[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-119248-en":3,"doc-seo-119248-105":30,"detail-sidebar-cat-0-en-105":91},{"code":4,"msg":5,"data":6},0,"success",{"doc_id":7,"user_id":8,"nickname":9,"user_avatar":10,"doc_module":4,"category_id":11,"category_name":12,"doc_title":13,"doc_description":14,"doc_content":15,"file_id":16,"file_url":17,"file_type":18,"file_size":19,"view_count":4,"is_deleted":4,"is_public":20,"is_downloadable":20,"audit_status":20,"page_count":21,"language":22,"language_code":23,"site_id":24,"html_lang":23,"table_of_contents":25,"faqs":26,"seo_title":27,"seo_description":14,"update_tm":28,"read_time":29},119248,7971461740886,"Theodore","https://ap-avatar.wpscdn.com/davatar_3d24733baf745e90a7e4bdd5f77d97b2",8,"Research & Report","Predictive Density Combination Using Bayesian Machine Learning","Bayesian predictive synthesis (BPS) provides a framework for combining predictive distributions under model uncertainty. This paper generalizes parametric BPS by using interpretable Bayesian tree-based machine learning to combine competing probabilistic forecasts. The method improves forecast accuracy and interpretability through two macroeconomic applications: combining euro-area GDP growth density forecasts from the Survey of Professional Forecasters, and synthesizing U.S. inflation density forecasts from many simple regression models.","INTERNATIONAL ECONOMIC REVIEW  \nVol. 0, No. 0, February 2025 DOI: 10.1111/iere.12759  \nPREDICTIVE DENSITY COMBINATION USING BAYESIAN MACHINE  \nLEARNING∗  \nBy Tony Chernis, Niko Hauzenberger, Florian Huber, Gary Koop, and James Mitchell  \nBank of Canada, Canada; University of Strathclyde, U.K. ; University of Salzburg, Austria;  \nFederal Reserve Bank of Cleveland, U.S.A.  \nBased on agent opinion analysis theory, Bayesian predictive synthesis (BPS) is a framework for combining predictive distributions in the face of model uncertainty. In this article, we generalize existing parametric implementations of BPS by showing how to combine competing probabilistic forecasts using interpretable Bayesian tree-based machine learning methods. We demonstrate the advantages of our approach—in terms of improved forecast accuracy and interpretability—via two macroeconomic forecasting applications. The first uses density forecasts for GDP growth from the euro area’s Survey of Professional Forecasters. The second combines density forecasts of U.S. inflation produced by many simple regression models.  \n1. introduction  \nForecasts of macroeconomic and financial variables are used by forward-looking decision makers, not least by central banks given that changes in their policy tools take time to have an impact on the macroeconomy. This requires them to set monetary policy targeting forecasts of future macroeconomic values (e.g., see Woodford, 2007) . Increasingly, as popularized by the Bank of England’s “fan charts” for inflation and GDP growth, these forecasts take the form of density forecasts and thus provide a full probabilistic representation of the uncertainty inherent in any single-valued (point) forecast. The decision maker is then aware of the risks associated with the forecast and can extract probability event forecasts of specific interest and/or credible intervals from the underlying density forecast.  \nAs well as the uncertainty associated with any given forecast, there is uncertainty about the“best” forecasting model. Competing density forecasts can come from different reduced-form or structural macroeconomic models estimated by Bayesian or frequentist methods, and/or be subjective and come from surveys. One way or another, all these multiple density forecasts are likely wrong or “incomplete,” to use terminology from Geweke (2010) discussed further below. So the decision maker should not select one single forecast alone. Instead, building on the idea of combining point forecasts (Bates and Granger, 1969), a growing literature has found that combining multiple density forecasts can be effective both in improving accuracy and in  \n∗ Manuscript received July 2024; revised November 2024 .  \nThe views expressed herein are solely those of the authors and do not necessarily reflect the views of the Bank of Canada, the Federal Reserve Bank of Cleveland, or the Federal Reserve System. We thank the editor, two anonymous referees, conference and seminar participants at MacroFor, Notre Dame, OeNB Freitagsseminar, Örebro, the SoFiE summer school, Surrey, including Christiane Baumeister, Drew Creal, Helmut Elsinger, Markus Knell, Malte Knüppel, Christine de Mol, Eoghan O’Neill, Michael Pfarrhofer, Luca Rossini, Anna Stelzer, Mattias Villani, and Mike West for helpful comments. Niko Hauzenberger gratefully acknowledges financial support from the Austrian Science Fund (FWF, ZK-35) and the Austrian Central Bank (Anniversary Fund, Project No. 18763) . Florian Huber gratefully acknowledges financial support from the Austrian Science Fund (FWF, ZK-35) . Please address correspondence to: Niko Hauzenberger, Department of Economics, University of Strathclyde, 16 Richmond St, Glasgow G1  \n1XQ, [U.K. E-mail:](U.K. E-mail: niko.hauzenberger@strath.ac.uk)[ niko.hauzenberger@strath.ac.uk](U.K. E-mail: niko.hauzenberger@strath.ac.uk).  \n1  \n© 2025 Bank of Canada and The Author(s) . International Economic Review published by Wiley Periodicals LLC on behalf of The Economics","cbCailokZNUkbEud","https://ap.wps.com/l/cbCailokZNUkbEud","pdf",673733,1,29,"English","en",105,"# Introduction\n## Forecasting under uncertainty and model incompleteness\n## Combining density forecasts and decision-making needs","[{\"question\":\"What problem does Bayesian predictive synthesis (BPS) address in forecasting?\",\"answer\":\"BPS addresses how to combine predictive distributions when the forecasting model is uncertain and no single forecast is fully reliable or complete.\"},{\"question\":\"How does this paper extend existing BPS implementations?\",\"answer\":\"It generalizes parametric BPS by combining competing probabilistic forecasts using interpretable Bayesian tree-based machine learning methods.\"},{\"question\":\"What are the two macroeconomic forecasting applications used to evaluate the approach?\",\"answer\":\"The paper first combines euro-area GDP growth density forecasts from the Survey of Professional Forecasters, and second combines U.S. inflation density forecasts produced by many simple regression models.\"}]","Predictive Density Combination Using Bayesian Machine Learning | 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