China
Africa
Explore chapters and articles related to this topic
Probabilistic risk analysis
Published in Vicki Bier, Risk in Extreme Environments, 2018
A model typically expresses risk (e.g., probability of failure by a certain time) as a function of the performance of model components and/or input parameters. These must be quantified from available data, perhaps using a combination of expert judgment and Bayesian statistics (due to the sparseness of directly relevant data). In Bayesian statistics, a subjective prior distribution (e.g., based on expert opinion) is updated with observed data to yield a posterior probability distribution for the quantity of interest (Lee 2004). Thus, Bayesian methods balance how likely a particular event was thought to be before evidence was available (based on expert opinion) against how consistent that opinion is with the new evidence.
Introductory Bayesian Statistics
Published in Daniel B. Rowe, Multivariate Bayesian Statistics, 2002
Bayesian Statistics is based on Bayes’ rule or conditional probability. It is well known that the probability of events A and B both occurring can be written as the probability of A occurring multiplied by the probability of B occurring given that A has occurred. This is written as P(AandB)=P(A)P(B|A)
Application of Bayesian machine learning for estimation of uncertainty in forecasted plume directions by atmospheric dispersion simulations
Published in Journal of Nuclear Science and Technology, 2023
Masanao Kadowaki, Haruyasu Nagai, Toshiya Yoshida, Hiroaki Terada, Katsunori Tsuduki, Hiroki Sawa
This study expands the previous study and develops a prediction method for uncertainty in the directions of forecasted radioactive plumes based on Bayesian machine learning using an accumulated dataset of simulations by WSPEEDI-DB. The Bayesian statistics is a probabilistic approach to estimate the posterior distribution given the likelihood and the prior distribution. It is known as an effective method to estimate values of physical variables that cannot be directly measured and the uncertainty of parameters with large errors, e.g. those included in ATDMs [16]. The unclear values and uncertainty are estimated by the Bayesian statistics model constructed using dataset of measurement and ATDM results. Smith et al. [17] estimated the uncertainties of employed parameters in the ATDM from the Bayesian statistics. In addition, the method using the Bayesian statistics was applied to the source term estimation for the FDNPP accident [18], the estimation of air concentrations of radionuclides by the ATDM [19], and the prediction of spatial deposition distributions with a machine learning [20]. In this study, the Bayesian statistics is applied to estimate a probabilistic distribution of the discrepancy angle in the plume directions between the analysis and forecast outputs for a certain feature of the forecast output. The Bayesian statistics model based on the estimation results can predict the variability of the discrepancy angle from the forecasted plume direction, which is provided as the uncertainty in the forecasted plume direction.
A novel pro-active approach towards SHM-based bridge management supported by FE analysis and Bayesian methods
Published in Structure and Infrastructure Engineering, 2020
Helder Sousa, Arpad Rozsas, Arthur Slobbe, Wim Courage
From a conceptual point of view, Bayesian statistics treats parameters as random variables and assigns probability distributions to them. This view is convenient when the inferred parameters are inputs in further analysis and the full representation of their uncertainty is needed. Additionally, Bayesian statistics can handle complex problems with messy data (Johnson & Milliken, 2006) and can combine information from different sources. These characteristics distinguish the Bayesian approach from the other, commonly used approach: frequentist statistics that focuses on data variability given a parameter value (Spiegelhalter & Rice, 2009). The main mathematical instrument of Bayesian statistics is the Bayes’ rule, which combines the information conveyed by new data and prior knowledge through the likelihood function and prior probabilities of parameters, respectively.
Macro-level hazardous material transportation safety analysis in China using a Bayesian negative binomial model combined with conditional autoregression prior
Published in Journal of Transportation Safety & Security, 2022
Shiwen Zhang, Shengdi Chen, Yingying Xing, H. Michael Zhang, Jian Lu, Sijin Long
Bayesian statistics are a combination of prior information and sample information of unknown parameters. The posterior distribution is obtained, and the statistical method of inferring unknown parameters is based on the posterior distribution (Wen et al. 2018). The Bayesian methods are usually calculated using the Markov chain Monte Carlo algorithm. The Gibbs sampling method is used in the software WinBUGS (Ntzoufras 2011) to complete the calibration of the Bayesian model. Because there is no reliable prior information, all regression coefficients are assumed to follow the normal distribution N (0, 105) according to the literature (Wen et al. 2018). The variance of random effects (bi) obeys the gamma distribution bi ∼ gamma (0.5, 0.0005). The discrete coefficient r of the NB distribution obeys the gamma distribution r ∼ gamma (0.001, 0.001). Two Markov chains are set to perform 10,000 iterations, the first 4,000 samples are discarded, and then a Bayesian CAR NB model is established. The posterior distribution of the THM, SI, and DIC values of the Bayesian CAR NB model are shown in Tables 2 and 3. The variables are significant if their confidence interval does not include zero (Aguero and Jovanis 2006). Thus, the GDPIndex, permanent resident population, mileage of substandard highways, road density, mileage of urban roads, number of hazmat transportation vehicles, and number of hazmat loaders are significant at the 95% Bayesian confidence interval (BCI). The number of hazmat transportation drivers is significant at the 90% BCI of hazmat crashes (Table 2). The permanent resident population, hospital density, mileage of high-grade highways, road density, mileage of urban roads, and number of hazmat loaders are significant at the 95% BCI. The mileage of substandard highways, mileage of low-grade highways, and number of companies transporting hazmat are significant at the 90% BCI of the number of severe hazmat crashes (Table 3).