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A method for the calculation of the probability of failure of a structural system based on interval probability theory is proposed.
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This method based on interval-parameter programming and two-stage stochastic programming so that it allows uncertainties expressed as both interval values and probability distributions to be incorporated within a common optimization framework.
With the aim of assessing agreement between two devices of continuous measurements via the total deviation index (TDI), the present study evaluated the performance of a simplified technical approximation of the TDI based on probability intervals and a tolerance interval (TI) approach for inference about the resulting TDI estimate.
The TDI based on probability intervals can also be used to assess inter- and intra-method agreement measures.
We propose to use the restricted maximum likelihood estimation (REML) method [ 22] to obtain the model parameter estimates in (1) and furthermore compute the TDI estimate based on probability intervals by plugging in the REML estimates of μ D and σ D in (4).
Based on the probability interval approach a direct inference method about this estimate is derived via the TI.
Dose finding was based on toxicity probability intervals [ 14].
In the gun backcross, 3 out of 316 1-cM intervals (0.9%) exhibit QTL for both wing spot and courtship score, which is not different from expected (9 1-cM intervals based on the probability of overlap from 47 for wing spot and 52 for courtship; Fisher's exact test, two-tailed P = 0.1422).
In the ele backcross, 23 of 285 1-cM intervals (8.1%) exhibit QTL for both wing spot (including the results of CIM from Spot size 1 and Spot size 2) and courtship score (the results of CIM), which is significantly greater than expected (9 1-cM intervals based on the probability of overlap from 47 for wing spot and 52 for courtship; Fisher's exact test, two-tailed P = 0.0168).
A confidence interval is based on the probability distribution of the estimated parameter, and should not be interpreted as a probability statement about the parameter of interest, which is assumed to be fixed (nonrandom) but unknown.
The interval is updated based on the probability of observing each symbol in a particular context.
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