{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T01:44:57Z","timestamp":1760060697801,"version":"build-2065373602"},"reference-count":39,"publisher":"MDPI AG","issue":"9","license":[{"start":{"date-parts":[[2025,9,13]],"date-time":"2025-09-13T00:00:00Z","timestamp":1757721600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>This paper proposes a novel transport quasi-Monte Carlo framework that combines randomized quasi-Monte Carlo sampling with a neural autoregressive flow architecture for efficient sampling and integration over complex, high-dimensional distributions. The method constructs a sequence of invertible transport maps to approximate the target density by decomposing it into a series of lower-dimensional marginals. Each sub-model leverages normalizing flows parameterized via monotonic beta-averaging transformations and is optimized using forward Kullback\u2013Leibler (KL) divergence. To enhance computational efficiency, a hidden-variable mechanism that transfers optimized parameters between sub-models is adopted. Numerical experiments on a banana-shaped distribution demonstrate that this new approach outperforms standard Monte Carlo-based normalizing flows in both sampling accuracy and integral estimation. Further, the model is applied to A-share stock return data and shows reliable predictive performance in semiannual return forecasts, while accurately capturing covariance structures across assets. The results highlight the potential of transport quasi-Monte Carlo (TQMC) in financial modeling and other high-dimensional inference tasks.<\/jats:p>","DOI":"10.3390\/e27090952","type":"journal-article","created":{"date-parts":[[2025,9,16]],"date-time":"2025-09-16T08:56:46Z","timestamp":1758013006000},"page":"952","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["A Quasi-Monte Carlo Method Based on Neural Autoregressive Flow"],"prefix":"10.3390","volume":"27","author":[{"given":"Yunfan","family":"Wei","sequence":"first","affiliation":[{"name":"School of Mathematics, South China University of Technology, Guangzhou 510641, China"}]},{"given":"Wei","family":"Xi","sequence":"additional","affiliation":[{"name":"School of Statistics, Beijing Normal University, Beijing 100875, China"}]}],"member":"1968","published-online":{"date-parts":[[2025,9,13]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1017\/S0962492900002804","article-title":"Monte carlo and quasi-monte carlo methods","volume":"7","author":"Caflisch","year":"1998","journal-title":"Acta Numer."},{"key":"ref_2","doi-asserted-by":"crossref","unstructured":"Kalos, M.H., and Whitlock, P.A. 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