In this paper, we developed and compared several expectation-maximization (EM) algorithms to find maximum likelihood estimates of individual inbreeding coefficients using molecular marker information. The first method estimates the inbreeding coefficient for a single individual and assumes that allele frequencies are known without error. The second method jointly estimates inbreeding coefficients and allele frequencies for a set of individuals that have been genotyped at several loci. The third method generalizes the second method to include the case in which null alleles may be present. In particular, it is able to jointly estimate individual inbreeding coefficients and allele frequencies, including the frequencies of null alleles, and accounts for missing data. We compared our methods with several other estimation procedures using simulated data and found that our methods perform well. The maximum likelihood estimators consistently gave among the lowest root-mean-square-error (RMSE) of all the estimators that were compared. Our estimator that accounts for null alleles performed particularly well and was able to tease apart the effects of null alleles, randomly missing genotypes and differing degrees of inbreeding among members of the datasets we analysed. To illustrate the performance of our estimators, we analysed previously published datasets on mice (Mus musculus) and white-tailed deer (Odocoileus virginianus).
Testing of the disjunction hypothesis is appropriate when each gene or location studied is associated with multiple p-values, each of which is of individual interest. This can occur when more than one aspect of an underlying process is measured. For example, cancer researchers may hope to detect genes that are both differentially expressed on a transcriptomic level and show evidence of copy number aberration. Currently used methods of p-value combination for this setting are overly conservative, resulting in very low power for detection. In this work, we introduce a method to test the disjunction hypothesis by using cumulative areas from the Voronoi diagram of two-dimensional vectors of p-values. Our method offers much improved power over existing methods, even in challenging situations, while maintaining appropriate error control. We apply the approach to data from two published studies: the first aims to detect periodic genes of the organism Schizosaccharomyces pombe, and the second aims to identify genes associated with prostate cancer.
This article provides a brief introduction to the definition, properties, and use of Voronoi diagrams, including the special cases of the Poisson-Voronoi and centroidal Voronoi diagrams. It highlights applications to problems in spatial statistics, probability, and large-scale simultaneous hypothesis testing. Generalizations of the Voronoi diagram and computational considerations are also discussed. These diagrams have been widely used in the fields of statistics, mathematics, computational geometry, and various applied sciences, making them an important topic of study.
The Waveform and Sonicboom Perception and Response (WSPR) Program conducted a field study of subjective response to noise from multiple low-amplitude sonic booms. The team was led by Wyle and included researchers from Penn State, Tetra Tech and Gulfstream Aerospace Corp. The test exposed residents in the Edwards Air Force Base (EAFB) Housing area to two weeks of low-amplitude sonic booms while recording their responses via surveys. There were 52 participants divided across three response modes. The response instruments included Baseline Surveys, Single Event Surveys submitted each time a participant heard a boom, and Daily Surveys submitted at the end of each day. The analysis included assessments of single events and cumulative daily ratings of annoyance and categorical variables including loudness, interference, startle, vibration, and rattle. The WSPR daily annoyance data was analyzed by computing percent highly annoyed (%HA) and relating it to the cumulative noise exposure and by relating the subjective annoyance rating directly to the daily noise exposure. The WSPR design was established to cover the full range of noise exposures and annoyance factors so that sufficient data would be gathered to facilitate analyses of %HA and noise metrics. The statistical analyses examining these relationships will be presented.
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