{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,5]],"date-time":"2026-08-05T13:48:03Z","timestamp":1785937683973,"version":"3.56.0"},"reference-count":70,"publisher":"MDPI AG","issue":"15","license":[{"start":{"date-parts":[[2026,8,5]],"date-time":"2026-08-05T00:00:00Z","timestamp":1785888000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>Accurate classification of infrasound signals is essential for nuclear-test verification, natural-hazard warning, and geophysical monitoring. Conventional convolutional neural networks (CNN) applied to this task tend to overfit small, class-imbalanced datasets and cannot quantify predictive uncertainty. To address these limitations, we introduce a Bayesian CNN framework that treats network weights as probability distributions and performs inference by variational approximation. LeNet-5, AlexNet, and 4Conv3Fc network serve as baselines and are converted into Bayes LeNet-5, Bayes AlexNet, and Bayes 4Conv3Fc. The short-time Fourier transform (STFT) provides time\u2013frequency spectrograms as model input. On a highly imbalanced dataset comprising nuclear tests, chemical explosions, volcanic eruptions, rocket launches, earthquakes, and lightning, Bayes 4Conv3Fc reaches an overall accuracy of 99.14% without any data augmentation. Relative to the deterministic baselines, precision, recall, and F1-score increase by up to 6.91, 7.12, and 7.20 percentage points, respectively, and Cohen\u2019s Kappa coefficient by up to 8.86 percentage points. Against class-weighted cross-entropy, a standard imbalance-handling baseline, the Bayesian models yield consistently lower Brier scores, indicating that the gains stem from principled uncertainty modelling rather than loss re-weighting alone.. This study quantifies both epistemic and aleatoric uncertainty in an infrasound signal classification model, and the calibration analysis validates that these uncertainty estimates are reliable, providing a basis for evaluating prediction reliability and diagnosing potential failure modes, thereby contributing to improved model interpretability. Coupled with an event-level data partitioning strategy, the evaluation faithfully reflects the model\u2019s generalization to unseen events and offers a promising direction toward uncertainty-aware infrasound monitoring.<\/jats:p>","DOI":"10.3390\/s26154955","type":"journal-article","created":{"date-parts":[[2026,8,5]],"date-time":"2026-08-05T13:16:29Z","timestamp":1785935789000},"page":"4955","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Bayesian Convolutional Neural Networks for Uncertainty-Aware Classification of Infrasound Events"],"prefix":"10.3390","volume":"26","author":[{"given":"Hao","family":"Yin","sequence":"first","affiliation":[{"name":"Key Laboratory of Chemistry for NBC Hazards Protection, Beijing 102205, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Kai","family":"Zhang","sequence":"additional","affiliation":[{"name":"Key Laboratory of Chemistry for NBC Hazards Protection, Beijing 102205, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Yu","family":"Lu","sequence":"additional","affiliation":[{"name":"Key Laboratory of Chemistry for NBC Hazards Protection, Beijing 102205, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Yunfen","family":"Chang","sequence":"additional","affiliation":[{"name":"Key Laboratory of Chemistry for NBC Hazards Protection, Beijing 102205, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Yunhui","family":"Wu","sequence":"additional","affiliation":[{"name":"Key Laboratory of Chemistry for NBC Hazards Protection, Beijing 102205, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Fan","family":"Yang","sequence":"additional","affiliation":[{"name":"Key Laboratory of Chemistry for NBC Hazards Protection, Beijing 102205, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Xuexu","family":"Li","sequence":"additional","affiliation":[{"name":"Key Laboratory of Chemistry for NBC Hazards Protection, Beijing 102205, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Jiaoheng","family":"Xu","sequence":"additional","affiliation":[{"name":"Key Laboratory of Chemistry for NBC Hazards Protection, Beijing 102205, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Xinliang","family":"Pang","sequence":"additional","affiliation":[{"name":"Key Laboratory of Chemistry for NBC Hazards Protection, Beijing 102205, China"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2026,8,5]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"1682","DOI":"10.1093\/gji\/ggv387","article-title":"Improved Bayesian Infrasonic Source Localization for Regional Infrasound","volume":"203","author":"Blom","year":"2015","journal-title":"Geophys. J. Int."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"917","DOI":"10.1007\/s10064-020-01982-w","article-title":"Method for Feature Analysis and Intelligent Recognition of Infrasound Signals of Soil Landslides","volume":"80","author":"Liu","year":"2021","journal-title":"Bull. Eng. Geol. Environ."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"e2024GL109276","DOI":"10.1029\/2024GL109276","article-title":"Retrieving Seismic Source Characteristics Using Seismic and Infrasound Data: The 2020 ML 4.1 Kiruna Minequake, Sweden","volume":"51","author":"Turquet","year":"2024","journal-title":"Geophys. Res. Lett."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"4735","DOI":"10.1002\/2014GL060375","article-title":"Location and Analysis of Acoustic Infrasound Pulses in Lightning","volume":"41","author":"Arechiga","year":"2014","journal-title":"Geophys. Res. Lett."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"L15802","DOI":"10.1029\/2008GL034193","article-title":"Characterization of Infrasound from Lightning","volume":"35","author":"Assink","year":"2008","journal-title":"Geophys. Res. Lett."},{"key":"ref_6","doi-asserted-by":"crossref","unstructured":"Farges, T., Hupe, P., Pichon, A.L., Ceranna, L., Listowski, C., and Diawara, A. (2021). Infrasound Thunder Detections across 15 Years over Ivory Coast: Localization, Propagation, and Link with the Stratospheric Semi-Annual Oscillation. Atmosphere, 12.","DOI":"10.3390\/atmos12091188"},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"e2024JB029194","DOI":"10.1029\/2024JB029194","article-title":"Detection and Characterization of Seismic and Acoustic Signals at Pavlof Volcano, Alaska, Using Deep Learning","volume":"129","author":"Tan","year":"2024","journal-title":"J. Geophys. Res. Solid Earth"},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"44","DOI":"10.1007\/s00445-022-01544-w","article-title":"Volcano Infrasound: Progress and Future Directions","volume":"84","author":"Watson","year":"2022","journal-title":"Bull. Volcanol."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"3526","DOI":"10.1002\/2016GL068497","article-title":"On the Infrasound Detected from the 2013 and 2016 DPRK\u2019s Underground Nuclear Tests","volume":"43","author":"Assink","year":"2016","journal-title":"Geophys. Res. Lett."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"L22802","DOI":"10.1029\/2009GL041017","article-title":"Infrasound Observation of the Apparent North Korean Nuclear Test of 25 May 2009","volume":"36","author":"Che","year":"2009","journal-title":"Geophys. Res. Lett."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"495","DOI":"10.1093\/gji\/ggu150","article-title":"Infrasound Signals from the Underground Nuclear Explosions of North Korea","volume":"198","author":"Che","year":"2014","journal-title":"Geophys. J. Int."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"e2021GL094861","DOI":"10.1029\/2021GL094861","article-title":"Infrasound from a Buried Chemical Explosion Recorded on a Balloon in the Lower Stratosphere","volume":"48","author":"Bowman","year":"2021","journal-title":"Geophys. Res. Lett."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"13027","DOI":"10.1038\/s41598-019-49494-2","article-title":"Rich Observations of Local and Regional Infrasound Phases Made by the AlpArray Seismic Network after Refinery Explosion","volume":"9","author":"Fuchs","year":"2019","journal-title":"Sci. Rep."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"908","DOI":"10.1029\/2018JB016705","article-title":"Seismoacoustic Analysis of Chemical Explosions at the Nevada National Security Site","volume":"124","author":"Pasyanos","year":"2019","journal-title":"J. Geophys. Res. Solid Earth"},{"key":"ref_15","first-page":"853","article-title":"Detecting Accidental Chemical Explosions Using the Seismo-Acoustic Network of Plo\u015ftina, Romania","volume":"68","author":"Stancu","year":"2016","journal-title":"Rom. Rep. Phys."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"1785","DOI":"10.1093\/gji\/ggy092","article-title":"Infrasound from the 2009 and 2017 DPRK Rocket Launches","volume":"213","author":"Evers","year":"2018","journal-title":"Geophys. J. Int."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"e2020GL092262","DOI":"10.1029\/2020GL092262","article-title":"1001 Rocket Launches for Space Missions and Their Infrasonic Signature","volume":"48","author":"Pilger","year":"2021","journal-title":"Geophys. Res. Lett."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"1375","DOI":"10.1007\/s00024-022-03055-3","article-title":"The State of the Stratosphere Throughout the Seasons: How Well Can Atmospheric Models Explain Infrasound Observations at Regional Distances?","volume":"180","author":"Pilger","year":"2023","journal-title":"Pure Appl. Geophys."},{"key":"ref_19","doi-asserted-by":"crossref","unstructured":"Iyer, A.S., Ham, F.M., and Garces, M.A. (2011). Neural Classification of Infrasonic Signals Associated with Hazardous Volcanic Eruptions. Proceedings of the 2011 International Joint Conference on Neural Networks, IEEE.","DOI":"10.1109\/IJCNN.2011.6033240"},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"e859","DOI":"10.1016\/j.na.2005.02.016","article-title":"Discrimination of Infrasound Events Using Parallel Neural Network Classification Banks","volume":"63","author":"Park","year":"2005","journal-title":"Nonlinear Anal. Theory Methods Appl."},{"key":"ref_21","first-page":"1","article-title":"Deep Wavelet Scattering Features for Infrasonic Threat Identification","volume":"Volume 10629","author":"Fountain","year":"2018","journal-title":"Proceedings of the Chemical, Biological, Radiological, Nuclear, and Explosives (CBRNE) Sensing XIX"},{"key":"ref_22","unstructured":"Chilo, J. (2007, January 12\u201315). Classification of Infrasound Events with Various Machine Learning Techniques. Proceedings of the International Conference on Cybernetics and Information Technologies, Orlando, FL, USA."},{"key":"ref_23","unstructured":"Fountain, A.W., Guicheteau, J.A., and Howle, C.R. (2018). Near-Field Infrasound Classification of Rocket Launch Signatures. Proceedings of the Chemical, Biological, Radiological, Nuclear, and Explosives (CBRNE) Sensing XIX, SPIE."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"116","DOI":"10.1016\/j.apacoust.2016.06.019","article-title":"Infrasound Signal Classification Based on Spectral Entropy and Support Vector Machine","volume":"113","author":"Li","year":"2016","journal-title":"Appl. Acoust."},{"key":"ref_25","doi-asserted-by":"crossref","unstructured":"Zhang, Y., Chen, Q., Su, P., Liu, D., Cui, J., Chen, J., Ma, J., Xing, Q., Xu, F., and Fan, Y. (2023). Research on the Response Characteristics and Identification of Infrasound Signals in the Jialongcuo Ice Avalanche, Tibet. Remote Sens., 15.","DOI":"10.3390\/rs15184482"},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"456818","DOI":"10.1155\/2014\/456818","article-title":"A New Classification Method of Infrasound Events Using Hilbert-Huang Transform and Support Vector Machine","volume":"2014","author":"Liu","year":"2014","journal-title":"Math. Probl. Eng."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"253","DOI":"10.1111\/j.1365-246X.2011.04951.x","article-title":"Clustering and Classification of Infrasonic Events at Mount Etna Using Pattern Recognition Techniques","volume":"185","author":"Cannata","year":"2011","journal-title":"Geophys. J. Int."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"191","DOI":"10.24425\/aoa.2023.145230","article-title":"Infrasound Signal Classification Based on ICA and SVM","volume":"48","author":"Lu","year":"2023","journal-title":"Arch. Acoust."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"921","DOI":"10.1785\/0220190116","article-title":"Benchmarking Current and Emerging Approaches to Infrasound Signal Classification","volume":"91","author":"Albert","year":"2020","journal-title":"Seismol. Res. Lett."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"403","DOI":"10.24425\/aoa.2023.145247","article-title":"VMD and CNN-Based Classification Model for Infrasound Signal","volume":"48","author":"Lu","year":"2023","journal-title":"Arch. Acoust."},{"key":"ref_31","first-page":"457","article-title":"Classification of chemical explosion and earthquake infrasound based on 1-D convolutional neural network","volume":"40","author":"Tan","year":"2021","journal-title":"J. Appl. Acoust."},{"key":"ref_32","unstructured":"Fountain, A.W., Guicheteau, J.A., and Howle, C.R. (2018). Infrasound Threat Classification: A Statistical Comparison of Deep Learning Architectures. Proceedings of the Chemical, Biological, Radiological, Nuclear, and Explosives (CBRNE) Sensing XIX, SPIE."},{"key":"ref_33","first-page":"28","article-title":"Regional Infrasonic and Seismic Event Classification with Machine Learning","volume":"Volume 12116","author":"Guicheteau","year":"2022","journal-title":"Proceedings of the Chemical, Biological, Radiological, Nuclear, and Explosives (CBRNE) Sensing XXIII"},{"key":"ref_34","first-page":"758","article-title":"Research on Deep Learning Method of Atmospheric Low Frequency Acoustic Signal Recognition","volume":"49","author":"Wu","year":"2020","journal-title":"J. Univ. Electron. Sci. Technol. China"},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"e2022GL097785","DOI":"10.1029\/2022GL097785","article-title":"Detecting Large Explosions With Machine Learning Models Trained on Synthetic Infrasound Data","volume":"49","author":"Witsil","year":"2022","journal-title":"Geophys. Res. Lett."},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"2434","DOI":"10.1121\/10.0014903","article-title":"Deep Learning Categorization of Infrasound Array Data","volume":"152","author":"Bishop","year":"2022","journal-title":"J. Acoust. Soc. Am."},{"key":"ref_37","doi-asserted-by":"crossref","unstructured":"Leng, X., Feng, L., Ou, O., Du, X., Liu, D., and Tang, X. (2022). Debris Flow Infrasound Recognition Method Based on Improved LeNet-5 Network. Sustainability, 14.","DOI":"10.3390\/su142315925"},{"key":"ref_38","first-page":"892","article-title":"Infrasound event classification with multi-channel multi-scale convolutional attention network","volume":"50","author":"Tan","year":"2025","journal-title":"Acta Acust."},{"key":"ref_39","doi-asserted-by":"crossref","unstructured":"Tan, X., Li, X., Li, H., Zeng, X., Liu, T., and Luo, S. (2025). A Deep Learning Approach for Distant Infrasound Signals Classification. Sensors, 25.","DOI":"10.3390\/s25072058"},{"key":"ref_40","doi-asserted-by":"crossref","unstructured":"Tan, X., Li, X., Li, H., Zeng, X., Luo, S., and Liu, T. (2025). A Deep Learning Approach for Spatiotemporal Feature Classification of Infrasound Signals. Geosciences, 15.","DOI":"10.3390\/geosciences15070251"},{"key":"ref_41","doi-asserted-by":"crossref","first-page":"579","DOI":"10.1007\/s11770-024-1089-4","article-title":"Infrasound Event Classification Fusion Model Based on Multiscale SE-CNN and BiLSTM","volume":"21","author":"Li","year":"2024","journal-title":"Appl. Geophys."},{"key":"ref_42","doi-asserted-by":"crossref","first-page":"667","DOI":"10.1007\/s11770-024-1112-9","article-title":"Classification Method of Infrasound Events Based on the MVIDA Algorithm and MS-SE-ResNet","volume":"21","author":"Tan","year":"2024","journal-title":"Appl. Geophys."},{"key":"ref_43","first-page":"3755","article-title":"TimeGAN and Coordinated Attention Prototype Network Based Prediction Model for Infrasound Signal","volume":"51","author":"Lu","year":"2026","journal-title":"Arch. Acoust."},{"key":"ref_44","first-page":"1193","article-title":"A method for classification of few-shot infrasound signals applying prototype network","volume":"43","author":"Zhao","year":"2024","journal-title":"J. Appl. Acoust."},{"key":"ref_45","first-page":"38","article-title":"Study on classification of Infrasound Signals Based on Short-Time Fourier Transform and Convolutional Neural Network","volume":"3","author":"Yin","year":"2024","journal-title":"CBRN Def."},{"key":"ref_46","doi-asserted-by":"crossref","first-page":"e2022GL101528","DOI":"10.1029\/2022GL101528","article-title":"Global Nuclear Explosion Discrimination Using a Convolutional Neural Network","volume":"50","author":"Barama","year":"2023","journal-title":"Geophys. Res. Lett."},{"key":"ref_47","doi-asserted-by":"crossref","first-page":"249","DOI":"10.1016\/j.neunet.2018.07.011","article-title":"A Systematic Study of the Class Imbalance Problem in Convolutional Neural Networks","volume":"106","author":"Buda","year":"2018","journal-title":"Neural Netw."},{"key":"ref_48","doi-asserted-by":"crossref","first-page":"1558","DOI":"10.1109\/PROC.1977.10770","article-title":"A Unified Approach to Short-Time Fourier Analysis and Synthesis","volume":"65","author":"Allen","year":"1977","journal-title":"Proc. IEEE"},{"key":"ref_49","doi-asserted-by":"crossref","first-page":"55","DOI":"10.1109\/TASSP.1980.1163359","article-title":"Time-Frequency Representation of Digital Signals and Systems Based on Short-Time Fourier Analysis","volume":"28","author":"Portnoff","year":"1980","journal-title":"IEEE Trans. Acoust. Speech Signal Process."},{"key":"ref_50","doi-asserted-by":"crossref","first-page":"203","DOI":"10.1190\/1.1441328","article-title":"Wave Propagation and Sampling Theory; Part I, Complex Signal and Scattering in Multilayered Media","volume":"47","author":"Morlet","year":"1982","journal-title":"Geophysics"},{"key":"ref_51","doi-asserted-by":"crossref","first-page":"222","DOI":"10.1190\/1.1441329","article-title":"Wave Propagation and Sampling Theory; Part II, Sampling Theory and Complex Waves","volume":"47","author":"Morlet","year":"1982","journal-title":"Geophysics"},{"key":"ref_52","doi-asserted-by":"crossref","first-page":"903","DOI":"10.1098\/rspa.1998.0193","article-title":"The Empirical Mode Decomposition and the Hilbert Spectrum for Nonlinear and Non-Stationary Time Series Analysis","volume":"454","author":"Huang","year":"1998","journal-title":"Proc. R. Soc. A Math. Phys. Eng. Sci."},{"key":"ref_53","doi-asserted-by":"crossref","unstructured":"Yin, H., Lu, Y., Chang, Y., Zhang, K., Wu, Y., Yang, F., Li, X., Pang, X., and Li, P. (2026). Classification of Infrasonic Signals Based on Time-Frequency Representation. Front. Signal Process., 6.","DOI":"10.3389\/frsip.2026.1844194"},{"key":"ref_54","first-page":"5436","article-title":"Being Bayesian, Even Just a Bit, Fixes Overconfidence in ReLU Networks","volume":"Volume 119","author":"Kristiadi","year":"2020","journal-title":"Proceedings of the 37th International Conference on Machine Learning (ICML\u201920)"},{"key":"ref_55","doi-asserted-by":"crossref","first-page":"243","DOI":"10.1016\/j.inffus.2021.05.008","article-title":"A Review of Uncertainty Quantification in Deep Learning: Techniques, Applications and Challenges","volume":"76","author":"Abdar","year":"2021","journal-title":"Inf. Fusion"},{"key":"ref_56","doi-asserted-by":"crossref","first-page":"5506305","DOI":"10.1109\/LGRS.2023.3287504","article-title":"Bayesian Convolutional Neural Networks for Limited Data Hyperspectral Remote Sensing Image Classification","volume":"20","author":"Joshaghani","year":"2023","journal-title":"IEEE Geosci. Remote Sens. Lett."},{"key":"ref_57","doi-asserted-by":"crossref","first-page":"70519","DOI":"10.1109\/ACCESS.2024.3401234","article-title":"Bayesian Neural Networks via MCMC: A Python-Based Tutorial","volume":"12","author":"Chandra","year":"2024","journal-title":"IEEE Access"},{"key":"ref_58","doi-asserted-by":"crossref","unstructured":"Robert, C.P., and Casella, G. (2004). Monte Carlo Statistical Methods, Springer. Springer Texts in Statistics.","DOI":"10.1007\/978-1-4757-4145-2"},{"key":"ref_59","doi-asserted-by":"crossref","first-page":"254","DOI":"10.1198\/0003130032413","article-title":"A History of the Metropolis\u2013Hastings Algorithm","volume":"57","author":"Hitchcock","year":"2003","journal-title":"Am. Stat."},{"key":"ref_60","doi-asserted-by":"crossref","first-page":"207","DOI":"10.1016\/0304-4149(94)90134-1","article-title":"Simple Conditions for the Convergence of the Gibbs Sampler and Metropolis-Hastings Algorithms","volume":"49","author":"Roberts","year":"1994","journal-title":"Stoch. Processes Their Appl."},{"key":"ref_61","doi-asserted-by":"crossref","first-page":"281","DOI":"10.1007\/s00180-018-00861-z","article-title":"Neural Network Gradient Hamiltonian Monte Carlo","volume":"34","author":"Li","year":"2019","journal-title":"Comput. Stat."},{"key":"ref_62","doi-asserted-by":"crossref","first-page":"11773","DOI":"10.1007\/s10462-023-10443-1","article-title":"Bayesian Learning for Neural Networks: An Algorithmic Survey","volume":"56","author":"Magris","year":"2023","journal-title":"Artif. Intell. Rev."},{"key":"ref_63","doi-asserted-by":"crossref","first-page":"859","DOI":"10.1080\/01621459.2017.1285773","article-title":"Variational Inference: A Review for Statisticians","volume":"112","author":"Blei","year":"2017","journal-title":"J. Am. Stat. Assoc."},{"key":"ref_64","unstructured":"Graves, A. (2011, January 12\u201314). Practical Variational Inference for Neural Networks. Proceedings of the Advances in Neural Information Processing Systems, Granada, Spain."},{"key":"ref_65","doi-asserted-by":"crossref","first-page":"25","DOI":"10.1023\/A:1008932416310","article-title":"Bayesian Parameter Estimation via Variational Methods","volume":"10","author":"Jaakkola","year":"2000","journal-title":"Stat. Comput."},{"key":"ref_66","doi-asserted-by":"crossref","unstructured":"Cinelli, L.P., Marins, M.A., Barros Da Silva, E.A., and Netto, S.L. (2021). Variational Methods for Machine Learning with Applications to Deep Networks, Springer International Publishing.","DOI":"10.1007\/978-3-030-70679-1"},{"key":"ref_67","unstructured":"Blundell, C., Cornebise, J., Kavukcuoglu, K., and Wierstra, D. (2015). Weight Uncertainty in Neural Networks. Proceedings of the 32nd International Conference on Machine Learning, PMLR."},{"key":"ref_68","unstructured":"Kingma, D.P., Salimans, T., and Welling, M. (2015, January 7\u201312). Variational Dropout and the Local Reparameterization Trick. Proceedings of the Advances in Neural Information Processing Systems 28 (NIPS 2015), Montreal, QC, Canada."},{"key":"ref_69","unstructured":"Shridhar, K., Laumann, F., and Liwicki, M. (2019). A Comprehensive Guide to Bayesian Convolutional Neural Network with Variational Inference. arXiv."},{"key":"ref_70","doi-asserted-by":"crossref","first-page":"159","DOI":"10.2307\/2529310","article-title":"The Measurement of Observer Agreement for Categorical Data","volume":"33","author":"Landis","year":"1977","journal-title":"Biometrics"}],"container-title":["Sensors"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1424-8220\/26\/15\/4955\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,8,5]],"date-time":"2026-08-05T13:18:21Z","timestamp":1785935901000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1424-8220\/26\/15\/4955"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,8,5]]},"references-count":70,"journal-issue":{"issue":"15","published-online":{"date-parts":[[2026,8]]}},"alternative-id":["s26154955"],"URL":"https:\/\/doi.org\/10.3390\/s26154955","relation":{},"ISSN":["1424-8220"],"issn-type":[{"value":"1424-8220","type":"electronic"}],"subject":[],"published":{"date-parts":[[2026,8,5]]}}}