solution of Darcy's equation with a random permeability field, the framework broadly applies to solutions of other PDE with random coefficients.Comment: 20 pages, 8 figures, 1 tabl

Membrane Insertion for the Detection of Lipopolysaccharides: Exploring the Dynamics of Amphiphile-in-Lipid Assays

Shiga toxin-producing Escherichia coli is an important cause of foodborne illness, with cases attributable to beef, fresh produce and other sources. Many serotypes of the pathogen cause disease, and differentiating one serotype from another requires specific identification of the O antigen located on the lipopolysaccharide (LPS) molecule. The amphiphilic structure of LPS poses a challenge when using classical detection methods, which do not take into account its lipoglycan biochemistry. Typically, detection of LPS requires heat or chemical treatment of samples and relies on bioactivity assays for the conserved lipid A portion of the molecule. Our goal was to develop assays to facilitate the direct and discriminative detection of the entire LPS molecule and its O antigen in complex matrices using minimal sample processing. To perform serogroup identification of LPS, we used a method called membrane insertion on a waveguide biosensor, and tested three serogroups of LPS. The membrane insertion technique allows for the hydrophobic association of LPS with a lipid bilayer, where the exposed O antigen can be targeted for specific detection. Samples of beef lysate were spiked with LPS to perform O antigen specific detection of LPS from E. coli O157. To validate assay performance, we evaluated the biophysical interactions of LPS with lipid bilayers both in- and outside of a flow cell using fluorescence microscopy and fluorescently doped lipids. Our results indicate that membrane insertion allows for the qualitative and reliable identification of amphiphilic LPS in complex samples like beef homogenates. We also demonstrated that LPS-induced hole formation does not occur under the conditions of the membrane insertion assays. Together, these findings describe for the first time the serogroup-specific detection of amphiphilic LPS in complex samples using a membrane insertion assay, and highlight the importance of LPS molecular conformations in detection architectures

Accounting for seasonal patterns in syndromic surveillance data for outbreak detection

BACKGROUND: Syndromic surveillance (SS) can potentially contribute to outbreak detection capability by providing timely, novel data sources. One SS challenge is that some syndrome counts vary with season in a manner that is not identical from year to year. Our goal is to evaluate the impact of inconsistent seasonal effects on performance assessments (false and true positive rates) in the context of detecting anomalous counts in data that exhibit seasonal variation. METHODS: To evaluate the impact of inconsistent seasonal effects, we injected synthetic outbreaks into real data and into data simulated from each of two models fit to the same real data. Using real respiratory syndrome counts collected in an emergency department from 2/1/94–5/31/03, we varied the length of training data from one to eight years, applied a sequential test to the forecast errors arising from each of eight forecasting methods, and evaluated their detection probabilities (DP) on the basis of 1000 injected synthetic outbreaks. We did the same for each of two corresponding simulated data sets. The less realistic, nonhierarchical model's simulated data set assumed that "one season fits all," meaning that each year's seasonal peak has the same onset, duration, and magnitude. The more realistic simulated data set used a hierarchical model to capture violation of the "one season fits all" assumption. RESULTS: This experiment demonstrated optimistic bias in DP estimates for some of the methods when data simulated from the nonhierarchical model was used for DP estimation, thus suggesting that at least for some real data sets and methods, it is not adequate to assume that "one season fits all." CONCLUSION: For the data we analyze, the "one season fits all " assumption is violated, and DP performance claims based on simulated data that assume "one season fits all," for the forecast methods considered, except for moving average methods, tend to be optimistic. Moving average methods based on relatively short amounts of training data are competitive on all three data sets, but are particularly competitive on the real data and on data from the hierarchical model, which are the two data sets that violate the "one season fits all" assumption