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Integration of structural health monitoring in a system performance based life-cycle bridge management framework
Published in Dan M. Frangopol, Structures and Infrastructure Systems, 2019
Nader M. Okasha, Dan M. Frangopol
To produce quality samples efficiently with MH algorithm, it is crucial to select a good proposal distribution. If it is difficult to find an efficient proposal distribution, the slice sampling algorithm without explicitly specifying a proposal distribution can be used (MathWorks 2009). Slice sampling originates with the observation that to sample from a univariate distribution, points can be sampled uniformly from the region under the curve of its PDF and then only the horizontal coordinates of the sample points are looked at (Neal 2003). The following is a brief description of the algorithm based on MathWorks (2009): Assume an initial value x(t) within the domain of f(x).Draw a real value y uniformly from (0, f(x(t))), thereby defining a horizontal ‘slice’ as S = {x: y < f(x)}.Find an interval I = (L, R) around x(t) that contains all, or much of the ‘slice’ S.Draw the new point x(t + 1) within this interval.Increment t → t + 1 and repeat steps 2 through 4 until the desired number of samples are obtained.
Quality and Reliability
Published in Nezameddin Faghih, Ebrahim Bonyadi, Lida Sarreshtehdari, Quality Management and Operations Research, 2021
Nezameddin Faghih, Ebrahim Bonyadi, Lida Sarreshtehdari
Slice sampling is one of the specific states of the MCMC simulation and is based on uniform sampling from the surface beneath the conditional density curve or a prorate function thereto. As a result, applying this method only requires a simulation of the uniform distribution. This method is often used when the domain of the density function is finite or can be approximated in a finite area. The simplest model of slice sampling method is as follows.
Variable selection for kriging in computer experiments
Published in Journal of Quality Technology, 2020
Hengzhen Huang, Dennis K. J. Lin, Min-Qian Liu, Qiaozhen Zhang
Step 3 to Step 7 are straightforward. Note that, in Step 6, the right-hand side of Eq. [11] only gives up to a normalization constant, which is typically difficult to obtain. One popular approach to solving this sampling problem is to insert the “slice sampling” into this step (Neal 2003). The slice sampling algorithm is another MCMC method that can be used to generate samples from a distribution, and it is also ergodic under some weak conditions. One appealing feature of the slice sampling is that it only requires the density function up to a normalization constant and thus can deal with the sampling problem encountered in Eq. [11]. Some other sampling techniques that only require the density function up to a normalization constant, such as the Metropolis-Hastings algorithm (Hastings 1970), can be adopted to deal with Eq. [11] as well. Although the distribution (up to a normalization constant) may be obtained in the usual way, we do not recommend using the slice sampling to deal with it directly because of its high dimensionality. Also of note is that Steps 4 and 6 can be modified if other correlation functions are used. In other words, the correlation matrix R appearing on the right-hand sides of Eqs. [9] and [11] is of a general form.
Generalized Computer Model Calibration for Radiation Transport Simulation
Published in Technometrics, 2021
Michael Grosskopf, Derek Bingham, Marvin L. Adams, W. Daryl Hawkins, Delia Perez-Nunez
The key observation by Murray et al. is that the transition scale parameter in the sampling method proposed by Neal (1998) defines an ellipse connecting a sample from the prior and the current state. Instead of being fixed, the scale parameter is treated as an augmented variable for the sampler, with slice sampling used to sample its value and define the balance between the draw from the prior and the current state in sampling the latent function. The slice sampling approach shrinks the interval for sampling the scale parameter around the current state until a likelihood threshold is met (Murray, Adams, and MacKay 2010). This ensures a new sample for the latent function is always accepted. Because the method proposes new latent function values as a batch and adaptively chooses the transition size based on the concentration of the posterior, elliptical slice sampling reduces problems due to correlation between the latent function values that exist when sampling by single-site Metropolis. An additional benefit of elliptical slice sampling is that the computational cost of drawing from the prior GP, , only happens once per MCMC iteration, and each check if the likelihood exceeds the threshold for different scale parameter values only costs . Elliptical slice sampling would not be as useful for other parameters which would require the GP covariance matrix inversion for each check of the likelihood threshold. The full sampling approach used is summarized in Algorithm 1 and discussed in more detail in the supplementary materials.
Probabilistic multi-objective optimum combined inspection and monitoring planning and decision making with updating
Published in Structure and Infrastructure Engineering, 2022
Sunyong Kim, Dan M. Frangopol, Baixue Ge
When the multiple probabilistic parameters θ are represented by the high dimensional joint distribution and are updated simultaneously, it is difficult to compute the updated PDF numerically. In this case, the MCMC algorithms may efficiently find the updated PDF by generating the samples associated with the parameters of the damage prediction model. The MCMC can be based on several sampling methods such as Metropolis-Hastings sampling, slice sampling, blockwise sampling, Componentwise Metropolis sampling, and Gibbs sampling methods. More details on these sampling methods can be found in Hasting (1970), Neal (2003), Steyvers (2011), and Rastogi et al. (2017).