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Statistical Analysis of Fatigue Test Data according to Eurocode 3
Published in Nigel Powers, Dan M. Frangopol, Riadh Al-Mahaidi, Colin Caprani, Maintenance, Safety, Risk, Management and Life-Cycle Performance of Bridges, 2018
For design purpose the prediction interval and its lower bound is more important than the confidence interval as the latter only claims to include the true intercept of the S-N curve for past tests. The prediction interval is an estimate of an interval in which the mean of m future observations is expected to fall in with a certain probability. Similarly to Equation 9, the lower prediction bound for the intercept of the S-N curve is computed by (Hahn & Meeker 1991, Eq. 4.2): () loga^−t1−α,n−1⋅s⋅1m+1n
Prediction models for international roughness index and rut depth
Published in Maurizio Crispino, Pavement and Asset Management, 2019
Completing missing values can be done by the exactly same procedure as prediction of future observations, though only prediction is discussed below. Point prediction and error margins should be used to form interval prediction, but there are two types of intervals. A confidence interval aims at finding an interval for the expectation of a new or a missing observation at some time while a prediction interval aims at finding an interval where a new observation at some time is likely to occur, the latter being wider because of the individual variation around the regression function.
Multivariable Linear Regression
Published in Harry G. Perros, An Introduction to IoT Analytics, 2021
A prediction interval is an estimate of an interval within which a future observation corresponding to the same input x will lie with a given level of confidence, such as 95%. Otherwise stated, if we happen to obtain an observation in the future for an input x, then this observation will lie in the prediction interval with probability 0.95. Other levels of confidence can be used, as in the case of confidence intervals.
Developing the quality assurance thresholds for screening automated pavement condition data using prediction interval methods
Published in International Journal of Pavement Engineering, 2023
Jueqiang Tao, Feng Wang, Xiaohua Luo, Haitao Gong, Xin Qiu, Ajmain Faieq
With a given observation , the prediction interval estimates the range of possible true values according to the regression model. A diagram of the prediction interval is illustrated in Figure 1. The straight line is the regression line and is calculated according to the historical data points (xi, yi). Given a specific predictor and significance level , a prediction interval means that the probability of a true value corresponding to being within the prediction interval (PIlow, PIup) is . PIlow and PIup are the lower bound and upper bound of a prediction interval, respectively. Equivalently to say, there is a confidence that the true values would be included in the prediction interval (PIlow, PIup).
A comprehensive toolbox for the gamma distribution: The gammadist package
Published in Journal of Quality Technology, 2023
Piao Chen, Kilian Buis, Xiujie Zhao
The prediction interval is another important statistical interval, which predicts the range of a future observation with a certain probability. Consider two statistics and and the next sample variable A prediction interval satisfies where is the confidence level. The one-sided prediction limits can be easily constructed as the open-ended version of the prediction interval. Regarding the gamma distribution, its prediction limits construction plays an important role in applications such as environment monitoring and quality control (Chen and Ye 2017a; Wang and Wu 2018). The GQP method can again be invoked. In specific, for each pair of realizations a gamma variable is generated. Afterwards, B gamma variables will be generated based on B realizations of whose empirical percentiles can be used as the prediction limits. The detailed procedures are summarized in Algorithm 5.
Application of NARX neural network for predicting marine engine performance parameters
Published in Ships and Offshore Structures, 2020
Yiannis Raptodimos, Iraklis Lazakis
The main aim of time series modelling is to carefully collect and rigorously study the past observations of a time series to develop an appropriate model which describes the inherent structure of the series. This model is then used to generate future values for the series. The procedure of fitting a time series to a proper model is termed as time series analysis, while time series forecasting can be termed as the act of predicting the future by understanding the past (Hipel and McLeod 1994). An important task when forecasting a value of y from one or more predictor variables is to obtain an estimate of the likely amount of error inherent in the forecast (Chatfield 1995). A prediction interval is an assessment of this forecast error and is a range that is probable to contain the response value of a single new observation and allows assessment of future uncertainty (Chatfield 1993). The NARX network provided highly accurate forecasted results contained in their calculated prediction intervals. This outcome provides a high level of confidence in the model predictions by addressing uncertainty in the predictions.