{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,9,27]],"date-time":"2025-09-27T00:06:02Z","timestamp":1758931562366,"version":"3.44.0"},"reference-count":14,"publisher":"MDPI AG","issue":"10","license":[{"start":{"date-parts":[[2025,9,26]],"date-time":"2025-09-26T00:00:00Z","timestamp":1758844800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":["www.mdpi.com"],"crossmark-restriction":true},"short-container-title":["Entropy"],"abstract":"<jats:p>A Bayesian approach for constructing ARMA probability density estimators is proposed. Such estimators are ratios of trigonometric polynomials and have a number of advantages over Fourier series estimators, including parsimony and greater efficiency under common conditions. The Bayesian approach is carried out via MCMC, the output of which can be used to obtain probability intervals for unknown parameters and the underlying density. Finite sample efficiency and methods for choosing the estimator\u2019s smoothing parameter are considered in a simulation study, and the ideas are illustrated with data on a wine attribute.<\/jats:p>","DOI":"10.3390\/e27101001","type":"journal-article","created":{"date-parts":[[2025,9,26]],"date-time":"2025-09-26T08:31:28Z","timestamp":1758875488000},"page":"1001","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["A Bayesian ARMA Probability Density Estimator"],"prefix":"10.3390","volume":"27","author":[{"given":"Jeffrey D.","family":"Hart","sequence":"first","affiliation":[{"name":"Department of Statistics, Texas A&M University, College Station, TX 77843, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2025,9,26]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"842","DOI":"10.1214\/aos\/1176350839","article-title":"An ARMA type probability density estimator","volume":"16","author":"Hart","year":"1988","journal-title":"Ann. 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Density Estimation for Statistics and Data Analysis, Chapman & Hall\/CRC."},{"key":"ref_6","doi-asserted-by":"crossref","unstructured":"Woodward, W.A., Gray, H.L., and Elliott, A.C. (2012). Applied Time Series Analysis, CRC Press.","DOI":"10.1201\/b11459"},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"480","DOI":"10.1214\/aoms\/1177704159","article-title":"On the estimation of the probability density. I","volume":"34","author":"Watson","year":"1963","journal-title":"Ann. Math. Stat."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"1496","DOI":"10.1214\/aoms\/1177697523","article-title":"Density estimation by orthogonal series","volume":"40","author":"Watson","year":"1969","journal-title":"Ann. Math. 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Expansions and Asymptoics for Statistics, Chapman & Hall\/CRC."},{"key":"ref_13","unstructured":"R Core Team (2025). R: A Language and Environment for Statistical Computing, R Foundation for Statistical Computing. Available online: https:\/\/www.R-project.org\/."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"1065","DOI":"10.1016\/0031-3203(94)90145-7","article-title":"Comparative analysis of statistical pattern recognition methods in high dimensional settings","volume":"27","author":"Aeberhard","year":"1994","journal-title":"Pattern Recognit."}],"container-title":["Entropy"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1099-4300\/27\/10\/1001\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,9,26]],"date-time":"2025-09-26T08:38:53Z","timestamp":1758875933000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1099-4300\/27\/10\/1001"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,9,26]]},"references-count":14,"journal-issue":{"issue":"10","published-online":{"date-parts":[[2025,10]]}},"alternative-id":["e27101001"],"URL":"https:\/\/doi.org\/10.3390\/e27101001","relation":{},"ISSN":["1099-4300"],"issn-type":[{"value":"1099-4300","type":"electronic"}],"subject":[],"published":{"date-parts":[[2025,9,26]]}}}