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

Seborrheic Dermatitis

Seborrheic dermatitis is a common chronic inflammatory skin disease characterized by erythema and greasy scales affecting areas rich in sebaceous glands. Seborrheic dermatitis has two incidence peaks, the first in the first three months of life and the second beginning at puberty, reaching its apex at 30 to 40 years of age. Infants with seborrheic dermatitis often present with focal or diffuse scaling and crusting of the scalp. Erythematous or salmon-colored sharply demarcated patches with yellow-white scales may involve the face, postauricular areas, trunk, and intertriginous and flexural areas of the body. In the diaper area, infantile seborrheic dermatitis presents as a sharply demarcated, erythematous, scaly eruption with a tendency to coalesce, resulting in the formation of a large confluent lesion. Pruritus is characteristically absent. In adolescence and beyond, seborrheic dermatitis usually presents as greasy scaling of the scalp. It may also present as ill-defined erythematous patches with yellow-white, greasy scales affecting the nasolabial folds, eyelids, eyebrows, glabella, postauricular area, anterior chest, and less commonly the upper back. Mild periodic pruritus is common in adolescent seborrheic dermatitis. Scalp lesions in infantile seborrheic dermatitis usually respond to simple daily shampooing alone or in combination with non-prescription mild shampoos specific for seborrheic dermatitis. For infantile scalp seborrheic dermatitis that does not respond to the above measures, for seborrheic dermatitis lesions elsewhere, and for adolescent or adult seborrheic dermatitis, the use of topical antifungals, calcineurin inhibitors, and low to mid potency corticosteroids should be considered. A compounded mixture of these ingredients is also often employed