Bayesian approach for probabilistic characterization of sand friction angles

“…In other previous studies, the statistical uncertainty may have been treated implicitly by lumping with other sources of uncertainties. For instance, Wang et al (2010) proposed a Bayesian method of characterizing the uncertainties in (µ,σ,δ). The resulting posterior probability distribution actually incorporates the statistical uncertainties in (µ,σ,δ).…”

Section: Introductionmentioning

confidence: 99%

“…There are several techniques that can be employed to estimate σ and δ (in particular δ), such as the method of moments (Uzielli et al 2005;Dasaka and Zhang 2012;Firouzianbandpey et al 2014;Lloret-Cabot et al 2014), the fluctuation function method (Wickremesinghe and Campanella 1993;Cafaro and Cherubini 2002), the maximum likelihood (ML) method (DeGroot and Baecher 1993), and the Bayesian method (Wang et al 2010). Phoon and Fenton (2004) proposed a practical bootstrap technique to obtain a more robust estimate of the autocorrelation function and to gain an appreciation of the underlying variability in the estimate with minimal assumptions.…”

Section: Introductionmentioning

confidence: 99%

Statistical characterization of random field parameters using frequentist and Bayesian approaches

Ching

Phoon

2016

Can. Geotech. J.

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Due to limited information in site investigation, it is not possible to obtain the actual values for the mean, standard deviation, and scale of fluctuation of a soil property of interest. The deviation between the estimated values and the actual values is called the statistical uncertainty. There are at least two schools of thoughts on how to model the statistical uncertainty: frequentist thought and Bayesian thought. The purpose of this paper is to discuss their philosophical difference, to show how to quantify the statistical uncertainty based on these two distinct schools of thoughts, and to compare their performances. For the frequentist school of thought, the confidence interval will be used to quantify the statistical uncertainty, whereas the posterior probability distribution will be used for the Bayesian school of thought. Examples will be presented to compare the performances of these two schools of thoughts in terms of their consistencies. The results show that in general the Bayesian thought performs better in terms of consistency. In particular, the Markov chain Monte Carlo method is recommended when the information amount is very limited.

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“…The most suitable probabilistic model tends to be problem-specific since the associated physical insight tends to be different for different problems. The authors have developed different probabilistic models for various geotechnical problems, such as characterisation of sand friction angles and soil stratum identification using cone penetration test data (Wang et al, 2010a;. Cao & Wang (2014a, 2014b further developed a Bayesian model comparison method to quantitatively compare various probabilistic models and to select the most suitable model for the geotechnical engineering problem in hand.…”

Section: Authors' Replymentioning

confidence: 99%