{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,2]],"date-time":"2026-05-02T07:00:04Z","timestamp":1777705204869,"version":"3.51.4"},"reference-count":43,"publisher":"SAGE Publications","issue":"4","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["IFS"],"published-print":{"date-parts":[[2024,4,18]]},"abstract":"<jats:p>The conventional approaches to constructing Prediction Intervals (PIs) always follow the principle of \u2018high coverage and narrow width\u2019. However, the deviation information has been largely neglected, making the PIs unsatisfactory. For high-risk forecasting tasks, the cost of forecast failure may be prohibitive. To address this, this work introduces a multi-objective loss function that includes Prediction Interval Accumulation Deviation (PIAD) within the Lower Upper Bound Estimation (LUBE) framework. The proposed model can achieve the goal of \u2018high coverage, narrow width, and small bias\u2019 in PIs, thus minimizing costs even in cases of prediction failure. A salient feature of the LUBE framework is its ability to discern uncertainty without explicit uncertainty labels, where the data uncertainty and model uncertainty are learned by Deep Neural Networks (DNN) and a model ensemble, respectively. The validity of the proposed method is demonstrated through its application to the prediction of carbon prices in China. Compared with conventional uncertainty quantification methods, the improved interval optimization method can achieve narrower PI widths.<\/jats:p>","DOI":"10.3233\/jifs-237524","type":"journal-article","created":{"date-parts":[[2024,3,8]],"date-time":"2024-03-08T10:16:21Z","timestamp":1709892981000},"page":"10441-10456","source":"Crossref","is-referenced-by-count":0,"title":["Constructing prediction intervals to explore uncertainty based on deep neural networks"],"prefix":"10.1177","volume":"46","author":[{"given":"Jingling","family":"Yang","sequence":"first","affiliation":[{"name":"School of Big Data and Statistics, Anhui University, Hefei, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Liren","family":"Chen","sequence":"additional","affiliation":[{"name":"School of Marine Science and Technology, Tianjin University, Tianjin, 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