Existence of the signal in the signal plus background model

Searching for evidence of neutrino oscillations is an important problem in particle physics. Suppose that evidence for neutrino oscillations from an LSND experiment reports a significant positive oscillation probability, but that the LSND result is not confirmed by other experiments. In statistics, such a problem can be proposed as the detection of signal events in the Poisson signal plus background model. Suppose that an observed count $X$ is of the form $X=B+S$, where the background $B$ and the signal $S$ are independent Poisson random variables with parameters $b$ and $\theta$ respectively, $b$ is known but $\theta$ is not. Some recent articles have suggested conditioning on the observed bound for $B$; that is, if $X=n$ is observed, the suggestion is to base the inference on the conditional distribution of $X$ given $B\le n$. This suggestion is used here to derive an estimator of the probability of the existence of the signal event. The estimator is examined from the view of decision theory and is shown to be admissible.Comment: Published at http://dx.doi.org/10.1214/074921706000000653 in the IMS Lecture Notes--Monograph Series (http://www.imstat.org/publications/lecnotes.htm) by the Institute of Mathematical Statistics (http://www.imstat.org

On the false discovery rates of a frequentist: Asymptotic expansions

Consider a testing problem for the null hypothesis $H_0:\theta\in\Theta_0$. The standard frequentist practice is to reject the null hypothesis when the p-value is smaller than a threshold value $\alpha$, usually 0.05. We ask the question how many of the null hypotheses a frequentist rejects are actually true. Precisely, we look at the Bayesian false discovery rate $\delta_n=P_g(\theta\in\Theta_0|p-value<\alpha)$ under a proper prior density $g(\theta)$. This depends on the prior $g$, the sample size $n$, the threshold value $\alpha$ as well as the choice of the test statistic. We show that the Benjamini--Hochberg FDR in fact converges to $\delta_n$ almost surely under $g$ for any fixed $n$. For one-sided null hypotheses, we derive a third order asymptotic expansion for $\delta_n$ in the continuous exponential family when the test statistic is the MLE and in the location family when the test statistic is the sample median. We also briefly mention the expansion in the uniform family when the test statistic is the MLE. The expansions are derived by putting together Edgeworth expansions for the CDF, Cornish--Fisher expansions for the quantile function and various Taylor expansions. Numerical results show that the expansions are very accurate even for a small value of $n$ (e.g., $n=10$). We make many useful conclusions from these expansions, and specifically that the frequentist is not prone to false discoveries except when the prior $g$ is too spiky. The results are illustrated by many examples.Comment: Published at http://dx.doi.org/10.1214/074921706000000699 in the IMS Lecture Notes--Monograph Series (http://www.imstat.org/publications/lecnotes.htm) by the Institute of Mathematical Statistics (http://www.imstat.org

Loglinear Residual Tests of Moran’s I Autocorrelation: An Application to Kentucky Breast Cancer Data

Spatial regressions have been widely used, but their use with the permutation tests of residuals either in linear or loglinear models is rarely seen. In the present study, we have linked the Cliff-Ord permutation test of Moran’s I on linear regression errors to loglinear regression residuals under asymptotic normality. We devised both Pearson residual Moran’s IP R and deviance residual Moran’s IDR tests and applied them to a set of log-rate models for early stage and late-stage breast cancer together with socioeconomic and access-to-care data in Kentucky. The results showed that socioeconomic and access-to-care variables were sufficient to account for spatial clustering of early stage breast carcinomas with breast cancer screening and number of primary care providers being more persistent than county median family income. For late-stage carcinomas, in contrast, the late-stage incidence rate was negatively associated with breast cancer screening level. This result confirmed our expectation: a high screening level is associated with high incidence rate of early stage disease, which in turn reduces late-stage incidence rates. In addition, we located four late-stage breast cancer clusters that cannot be explained by socioeconomic and access-to-care variables

A Method for Testing Low-Value Spatial Clustering for Rare Diseases

This paper proposes a method that tests for the existence of low-value spatial clustering while accounting for the influence of high-value clustering. Although the method was developed in reference to the Tango test, it can be extended to other testing methods. The simulation results showed that the proposed method is able to effectively detect low-value clustering with substantially lower rates of type I errors than those of the Tango test, while maintaining comparable statistical power. Applying the method in a case study of leukemia in Minnesota demonstrated an overall tendency toward low-value clustering of leukemia mortality for males but provided inconclusive results for females

WI-SUN STABILIZATION FOR DISTRIBUTED AUTOMATION GATEWAYS BY DYNAMICALLY CONTROLLING ACCEPTABLE CHILDREN NUMBERS

Resilient mesh products (based on, for example, the Wireless Smart Utility Network (Wi-SUN) communication standard) have been available for many years and are widely used within Advanced Metering Infrastructure (AMI) and Distributed Automation (DA) settings. A DA Gateway (which, for convenience, may be referred to herein as a ‘DAGW’) follows the AMI elements’ rules in a Wi-SUN network, but that is not highly efficient while forwarding a significant amount of the third-party traffic. The root cause of such inefficiency is that the child AMI elements are not aware of a change in the available resources in a DAGW. To address these types of challenges, techniques are presented herein that support a DAGW periodically broadcasting its available resources in Destination Oriented Directed Acyclic Graph (DODAG) Information Object (DIO) messages. Aspects of the presented techniques support a DAGW adjusting the number of its attached child AMI elements, thus stabilizing the whole network