A Sharper discrepancy measure for post-election audits

Post-election audits use the discrepancy between machine counts and a hand tally of votes in a random sample of precincts to infer whether error affected the electoral outcome. The maximum relative overstatement of pairwise margins (MRO) quantifies that discrepancy. The electoral outcome a full hand tally shows must agree with the apparent outcome if the MRO is less than 1. This condition is sharper than previous ones when there are more than two candidates or when voters may vote for more than one candidate. For the 2006 U.S. Senate race in Minnesota, a test using MRO gives a $P$-value of 4.05% for the hypothesis that a full hand tally would find a different winner, less than half the value Stark [Ann. Appl. Statist. 2 (2008) 550--581] finds.Comment: Published in at http://dx.doi.org/10.1214/08-AOAS171 the Annals of Applied Statistics (http://www.imstat.org/aoas/) by the Institute of Mathematical Statistics (http://www.imstat.org

Testing earthquake predictions

Statistical tests of earthquake predictions require a null hypothesis to model occasional chance successes. To define and quantify `chance success' is knotty. Some null hypotheses ascribe chance to the Earth: Seismicity is modeled as random. The null distribution of the number of successful predictions -- or any other test statistic -- is taken to be its distribution when the fixed set of predictions is applied to random seismicity. Such tests tacitly assume that the predictions do not depend on the observed seismicity. Conditioning on the predictions in this way sets a low hurdle for statistical significance. Consider this scheme: When an earthquake of magnitude 5.5 or greater occurs anywhere in the world, predict that an earthquake at least as large will occur within 21 days and within an epicentral distance of 50 km. We apply this rule to the Harvard centroid-moment-tensor (CMT) catalog for 2000--2004 to generate a set of predictions. The null hypothesis is that earthquake times are exchangeable conditional on their magnitudes and locations and on the predictions--a common ``nonparametric'' assumption in the literature. We generate random seismicity by permuting the times of events in the CMT catalog. We consider an event successfully predicted only if (i) it is predicted and (ii) there is no larger event within 50 km in the previous 21 days. The $P$-value for the observed success rate is $<0.001$: The method successfully predicts about 5% of earthquakes, far better than `chance,' because the predictor exploits the clustering of earthquakes -- occasional foreshocks -- which the null hypothesis lacks. Rather than condition on the predictions and use a stochastic model for seismicity, it is preferable to treat the observed seismicity as fixed, and to compare the success rate of the predictions to the success rate of simple-minded predictions like those just described. If the proffered predictions do no better than a simple scheme, they have little value.Comment: Published in at http://dx.doi.org/10.1214/193940307000000509 the IMS Collections (http://www.imstat.org/publications/imscollections.htm) by the Institute of Mathematical Statistics (http://www.imstat.org

Limiting Risk by Turning Manifest Phantoms into Evil Zombies

Drawing a random sample of ballots to conduct a risk-limiting audit generally requires knowing how the ballots cast in an election are organized into groups, for instance, how many containers of ballots there are in all and how many ballots are in each container. A list of the ballot group identifiers along with number of ballots in each group is called a ballot manifest. What if the ballot manifest is not accurate? Surprisingly, even if ballots are known to be missing from the manifest, it is not necessary to make worst-case assumptions about those ballots--for instance, to adjust the margin by the number of missing ballots--to ensure that the audit remains conservative. Rather, it suffices to make worst-case assumptions about the individual randomly selected ballots that the audit cannot find. This observation provides a simple modification to some risk-limiting audit procedures that makes them automatically become more conservative if the ballot manifest has errors. The modification--phantoms to evil zombies (~2EZ)--requires only an upper bound on the total number of ballots cast. ~2EZ makes the audit P-value stochastically larger than it would be had the manifest been accurate, automatically requiring more than enough ballots to be audited to offset the manifest errors. This ensures that the true risk limit remains smaller than the nominal risk limit. On the other hand, if the manifest is in fact accurate and the upper bound on the total number of ballots equals the total according to the manifest, ~2EZ has no effect at all on the number of ballots audited nor on the true risk limit

Nonlinear limits to the information capacity of optical fiber communications

The exponential growth in the rate at which information can be communicated through an optical fiber is a key element in the so called information revolution. However, like all exponential growth laws, there are physical limits to be considered. The nonlinear nature of the propagation of light in optical fiber has made these limits difficult to elucidate. Here we obtain basic insights into the limits to the information capacity of an optical fiber arising from these nonlinearities. The key simplification lies in relating the nonlinear channel to a linear channel with multiplicative noise, for which we are able to obtain analytical results. In fundamental distinction to the linear additive noise case, the capacity does not grow indefinitely with increasing signal power, but has a maximal value. The ideas presented here have broader implications for other nonlinear information channels, such as those involved in sensory transduction in neurobiology. These have been often examined using additive noise linear channel models, and as we show here, nonlinearities can change the picture qualitatively.Comment: 1 figure, 7 pages, submitted to Natur

Jupiter as a Giant Cosmic Ray Detector

We explore the feasibility of using the atmosphere of Jupiter to detect Ultra-High-Energy Cosmic Rays (UHECR's). The large surface area of Jupiter allows us to probe cosmic rays of higher energies than previously accessible. Cosmic ray extensive air showers in Jupiter's atmosphere could in principle be detected by the Large Area Telescope (LAT) on the Fermi observatory. In order to be observed, these air showers would need to be oriented toward the Earth, and would need to occur sufficiently high in the atmosphere that the gamma rays can penetrate. We demonstrate that, under these assumptions, Jupiter provides an effective cosmic ray "detector" area of $3.3 \times 10^7$ km$^2$. We predict that Fermi-LAT should be able to detect events of energy $>10^{21}$ eV with fluence $10^{-7}$ erg cm$^{-2}$ at a rate of about one per month. The observed number of air showers may provide an indirect measure of the flux of cosmic rays $\gtrsim 10^{20}$ eV. Extensive air showers also produce a synchrotron signature that may be measurable by ALMA. Simultaneous observations of Jupiter with ALMA and Fermi-LAT could be used to provide broad constraints on the energies of the initiating cosmic rays.Comment: 8 pages, 5 figures. Accepted for publication in the Astrophysical Journal Letter

A Long and Winding Road: Federally Qualified Health Centers, Community Variation and Prospects Under Reform

Outlines growth in the number of, demand, and federal funding for FQHCs between 1997 and 2009 in twelve communities and factors that shape FQHC development, including variations in Medicaid eligibility rules, employer-sponsored coverage, and demographics