China
Africa
Explore chapters and articles related to this topic
Basic Analysis Techniques
Published in Russell G. Congalton, Kass Green, Assessing the Accuracy of Remotely Sensed Data, 2019
Russell G. Congalton, Kass Green
Z is standardized and normally distributed (i.e., standard normal deviate). Given the null hypothesis H0:K1=0 and the alternative H1:K1≠0, H0 is rejected if Z≥Zα/2, where α/2 is the confidence level of the two-tailed Z test, and the degrees of freedom are assumed to be ∞ (infinity).
Statistics for the Safety Professional
Published in W. David Yates, Safety Professional’s Reference and Study Guide, 2020
Standard scores are also called z-values, z-scores, normal scores, and standardized variables; the use of “Z” is because the normal distribution is also known as the “Z distribution.” They are most frequently used to compare a sample to a standard normal deviate (standard normal distribution, with μ = 0 and σ = 1), although they can be defined without assumptions of normality.
Statistics for the Safety Professional
Published in W. David Yates, Safety Professional’s, 2015
Standard scores are also called z-values, z-scores, normal scores, and standardized variables; the use of “Z” is because the normal distribution is also known as the “Z distribution.” They are most frequently used to compare a sample to a standard normal deviate (standard normal distribution, with μ = 0 and σ = 1), although they can be defined without assumptions of normality.
Effective grain orientation mapping of complex and locally anisotropic media for improved imaging in ultrasonic non-destructive testing
Published in Inverse Problems in Science and Engineering, 2020
K. M. M. Tant, E. Galetti, A. J. Mulholland, A. Curtis, A. Gachagan
The reversible-jump Markov chain Monte Carlo method allows dimensional jumps in the model space which can later be reversed [22]. The process possesses the Markov property so that each perturbation of the model is dependent only on its current state and not on its history. To begin, a parametrization of the material microstructure m is constructed using a Voronoi tessellation. The initial number of cells is chosen arbitrarily and each cell is assigned a crystal orientation drawn from a uniform distribution bounded by and . For each pair of transmit-receive elements, the travel time field is modelled throughout the locally anisotropic geometry using the AMSFMM (see Section 2.3), and the time taken for the wave to propagate to each receiver is estimated. These travel times are compared with the first time of arrival information as extracted from the observed dataset and the posterior for the initial model is calculated. The model is then perturbed to create a new model . Large steps through the model space can alter the complexity of the solution towards which the algorithm converges [42], and so to avoid this potential problem the model parameters are perturbed independently to isolate their effects. Each perturbation is made subject to a proposal distribution, which represents the conditional probabilities of proposing a state given m. In this work, the model can be perturbed in one of five ways: a cell birth, death or move, a system noise change or a cell orientation change. Details of the proposals on the first four of these perturbations can be found in [5]. The perturbation of the orientation in cell i is given by where is a standard normal deviate with mean 0 and variance 1, and is the standard deviation of the proposal distribution for orientation. Once a perturbation has been made, the posterior is calculated. The probability that a perturbation is accepted is subject to the Metropolis-Hastings criterion where is the proposal distribution; that is the probability of moving to model from m (the ratio of the reverse step to the forward step is equal to one if the perturbation is not transdimensional) [42]. If is rejected, the model is discarded and the original model m is perturbed again. If accepted, the model replaces the model m and the process begins again.