Abstract:The main objective of this paper is to find the relation between the adaptive significance level presented here and the sample size. We statisticians know of the inconsistency, or paradox, in the current classical tests of significance that are based on p-value statistics that are compared to the canonical significance levels (10%, 5%, and 1%): "Raise the sample to reject the null hypothesis" is the recommendation of some ill-advised scientists! This paper will show that it is possible to eliminate this problem of significance tests. We present here the beginning of a larger research project. The intention is to extend its use to more complex applications such as survival analysis, reliability tests, and other areas. The main tools used here are the Bayes factor and the extended Neyman-Pearson Lemma.
This article argues that researchers do not need to completely abandon the p-value, the best-known significance index, but should instead stop using significance levels that do not depend on sample sizes. A testing procedure is developed using a mixture of frequentist and Bayesian tools, with a significance level that is a function of sample size, obtained from a generalized form of the Neyman-Pearson Lemma that minimizes a linear combination of α, the probability of rejecting a true null hypothesis, and β, the probability of failing to reject a false null, instead of fixing α and minimizing β. The resulting hypothesis tests do not violate the Likelihood Principle and do not require any constraints on the dimensionalities of the sample space and parameter space. The procedure includes an ordering of the entire sample space and uses predictive probability (density) functions, allowing for testing of both simple and compound hypotheses. Accessible examples are presented to highlight specific characteristics of the new tests.
Abstract. We propose a class of models of random walks in a random environment where an exact solution can be given for a stationary distribution. The environment is cast in terms of a Jackson/Gordon-Newell network although alternative interpretations are possible. The main tool is the detailed balance equations. The difference with earlier works is that the position of the random walk influences the transition intensities of the network environment and vice versa, creating strong correlations. The form of the stationary distribution is closely related to the well-known productformula.
In the presence of abnormal fluid collection (e.g. ascites), the measurement of glomerular filtration rate (GFR) based on a small number (1-4) of plasma samples fails. This study investigated how a few samples will allow adequate characterization of plasma clearance to give a robust and accurate GFR measurement. A total of 68 nine-sample GFR tests (from 45 oncology patients) with abnormal clearance of a glomerular tracer were audited to develop a Monte Carlo model. This was used to generate 20 000 synthetic but clinically realistic clearance curves, which were sampled at the 10 time points suggested by the British Nuclear Medicine Society. All combinations comprising between four and 10 samples were then used to estimate the area under the clearance curve by nonlinear regression. The audited clinical plasma curves were all well represented pragmatically as biexponential curves. The area under the curve can be well estimated using as few as five judiciously timed samples (5, 10, 15, 90 and 180 min). Several seven-sample schedules (e.g. 5, 10, 15, 60, 90, 180 and 240 min) are tolerant to any one sample being discounted without significant loss of accuracy or precision. A research tool has been developed that can be used to estimate the accuracy and precision of any pattern of plasma sampling in the presence of 'third-space' kinetics. This could also be used clinically to estimate the accuracy and precision of GFR calculated from mistimed or incomplete sets of samples. It has been used to identify optimized plasma sampling schedules for GFR measurement.
Processo de Markov em tempo contínuo; rede de filas; rede de Jackson; exclusão simples; alcance zero; reversibilidade; probabilidade estacionária; forma produto; sistema interagente de partículas.
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