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Sampling the Imaginary
Published in Richard McElreath, Statistical Rethinking, 2020
It is more common to see scientific journals reporting an interval of defined mass, usually known as a confidence interval. An interval of posterior probability, such as the ones we are working with, may instead be called a credible interval. We’re going to call it a compatibility interval instead, in order to avoid the unwarranted implications of “confidence” and “credibility.”54 What the interval indicates is a range of parameter values compatible with the model and data. The model and data themselves may not inspire confidence, in which case the interval will not either.
Uncertainty quantification for characterization of rock elastic modulus based on P-velocity
Published in Georisk: Assessment and Management of Risk for Engineered Systems and Geohazards, 2023
Jian Liu, Quan Jiang, Dingping Xu, Hong Zheng, Fengqiang Gong, Jie Xin
In addition, a concept that corresponds to the confidence interval in the frequentist approach is the credible interval of the posterior distribution. In Bayesian analysis, the parameter is a random variable with a certain distribution; therefore, the Bayesian credible interval can be understood as the interval containing the parameters with a certain probability. Although in some cases the results obtained by confidence interval and Bayesian credible interval are consistent, nonetheless the Bayesian credible interval provides engineers with a more intuitive parameter definition (Contreras, Brown, and Ruest 2018). The Highest-Posterior Density (HPD) interval is the most commonly used Bayesian credible interval, defining the shortest interval that contains a given portion of the probability density and thus can be used for subsequent analysis.
Co-learning of extrusion deposition quality for supporting interconnected additive manufacturing systems
Published in IISE Transactions, 2023
An-Tsun Wei, Hui Wang, Tarik Dickens, Hongmei Chi
To narrow the sampling range, the credible intervals of estimated parameters need to be constructed on the marginal distribution of the covariance. A credible interval represents the probability that the unobserved parameter value would fall in this range. Since the credible ranges are not unique, one challenge is which interval is more justifiable to be sampled since the interval could vary with the posterior distribution. In this case, the narrowest credible interval with a 95% probability (95%-NCI) can be selected to include the most plausible value of every entry from the posterior (The visualization of with a 95%-NCI is shown in Appendix. 2.2)
Bayesian Sparse Regression for Mixed Multi-Responses with Application to Runtime Metrics Prediction in Fog Manufacturing
Published in Technometrics, 2023
Xiaoyu Chen, Xiaoning Kang, Ran Jin, Xinwei Deng
Moreover, we also investigate statistical inferences for the uncertainty quantification of the predicted mixed metrics. Figure 8(a) reports the median of the predicted latent responses by the BS-MRMR and the associated 95% credible intervals on the testing data. In Figure 8, 95% credible intervals are presented by the shaded region, the median values of the predicted latent variables are plotted in black solid lines, and the true responses are plotted in blue dotted lines. Figure 8(b) and (c) report the prediction and the associated 95% credible intervals on the testing data from the BS-GLM and HGT methods, respectively. It is noted that the true responses are mainly contained by the 95% credible intervals from the proposed BS-MRMR model, while the 95% credible intervals of the BS-GLM and HGT do not perform well to cover the true responses. The narrow credible intervals of the BS-MRMR model can be attributed to the joint modeling of mixed responses and the quantification of hidden associations among these mixed responses. Note that the narrow credible intervals indicate low uncertainty in predicting runtime performance metrics. In addition, it is seen that the BS-GLM with Poisson response provides unstable prediction, which leads to extremely large credible intervals (see in Figure 8(b)). Besides, FS-GLM cannot provide uncertainty quantification, hence, its intervals are not available.