IDEAS home Printed from https://ideas.repec.org/a/wly/japmet/v38y2023i4p577-595.html
   My bibliography  Save this article

Bayesian optimization of hyperparameters from noisy marginal likelihood estimates

Author

Listed:
  • Oskar Gustafsson
  • Mattias Villani
  • Pär Stockhammar

Abstract

Bayesian models often involve a small set of hyperparameters determined by maximizing the marginal likelihood. Bayesian optimization is an iterative method where a Gaussian process posterior of the underlying function is sequentially updated by new function evaluations. We propose a novel Bayesian optimization framework for situations where the user controls the computational effort and therefore the precision of the function evaluations. This is a common situation in econometrics where the marginal likelihood is often computed by Markov chain Monte Carlo or importance sampling methods. The new acquisition strategy gives the optimizer the option to explore the function with cheap noisy evaluations and therefore find the optimum faster. The method is applied to estimating the prior hyperparameters in two popular models on US macroeconomic time series data: the steady‐state Bayesian vector autoregressive (BVAR) and the time‐varying parameter BVAR with stochastic volatility.

Suggested Citation

  • Oskar Gustafsson & Mattias Villani & Pär Stockhammar, 2023. "Bayesian optimization of hyperparameters from noisy marginal likelihood estimates," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 38(4), pages 577-595, June.
  • Handle: RePEc:wly:japmet:v:38:y:2023:i:4:p:577-595
    DOI: 10.1002/jae.2961
    as

    Download full text from publisher

    File URL: https://doi.org/10.1002/jae.2961
    Download Restriction: no

    File URL: https://libkey.io/10.1002/jae.2961?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. Sungbae An & Frank Schorfheide, 2007. "Bayesian Analysis of DSGE Models—Rejoinder," Econometric Reviews, Taylor & Francis Journals, vol. 26(2-4), pages 211-219.
    2. Villani, Mattias & Kohn, Robert & Nott, David J., 2012. "Generalized smooth finite mixtures," Journal of Econometrics, Elsevier, vol. 171(2), pages 121-133.
    3. Marta Banbura & Domenico Giannone & Lucrezia Reichlin, 2010. "Large Bayesian vector auto regressions," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 25(1), pages 71-92.
    4. Newey, Whitney K & West, Kenneth D, 1987. "Hypothesis Testing with Efficient Method of Moments Estimation," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 28(3), pages 777-787, October.
    5. John Geweke, 1999. "Using simulation methods for bayesian econometric models: inference, development,and communication," Econometric Reviews, Taylor & Francis Journals, vol. 18(1), pages 1-73.
    6. Geweke, John & Keane, Michael, 2007. "Smoothly mixing regressions," Journal of Econometrics, Elsevier, vol. 138(1), pages 252-290, May.
    7. Carriero, Andrea & Kapetanios, George & Marcellino, Massimiliano, 2012. "Forecasting government bond yields with large Bayesian vector autoregressions," Journal of Banking & Finance, Elsevier, vol. 36(7), pages 2026-2047.
    8. Dimitrios P. Louzis, 2019. "Steady‐state modeling and macroeconomic forecasting quality," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 34(2), pages 285-314, March.
    9. Sungbae An & Frank Schorfheide, 2007. "Bayesian Analysis of DSGE Models," Econometric Reviews, Taylor & Francis Journals, vol. 26(2-4), pages 113-172.
    10. Domenico Giannone & Michele Lenza & Giorgio E. Primiceri, 2015. "Prior Selection for Vector Autoregressions," The Review of Economics and Statistics, MIT Press, vol. 97(2), pages 436-451, May.
    11. Pär Stockhammar & Pär Österholm, 2017. "The Impact of US Uncertainty Shocks on Small Open Economies," Open Economies Review, Springer, vol. 28(2), pages 347-368, April.
    12. Chib S. & Jeliazkov I., 2001. "Marginal Likelihood From the Metropolis-Hastings Output," Journal of the American Statistical Association, American Statistical Association, vol. 96, pages 270-281, March.
    13. repec:ulb:ulbeco:2013/13388 is not listed on IDEAS
    14. MacDonald, Blake & Ranjan, Pritam & Chipman, Hugh, 2015. "GPfit: An R Package for Fitting a Gaussian Process Model to Deterministic Simulator Outputs," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 64(i12).
    15. Marta Banbura & Domenico Giannone & Lucrezia Reichlin, 2010. "Large Bayesian vector auto regressions," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 25(1), pages 71-92.
    16. Malin Adolfson & Jesper Linde & Mattias Villani, 2007. "Bayesian Analysis of DSGE Models—Some Comments," Econometric Reviews, Taylor & Francis Journals, vol. 26(2-4), pages 173-185.
    17. Karlsson, Sune, 2013. "Forecasting with Bayesian Vector Autoregression," Handbook of Economic Forecasting, in: G. Elliott & C. Granger & A. Timmermann (ed.), Handbook of Economic Forecasting, edition 1, volume 2, chapter 0, pages 791-897, Elsevier.
    18. Gustafsson, Peter & Stockhammar, Pär & Österholm, Pär, 2016. "Macroeconomic effects of a decline in housing prices in Sweden," Journal of Policy Modeling, Elsevier, vol. 38(2), pages 242-255.
    19. Österholm, Pär, 2012. "The limited usefulness of macroeconomic Bayesian VARs when estimating the probability of a US recession," Journal of Macroeconomics, Elsevier, vol. 34(1), pages 76-86.
    20. Dieppe, Alistair & van Roye, Björn & Legrand, Romain, 2016. "The BEAR toolbox," Working Paper Series 1934, European Central Bank.
    21. John Geweke, 1999. "Using Simulation Methods for Bayesian Econometric Models," Computing in Economics and Finance 1999 832, Society for Computational Economics.
    22. Giorgio E. Primiceri, 2005. "Time Varying Structural Vector Autoregressions and Monetary Policy," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 72(3), pages 821-852.
    23. Mattias Villani, 2009. "Steady-state priors for vector autoregressions," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 24(4), pages 630-650.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Karlsson, Sune, 2013. "Forecasting with Bayesian Vector Autoregression," Handbook of Economic Forecasting, in: G. Elliott & C. Granger & A. Timmermann (ed.), Handbook of Economic Forecasting, edition 1, volume 2, chapter 0, pages 791-897, Elsevier.
    2. Sims, Christopher A. & Waggoner, Daniel F. & Zha, Tao, 2008. "Methods for inference in large multiple-equation Markov-switching models," Journal of Econometrics, Elsevier, vol. 146(2), pages 255-274, October.
    3. Warne, Anders & Coenen, Günter & Christoffel, Kai, 2010. "Forecasting with DSGE models," Working Paper Series 1185, European Central Bank.
    4. Ankargren Sebastian & Unosson Måns & Yang Yukai, 2020. "A Flexible Mixed-Frequency Vector Autoregression with a Steady-State Prior," Journal of Time Series Econometrics, De Gruyter, vol. 12(2), pages 1-41, July.
    5. Fuentes-Albero, Cristina & Melosi, Leonardo, 2013. "Methods for computing marginal data densities from the Gibbs output," Journal of Econometrics, Elsevier, vol. 175(2), pages 132-141.
    6. Chan, Joshua C.C., 2023. "Comparing stochastic volatility specifications for large Bayesian VARs," Journal of Econometrics, Elsevier, vol. 235(2), pages 1419-1446.
    7. Miranda-Agrippino, Silvia & Ricco, Giovanni, 2018. "Bayesian Vector Autoregressions," The Warwick Economics Research Paper Series (TWERPS) 1159, University of Warwick, Department of Economics.
    8. Koop, Gary & Korobilis, Dimitris, 2010. "Bayesian Multivariate Time Series Methods for Empirical Macroeconomics," Foundations and Trends(R) in Econometrics, now publishers, vol. 3(4), pages 267-358, July.
    9. Sebastian Ankargren & Mårten Bjellerup & Hovick Shahnazarian, 2017. "The importance of the financial system for the real economy," Empirical Economics, Springer, vol. 53(4), pages 1553-1586, December.
    10. Bekiros Stelios & Paccagnini Alessia, 2015. "Estimating point and density forecasts for the US economy with a factor-augmented vector autoregressive DSGE model," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 19(2), pages 107-136, April.
    11. repec:hal:spmain:info:hdl:2441/27od5pb99881folvtfs8s3k16l is not listed on IDEAS
    12. Bekiros, Stelios D. & Paccagnini, Alessia, 2014. "Bayesian forecasting with small and medium scale factor-augmented vector autoregressive DSGE models," Computational Statistics & Data Analysis, Elsevier, vol. 71(C), pages 298-323.
    13. repec:spo:wpmain:info:hdl:2441/27od5pb99881folvtfs8s3k16l is not listed on IDEAS
    14. Tim Oliver Berg, 2016. "Multivariate Forecasting with BVARs and DSGE Models," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 35(8), pages 718-740, December.
    15. Andrea Carriero & Todd E. Clark & Massimiliano Marcellino, 2016. "Large Vector Autoregressions with Stochastic Volatility and Flexible Priors," Working Papers (Old Series) 1617, Federal Reserve Bank of Cleveland.
    16. Carriero, Andrea & Clark, Todd E. & Marcellino, Massimiliano, 2019. "Large Bayesian vector autoregressions with stochastic volatility and non-conjugate priors," Journal of Econometrics, Elsevier, vol. 212(1), pages 137-154.
    17. Thomai Filippeli & Konstantinos Theodoridis, 2015. "DSGE priors for BVAR models," Empirical Economics, Springer, vol. 48(2), pages 627-656, March.
    18. Damian Stelmasiak & Grzegorz Szafrański, 2016. "Forecasting the Polish Inflation Using Bayesian VAR Models with Seasonality," Central European Journal of Economic Modelling and Econometrics, Central European Journal of Economic Modelling and Econometrics, vol. 8(1), pages 21-42, March.
    19. Dieppe, Alistair & van Roye, Björn & Legrand, Romain, 2016. "The BEAR toolbox," Working Paper Series 1934, European Central Bank.
    20. Hajargasht, Gholamreza & Rao, D.S. Prasada, 2019. "Multilateral index number systems for international price comparisons: Properties, existence and uniqueness," Journal of Mathematical Economics, Elsevier, vol. 83(C), pages 36-47.
    21. Andrea Carriero & Francesco Corsello & Massimiliano Marcellino, 2022. "The global component of inflation volatility," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 37(4), pages 700-721, June.
    22. Domenico Giannone & Michele Lenza & Giorgio E. Primiceri, 2015. "Prior Selection for Vector Autoregressions," The Review of Economics and Statistics, MIT Press, vol. 97(2), pages 436-451, May.

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:wly:japmet:v:38:y:2023:i:4:p:577-595. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Wiley Content Delivery (email available below). General contact details of provider: http://www.interscience.wiley.com/jpages/0883-7252/ .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.