Bayesian Bounds on Parameter Estimation Accuracy for Compact Coalescing Binary Gravitational Wave Signals

A global network of laser interferometric gravitational wave detectors is projected to be in operation by around the turn of the century. Here, the noisy output of a single instrument is examined. A gravitational wave is assumed to have been detected in the data and we deal with the subsequent problem of parameter estimation. Specifically, we investigate theoretical lower bounds on the minimum mean-square errors associated with measuring the parameters of the inspiral waveform generated by an orbiting system of neutron stars/black holes. Three theoretical lower bounds on parameter estimation accuracy are considered: the Cramer-Rao bound (CRB); the Weiss-Weinstein bound (WWB); and the Ziv-Zakai bound (ZZB). We obtain the WWB and ZZB for the Newtonian-form of the coalescing binary waveform, and compare them with published CRB and numerical Monte-Carlo results. At large SNR, we find that the theoretical bounds are all identical and are attained by the Monte-Carlo results. As SNR gradually drops below 10, the WWB and ZZB are both found to provide increasingly tighter lower bounds than the CRB. However, at these levels of moderate SNR, there is a significant departure between all the bounds and the numerical Monte-Carlo results.Comment: 17 pages (LaTeX), 4 figures. Submitted to Physical Review

Some results on a χ-divergence, an extended Fisher information and generalized Cramér-Rao inequalities

International audienceWe propose a modified χβ-divergence, give some of its properties, and show that this leads to the definition of a generalized Fisher information. We give generalized Cramér-Rao inequalities, involving this Fisher information, an extension of the Fisher information matrix, and arbitrary norms and power of the estimation error. In the case of a location parameter, we obtain new characterizations of the generalized q-Gaussians, for instance as the distribution with a given moment that minimizes the generalized Fisher information. Finally we indicate how the generalized Fisher information can lead to new uncertainty relations

Using the Minor Variant Finder software to identify and quantify the allelic burden level of somatic mutations in oncohematologic diseases

Background. There are problems related to both quantitative assessment of an allele burden level of a mutant gene and interpretation of results in DNA samples with the burden level of the mutant allele less than 15–20 %, when using Sanger sequencing for analyzing somatic mutations. Applied Biosystems (USA) has developed new software Minor Variant Finder, which allows determining mutations with the allele burden level from 5 %.The objective: to determine the allele burden level and identification of minor variants of somatic mutations in the ASXL1, JAK2 genes and BCR-ABL oncogene using Minor Variant Finder software in patients with myeloproliferative neoplasms.Materials and methods. The level of mutant allele burden for 15 patients with myeloproliferative neoplasms was determined by the identified mutations using the Minor Variant Finder software, after analysis of point somatic mutations in the ASXL1, JAK2 genes and BCR-ABL oncogene by Sanger sequencing.Results. The allele burden level in all 5 ASXL1-positive samples and BCR-ABL-positive sample was determined as higher than 20 % using the Minor Variant Finder software. The allele burden level in 2 cases was higher than 20 % and in 7 cases lower than 20 %, when we analyzed 9 JAK2-positive samples.Conclusion. Minor Variant Finder software can be used to estimate the allele burden level and to identify minor variants of somatic mutations in the ASXL, JAK2 and BCR-ABL genes