{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,28]],"date-time":"2026-02-28T04:23:40Z","timestamp":1772252620412,"version":"3.50.1"},"reference-count":28,"publisher":"MDPI AG","issue":"1","license":[{"start":{"date-parts":[[2021,1,3]],"date-time":"2021-01-03T00:00:00Z","timestamp":1609632000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Algorithms"],"abstract":"<jats:p>Bootstrap resampling techniques, introduced by Efron and Rubin, can be presented in a general Bayesian framework, approximating the statistical distribution of a statistical functional \u03d5(F), where F is a random distribution function. Efron\u2019s and Rubin\u2019s bootstrap procedures can be extended, introducing an informative prior through the Proper Bayesian bootstrap. In this paper different bootstrap techniques are used and compared in predictive classification and regression models based on ensemble approaches, i.e., bagging models involving decision trees. Proper Bayesian bootstrap, proposed by Muliere and Secchi, is used to sample the posterior distribution over trees, introducing prior distributions on the covariates and the target variable. The results obtained are compared with respect to other competitive procedures employing different bootstrap techniques. The empirical analysis reports the results obtained on simulated and real data.<\/jats:p>","DOI":"10.3390\/a14010011","type":"journal-article","created":{"date-parts":[[2021,1,3]],"date-time":"2021-01-03T19:54:46Z","timestamp":1609703686000},"page":"11","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":7,"title":["A Bayesian Nonparametric Learning Approach to Ensemble Models Using the Proper Bayesian Bootstrap"],"prefix":"10.3390","volume":"14","author":[{"given":"Marta","family":"Galvani","sequence":"first","affiliation":[{"name":"Department of Mathematics, University of Pavia, 27100 Pavia, Italy"}]},{"given":"Chiara","family":"Bardelli","sequence":"additional","affiliation":[{"name":"Department of Mathematics, University of Pavia, 27100 Pavia, Italy"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-5756-7831","authenticated-orcid":false,"given":"Silvia","family":"Figini","sequence":"additional","affiliation":[{"name":"Department of Political and Social Sciences, University of Pavia, 27100 Pavia, Italy"}]},{"given":"Pietro","family":"Muliere","sequence":"additional","affiliation":[{"name":"Department of Decision Sciences, Bocconi University, 20100 Milano, Italy"}]}],"member":"1968","published-online":{"date-parts":[[2021,1,3]]},"reference":[{"key":"ref_1","unstructured":"Breiman, L., Friedman, J., Olshen, R.A., and Stone, C.J. 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