Reliability of integrated parameters of operational efficiency of TPP power units

A new method and an algorithm of ensuring the uniformity of normalized samples of technical and economic parameters of power units of thermal power plants are presented. Uniformity and normalization are obligatory conditions at estimation of integrated parameters characterizing the efficiency of power units. The method is based on the fiducial approach. Boundary values of fiducial interval are traditionally calculated based on the statistical function of distribution and a set significance value, i.e. are calculated, in fact, "mechanically". As the "mechanical" approach is appropriate for homogeneous statistical data, whereas technical and economic parameters are multivariate data, application of this approach to the statistical function of fiducial distribution is associated with a high risk of an erroneous decision. The set of possible realizations of actual values of technical and economic parameters includes realizations caused by "gross" mistakes at data input in automated systems or at manual performance of individual calculations. Quite often, unconventional realizations are observed, e. g., in case of low-load operation for 10 days of a month. These data form boundary intervals that the authors refer to as “boundins” (or prigrins in Russian). Automated search and removal of boundins provides reliability of comparison and ranking of integrated parameters. It is shown that rate of variation of boundins is considerably below the rate of variation of typical realizations of technical and economic parameters. This fact was the basis for recognition of boundins.

Nonparametric generalized fiducial inference for survival functions under censoring

Summary Since the introduction of fiducial inference by Fisher in the 1930s, its application has been largely confined to relatively simple, parametric problems. In this paper, we present what might be the first time fiducial inference is systematically applied to estimation of a nonparametric survival function under right censoring. We find that the resulting fiducial distribution gives rise to surprisingly good statistical procedures applicable to both one-sample and two-sample problems. In particular, we use the fiducial distribution of a survival function to construct pointwise and curvewise confidence intervals for the survival function, and propose tests based on the curvewise confidence interval. We establish a functional Bernstein–von Mises theorem, and perform thorough simulation studies in scenarios with different levels of censoring. The proposed fiducial-based confidence intervals maintain coverage in situations where asymptotic methods often have substantial coverage problems. Furthermore, the average length of the proposed confidence intervals is often shorter than the length of confidence intervals for competing methods that maintain coverage. Finally, the proposed fiducial test is more powerful than various types of log-rank tests and sup log-rank tests in some scenarios. We illustrate the proposed fiducial test by comparing chemotherapy against chemotherapy combined with radiotherapy, using data from the treatment of locally unresectable gastric cancer.

Making Image Guidance Work: Understanding Control of Accuracy

Use of image-guided surgery is becoming increasingly common in both sinus surgery and neuro-otologic applications. The purpose of this study was to determine the effect of fiducial distribution and mean fiducial error on point accuracy. Using a plastic model, we determined that optimal navigation accuracy was achieved by surrounding the operative target with a widespread field of fiducials. True accuracy was always highest when we targeted a surface point. Accuracy was decreased at points removed from the center of the registration target zone created by the fiducials. Inaccurate registration resulted in increased mean fiducial error and lower accuracy at the target point. Understanding the registration process will enhance the utility of image-guided surgery in otolaryngology and skull base surgery.

Fiducial distribution of several parameters with application to a normal system

The notion of fiducial probability was introduced by R. A. Fisher and is now widely used in statistical work involving a single unknown parameter. Fisher has also considered the joint fiducial distribution of several parameters for which there exists a sufficient set of statistics, and has derived the fiducial distribution of the two parameters of the one-variate normal law*. Since Fisher's account is brief, we give a more extended description of the fiducial distribution of several independent parameters possessing a sufficient set of statistics.