A Bayesian Nonlinear Reduced Order Modeling Using Variational AutoEncoders by Nissrine Akkari, Fabien Casenave, Elie Hachem, David Ryckelynck

“…The parameters of the conditional posterior probability of the reduced coefficients are the ones of the encoder layers of the same autoencoder. …”
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Evidence and Credibility: Full Bayesian Significance Test for Precise Hypotheses by Julio Michael Stern, Carlos Alberto de Bragança Pereira

“…In fact, a set is defined in the parameter space and the posterior probability, its credibility, is evaluated. This set is the "Highest Posterior Density Region" that is "tangent" to the set that defines the null hypothesis. …”
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Application of Discriminative Training Algorithm Based on Intelligent Computing in English Translation Evaluation by Li Xue

“…This method combines the posterior probability and the phoneme accuracy rate to select the data. …”
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Evaluation of Bayesian methods of genomic association via chromosomic regions using simulated data by Leísa Pires Lima, Camila Ferreira Azevedo, Marcos Deon Vilela de Resende, Moysés Nascimento, Fabyano Fonseca e Silva

“…Among the selection criteria for SNPs or regions, selection criterion by percentage of variance can be explained by genomic regions (%var), selection of tag SNPs, and selection based on the window posterior probability of association (WPPA). To also detect potentially associated regions, we proposed measuring posterior probability of the interval PPint), which aims to select regions based on the markers of greatest effects. …”
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Research on an Optimized Evaluation Method of the Bearing Capacity of Reinforced Concrete Beam Based on the Bayesian Theory by Lifeng Wang, Ziwang Xiao, Fei Yu, Wei Li, Ning Fu

“…Then, based on a large amount of analysis data, the improved MH sampling method and TMCMC sampling method were used to establish a posterior probability distribution database. Finally, multiple posterior probability distributions were used to identify and predict the bearing capacity. …”
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Analysis of Structural Health Monitoring Data with Correlated Measurement Error by Bayesian System Identification: Theory and Application by He-Qing Mu, Xin-Xiong Liang, Ji-Hui Shen, Feng-Liang Zhang

“…Bayesian system identification is conducted to achieve not only the posterior probability density function (PDF) for the model parameters, but also the posterior probability of each candidate model class for selecting the most suitable/plausible model class for the measurement error. …”
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Quantitative prediction process and evaluation method for seafloor polymetallic sulfide resources by Mengyi Ren, Jianping Chen, Ke Shao, Miao Yu, Jie Fang

“…In stage two, the Chinese contract area of 48°–52°E has the highest posterior probability value, which can be selected as the reserved region for additional exploration. …”
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Bayesian Analysis for Parameters of Multivariate tFA model with Simulation by Ahmed Sami, hayfa saieed

“…We obtained a posterior probability criterion to choose the number of extracted factors for the two models. …”
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Multilevel Markov chain Monte Carlo for Bayesian inverse problem for Navier-Stokes equation by Yang, Juntao, Hoang, Viet Ha

“…The computation cost of sampling the posterior probability measure can be exceedingly high. We develop the Finite Element Multilevel Markov Chain Monte Carlo (FE-MLMCMC) sampling method for approximating ex-pectation with respect to the posterior probability measure of quantities of interest for a model problem of Navier-Stokes equation in the two dimensional periodic torus. …”
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Fine scale mapping of genetic loci associated with human disease by Maller, J

“…We defined using Bayes theorem sets of SNPs (credible sets) that were 95% likely (posterior probability) to contain the causal disease variants. …”

Review and prospect of structural equation modeling in geoscience data modeling and analysis by LIU Jiangtao, ZHAO Jie, WU Fafu

“…In response to the above three issues, this article reviews the concept and development of SEM, and introduces three application cases of SEM in geological data modeling.One is using lake sediment geochemical data to extract mineralization endogenous factors in gold mines which is modeled under weak constraints.The second is using the comprehensive parameter optimization method of SEM to weaken and correct CI problem of weight of evidence in the calculation of the posterior probability of gold prospecting by matching the posterior probability and the observation posterior probability. …”
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Immunomodulatory therapy in children with paediatric inflammatory multisystem syndrome temporally associated with SARS-CoV-2 (PIMS-TS, MIS-C; RECOVERY): a randomised, controlled, o... by RECOVERY Collaborative Group

“…Mean duration of hospital stay was 6·6 days (SD 0·7) in children assigned to second-line tocilizumab and 9·9 days (0·9) in children assigned to usual care (difference –3·3 days, 95% CrI –5·6 to –1·0; posterior probability >99%). Mean duration of hospital stay was 8·5 days (SD 1·2) in children assigned to anakinra (difference from usual care –1·4 days, 95% CrI –4·3 to 1·8; posterior probability 84%). …”

Bayesian probability updates using sampling/importance resampling: Applications in nuclear theory by Weiguang Jiang, Christian Forssén

“…To this end we both analyse a toy problem and demonstrate realistic applications of importance resampling to infer the posterior distribution for parameters of ΔNNLO interaction model based on chiral effective field theory and to estimate the posterior probability distribution of target observables. …”
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Data-Targeted Prior Distribution for Variational AutoEncoder by Nissrine Akkari, Fabien Casenave, Thomas Daniel, David Ryckelynck

“…We used inferential methods to compute a sharp approximation of the posterior probability of these parameters with the transient dynamics of the training velocity fields and to generate plausible velocity fields. …”
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Polar Sea Ice Detection Using a Rotating Fan Beam Scatterometer by Liling Liu, Xiaolong Dong, Wenming Lin, Shuyan Lang

“…The implementation of this method includes the definition of CSCAT backscatter space, an estimation of the sea ice Physical Model Function (GMF), a calculation of the sea ice backscatter distance to the sea ice GMF, a probability distribution function (PDF) estimation of the square distance to the GMF (sea ice GMF and wind GMF), and a calculation of the sea ice Bayesian posterior probability. This algorithm was used to generate a daily CSCAT polar sea ice mask during the CSCAT mission period (2019–2022) (by setting a 55% threshold on the Bayesian posterior probability). …”
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Sex Differentiation from Fingerprint Ridge Density by Jwala Kandel, Samjhana Ghimire, Rashmita Bhandari

“…Likelihood ratio and posterior probability using Baye’s theorem were calculated to interpret the possibility of gender differentiation from various fingerprint ridge densities. …”
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Joint Inversions of Ground Deformation, Extrusion Flux, and Gas Emissions Using Physics‐Based Models for the Mount St. Helens 2004–2008 Eruption by Ying‐Qi Wong, Paul Segall

“…We find models that fit all three data sets well. Posterior probability density functions suggest an elongate chamber with aspect ratio less than 0.55, located at 9–17 km depth. …”
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An efficient probabilistic workflow for estimating induced earthquake parameters in 3D heterogeneous media by L. O. M. Masfara, T. Cullison, C. Weemstra, C. Weemstra

“…Using the synthetic case, we find that our proposed workflow is able to recover the posterior probability of these source parameters rather well, even when the prior model information is inaccurate, imprecise, or both inaccurate and imprecise.…”
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Inverse uncertainty quantification using the modular Bayesian approach based on Gaussian Process, Part 2: Application to TRACE by Wu, Xu, Kozlowski, Tomasz, Meidani, Hadi, Shirvan, Koroush

“…The resulting posterior probability distributions of TRACE parameters can be used in future uncertainty, sensitivity and validation studies of TRACE code for nuclear reactor system design and safety analysis.…”
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Effect of convalescent plasma on organ support-free days in critically ill patients With COVID-19: a randomized clinical trial by Estcourt, LJ, Turgeon, AF, McQuilten, ZK, McVerry, BJ, Al-Beidh, F, Annane, D, Arabi, YM, Arnold, DM, Beane, A, Bégin, P, van Bentum-Puijk, W, Berry, LR, Bhimani, Z, Birchall, JE, Bonten, MJM, Bradbury, CA, Brunkhorst, FM, Buxton, M, Callum, JL, Chassé, M, Cheng, AC, Cove, ME, Daly, J, Derde, L, Detry, MA, De Jong, M, Evans, A, Fergusson, DA, Fish, M, Fitzgerald, M, Foley, C, Goossens, H, Gordon, AC, Gosbell, IB, Green, C, Haniffa, R, Harvala, H, Higgins, AM, Hills, TE, Hoad, VC, Horvat, C, Huang, DT, Hudson, CL, Ichihara, N, Laing, E, Lamikanra, AA, Lamontagne, F, Roberts, DJ

“…Futility was defined as the posterior probability of an OR less than 1.2 (threshold for trial conclusion of futility >95%). …”