Skip to main content
×
Home
    • Aa
    • Aa

Improving Predictions using Ensemble Bayesian Model Averaging

  • Jacob M. Montgomery (a1), Florian M. Hollenbach (a2) and Michael D. Ward (a2)
Abstract

We present ensemble Bayesian model averaging (EBMA) and illustrate its ability to aid scholars in the social sciences to make more accurate forecasts of future events. In essence, EBMA improves prediction by pooling information from multiple forecast models to generate ensemble predictions similar to a weighted average of component forecasts. The weight assigned to each forecast is calibrated via its performance in some validation period. The aim is not to choose some “best” model, but rather to incorporate the insights and knowledge implicit in various forecasting efforts via statistical postprocessing. After presenting the method, we show that EBMA increases the accuracy of out-of-sample forecasts relative to component models in three applied examples: predicting the occurrence of insurgencies around the Pacific Rim, forecasting vote shares in U.S. presidential elections, and predicting the votes of U.S. Supreme Court Justices.

Copyright
Corresponding author
e-mail: michael.d.ward@duke.edu (corresponding author)
Footnotes
Hide All

Authors' note: For generously sharing their data and models with us, we thank Alan Abramowitz, James Campbell, Robert Erikson, Ray Fair, Douglas Hibbs, Michael Lewis-Beck, Andrew D. Martin, Kevin Quinn, Stephen Shellman, Charles Tien, and Christopher Wlezien. We especially want to thank Adrian Raftery and Brendan Nyhan for their encouragement and feedback as this project evolved. The editor and the reviewers of Political Analysis provided especially salient suggestions that substantially improved our research.

Footnotes
Linked references
Hide All

This list contains references from the content that can be linked to their source. For a full set of references and notes please see the PDF or HTML where available.

S. J. Andriole , and R. A. Young 1977. Toward the development of an integrated crisis warning system. International Studies Quarterly 21: 107–50.

S. J. Andriole , and R. A. Young 1977. Toward the development of an integrated crisis warning system. International Studies Quarterly 21: 107–50.

J. S. Armstrong 2001. Combining forecasts. In Principles of forecasting: A handbook for researchers and practitioners, ed. J. S. Amstrong Norwell, MA: Kluwer Academic.

J. S. Armstrong 2001. Combining forecasts. In Principles of forecasting: A handbook for researchers and practitioners, ed. J. S. Amstrong Norwell, MA: Kluwer Academic.

L. M. Bartels 1997. Specification uncertainty and model averaging. American Journal of Political Science 41: 641–74.

L. M. Bartels 1997. Specification uncertainty and model averaging. American Journal of Political Science 41: 641–74.

D. S. Bennett , and A. C. Stam 2009. Revisiting predictions of war duration. Conflict Management and Peace Science 26: 256–67.

D. S. Bennett , and A. C. Stam 2009. Revisiting predictions of war duration. Conflict Management and Peace Science 26: 256–67.

J. E. Berg , F. D. Nelson , and T. A. Rietz 2008. Prediction market accuracy in the long run. International Journal of Forecasting 24: 285300.

J. E. Berg , F. D. Nelson , and T. A. Rietz 2008. Prediction market accuracy in the long run. International Journal of Forecasting 24: 285300.

V. J. Berrocal , A. E. Raftery , T. Gneiting , and R. C. Steed 2010. Probabilistic weather forecasting for winter road maintenance. Journal of the American Statistical Association 105: 522–37.

V. J. Berrocal , A. E. Raftery , T. Gneiting , and R. C. Steed 2010. Probabilistic weather forecasting for winter road maintenance. Journal of the American Statistical Association 105: 522–37.

P. T. Brandt , M. Colaresi , and J. R. Freeman 2008. The dynamics of reciprocity, accountability, and credibility. Journal of Conflict Resolution 52: 343–74.

P. T. Brandt , M. Colaresi , and J. R. Freeman 2008. The dynamics of reciprocity, accountability, and credibility. Journal of Conflict Resolution 52: 343–74.

P. T. Brandt , J. R. Freeman , and P. A. Schrodt 2011b. Real-time, time-series forecasting of inter- and intra-state political conflict. Conflict Management and Peace Science 28: 4164.

P. T. Brandt , J. R. Freeman , and P. A. Schrodt 2011b. Real-time, time-series forecasting of inter- and intra-state political conflict. Conflict Management and Peace Science 28: 4164.

G. W. Brier 1950. Verification of forecasts expressed in terms of probability. Monthly Weather Review 78: 13.

G. W. Brier 1950. Verification of forecasts expressed in terms of probability. Monthly Weather Review 78: 13.

W. A. Brock , S. N. Durlauf , and K. D. West 2007. Model uncertainty and policy evaluation: Some theory and empirics. Journal of Econometrics 136: 629–64.

W. A. Brock , S. N. Durlauf , and K. D. West 2007. Model uncertainty and policy evaluation: Some theory and empirics. Journal of Econometrics 136: 629–64.

L. B. Brown , and H. W. Chappell 1999. Forecasting presidential elections using history and polls. International Journal of Forecasting 15: 127–35.

L. B. Brown , and H. W. Chappell 1999. Forecasting presidential elections using history and polls. International Journal of Forecasting 15: 127–35.

B. Bueno de Mesquita 2011. A new model for predicting policy choices: Preliminary tests. Conflict Management and Peace Science 28: 6585.

B. Bueno de Mesquita 2011. A new model for predicting policy choices: Preliminary tests. Conflict Management and Peace Science 28: 6585.

J. E. Campbell 1992. Forecasting the presidential vote in the states. American Journal of Political Science 36: 386407.

J. E. Campbell 1992. Forecasting the presidential vote in the states. American Journal of Political Science 36: 386407.

J. E. Campbell , and K. A. Wink 1990. Trial-heat forecasts of the presidential vote. American Politics Research 18: 251–69.

J. E. Campbell , and K. A. Wink 1990. Trial-heat forecasts of the presidential vote. American Politics Research 18: 251–69.

A. P. Dawid 1982. The well-calibrated Bayesian (with discussion). Journal of the American Statistical Association 77: 605–13.

A. P. Dawid 1982. The well-calibrated Bayesian (with discussion). Journal of the American Statistical Association 77: 605–13.

S. de Marchi , C. Gelpi , and J. D. Grynaviski 2004. Untangling neural nets. American Political Science Review 98: 371–8.

S. de Marchi , C. Gelpi , and J. D. Grynaviski 2004. Untangling neural nets. American Political Science Review 98: 371–8.

W. Enders , and T. M. Sandler 2005. After 9/11: Is it all different now? Journal of Conflict Resolution 49: 259–77.

W. Enders , and T. M. Sandler 2005. After 9/11: Is it all different now? Journal of Conflict Resolution 49: 259–77.

J. D. Fearon , and D. D. Laitin 2003. Ethnicity, insurgency, and civil war. American Political Science Review 97: 7590.

J. D. Fearon , and D. D. Laitin 2003. Ethnicity, insurgency, and civil war. American Political Science Review 97: 7590.

S. A. Feder 2002. Forecasting for policy-making in the post-Cold War period. Annual Review of Political Science 5: 111–25.

S. A. Feder 2002. Forecasting for policy-making in the post-Cold War period. Annual Review of Political Science 5: 111–25.

M. Forthcoming Feldkircher 2012. Forecast combination and Bayesian model averaging: A prior sensitivity analysis. Journal of Forecasting.

M. Forthcoming Feldkircher 2012. Forecast combination and Bayesian model averaging: A prior sensitivity analysis. Journal of Forecasting.

C. Fraley , A. E. Raftery , and T. Gneiting 2010. Calibrating multimodel forecast ensembles with exchangeable and missing members using Bayesian model averaging. Monthly Weather Review 138: 190202.

C. Fraley , A. E. Raftery , and T. Gneiting 2010. Calibrating multimodel forecast ensembles with exchangeable and missing members using Bayesian model averaging. Monthly Weather Review 138: 190202.

J. R. Freeman , and B. L. Job 1979. Scientific forecasts in international relations: Problems of definition and epistemology. International Studies Quarterly 23: 113–43.

J. R. Freeman , and B. L. Job 1979. Scientific forecasts in international relations: Problems of definition and epistemology. International Studies Quarterly 23: 113–43.

J. Geer , and R. R. Lau 2006. Filling in the blanks: A new method for estimating campaign effects. British Journal of Political Science 36: 269–90.

J. Geer , and R. R. Lau 2006. Filling in the blanks: A new method for estimating campaign effects. British Journal of Political Science 36: 269–90.

J. Gill 2004. Introduction to the special issue. Political Analysis 12: 647–74.

J. Gill 2004. Introduction to the special issue. Political Analysis 12: 647–74.

T. Gneiting , and A. E. Raftery 2007. Strictly proper scoring rules, prediction, and estimation. Journal of the American Statistical Association 102: 359–78.

T. Gneiting , and A. E. Raftery 2007. Strictly proper scoring rules, prediction, and estimation. Journal of the American Statistical Association 102: 359–78.

B. D. Greenhill , M. D. Ward , and A. Sacks 2011. The separation plot: A new visual method for evaluating the fit of binary data. American Journal of Political Science 55: 9901002.

B. D. Greenhill , M. D. Ward , and A. Sacks 2011. The separation plot: A new visual method for evaluating the fit of binary data. American Journal of Political Science 55: 9901002.

T. R. Gurr , and M. I. Lichbach 1986. Forecasting internal conflict: A competitive evaluation of empirical theories. Comparative Political Studies 19: 338.

T. R. Gurr , and M. I. Lichbach 1986. Forecasting internal conflict: A competitive evaluation of empirical theories. Comparative Political Studies 19: 338.

T. S. Hamill , J. S. Whitaker , and X. Wei 2004. Ensemble reforecasting: Improving medium-range forecast skill using retrospective forecasts. Monthly Weather Review 132: 1434–47.

T. S. Hamill , J. S. Whitaker , and X. Wei 2004. Ensemble reforecasting: Improving medium-range forecast skill using retrospective forecasts. Monthly Weather Review 132: 1434–47.

T. Hastie , R. Tibshirani , and J. Friedman 2009. The elements of statistical learning: Data mining, inference, and prediction. New York: Springer.

T. Hastie , R. Tibshirani , and J. Friedman 2009. The elements of statistical learning: Data mining, inference, and prediction. New York: Springer.

L. Hausegger , and L. Baum 1999. Inviting congressional action: A study of Supreme Court motivations in statutory interpretation. American Journal of Political Science 43: 162–85.

L. Hausegger , and L. Baum 1999. Inviting congressional action: A study of Supreme Court motivations in statutory interpretation. American Journal of Political Science 43: 162–85.

D. A. Hibbs 2000. Bread and peace voting in U.S. presidential elections. Public Choice 104: 149–80.

D. A. Hibbs 2000. Bread and peace voting in U.S. presidential elections. Public Choice 104: 149–80.

D. K. Hildebrand , J. D. Laing , and H. Rosenthal 1976. Prediction analysis in political research. American Political Science Review 70: 509–35.

D. K. Hildebrand , J. D. Laing , and H. Rosenthal 1976. Prediction analysis in political research. American Political Science Review 70: 509–35.

J. Huisman , L. Breuer , H. Bormann , A. Bronstert , B. Croke , H.-G. Frede , T. Gräff , L. Hubrechts , A. Jakeman , G. Kite , et al. 2009. Assessing the impact of land-use change on hydrology by ensemble modeling (LUCHEM) II: Ensemble combinations and predictions. Advances in Water Resources 32: 147–58.

J. Huisman , L. Breuer , H. Bormann , A. Bronstert , B. Croke , H.-G. Frede , T. Gräff , L. Hubrechts , A. Jakeman , G. Kite , et al. 2009. Assessing the impact of land-use change on hydrology by ensemble modeling (LUCHEM) II: Ensemble combinations and predictions. Advances in Water Resources 32: 147–58.

K. Imai , and G. King 2004. Did illegal overseas absentee ballots decide the 2000 U.S. presidential election? Perspectives on Politics 2: 537–49.

K. Imai , and G. King 2004. Did illegal overseas absentee ballots decide the 2000 U.S. presidential election? Perspectives on Politics 2: 537–49.

B. Jerome , V. Jerome , and M. S. Lewis-Beck 1999. Polls fail in France: Forecasts of the 1997 legislative election. International Journal of Forecasting 15: 163–74.

B. Jerome , V. Jerome , and M. S. Lewis-Beck 1999. Polls fail in France: Forecasts of the 1997 legislative election. International Journal of Forecasting 15: 163–74.

G. King , and L. Zeng 2001. Improving forecasts of state failure. World Politics 53: 623–58.

G. King , and L. Zeng 2001. Improving forecasts of state failure. World Politics 53: 623–58.

D. E. Klein , and R. J. Hume 2003. Fear of reversal as an explanation of lower court compliance. Law & Society Review 37: 579606.

D. E. Klein , and R. J. Hume 2003. Fear of reversal as an explanation of lower court compliance. Law & Society Review 37: 579606.

G. A. Krause 1997. Voters, information heterogeneity, and the dynamics of aggregate economic expectations. American Journal of Political Science 41: 1170–200.

G. A. Krause 1997. Voters, information heterogeneity, and the dynamics of aggregate economic expectations. American Journal of Political Science 41: 1170–200.

D. Leblang , and S. Satyanath 2006. Institutions, expectations, and currency crises. International Organization 60: 245–62.

D. Leblang , and S. Satyanath 2006. Institutions, expectations, and currency crises. International Organization 60: 245–62.

M. S. Lewis-Beck 2005. Election forecasting: Principles and practice. British Journal of Politics & International Relations 7: 145–64.

M. S. Lewis-Beck 2005. Election forecasting: Principles and practice. British Journal of Politics & International Relations 7: 145–64.

K. Lock , and A. Gelman 2010. Bayesian combination of state polls and election forecasts. Political Analysis 18: 337–48.

K. Lock , and A. Gelman 2010. Bayesian combination of state polls and election forecasts. Political Analysis 18: 337–48.

D. Madigan , and A. E. Raftery 1994. Model selection and accounting for model uncertainty in graphical models using Occam's window. Journal of the American Statistical Association 89: 1535–46.

D. Madigan , and A. E. Raftery 1994. Model selection and accounting for model uncertainty in graphical models using Occam's window. Journal of the American Statistical Association 89: 1535–46.

A. D. Martin , K. M. Quinn , T. W. Ruger , and P. T. Kim 2004. Competing approaches to predicting Supreme Court decision-making. Perspectives on Politics 2: 761–7.

A. D. Martin , K. M. Quinn , T. W. Ruger , and P. T. Kim 2004. Competing approaches to predicting Supreme Court decision-making. Perspectives on Politics 2: 761–7.

T. C. McCandless , S. E. Haupt , and G. S. Young 2011. The effects of imputing missing data on ensemble temperature forecasts. Journal of Computers 6: 162–71.

T. C. McCandless , S. E. Haupt , and G. S. Young 2011. The effects of imputing missing data on ensemble temperature forecasts. Journal of Computers 6: 162–71.

S.-K. Min , and A. Hense 2006. A Bayesian approach to climate model evaluation and multi-model averaging with an application to global mean surface temperatures from IPCC AR4 coupled climate models. Geophysical Research Letters 33: L08708.

S.-K. Min , and A. Hense 2006. A Bayesian approach to climate model evaluation and multi-model averaging with an application to global mean surface temperatures from IPCC AR4 coupled climate models. Geophysical Research Letters 33: L08708.

S.-K. Min , D. Simonis , and A. Hense 2007. Probabilistic climate change predictions applying Bayesian model averaging. Philosophical Transactions of the Royal Society A: Mathematical, Physical, and Engineering Sciences 365: 2103–16.

S.-K. Min , D. Simonis , and A. Hense 2007. Probabilistic climate change predictions applying Bayesian model averaging. Philosophical Transactions of the Royal Society A: Mathematical, Physical, and Engineering Sciences 365: 2103–16.

J. M. Montgomery , and B. Nyhan 2010. Bayesian model averaging: Theoretical developments and practical applications. Political Analysis 18: 245–70.

J. M. Montgomery , and B. Nyhan 2010. Bayesian model averaging: Theoretical developments and practical applications. Political Analysis 18: 245–70.

M. D. Muhlbaier , and R. Polikar 2007. An ensemble approach for incremental learning in nonstationary environments. Multiple Classifier Systems 4472: 490500.

M. D. Muhlbaier , and R. Polikar 2007. An ensemble approach for incremental learning in nonstationary environments. Multiple Classifier Systems 4472: 490500.

S. P. O'Brien 2002. Anticipating the good, the bad, and the ugly: An early warning approach to conflict and instability analysis. Journal of Conflict Resolution 46: 791811.

S. P. O'Brien 2002. Anticipating the good, the bad, and the ugly: An early warning approach to conflict and instability analysis. Journal of Conflict Resolution 46: 791811.

S. P. O'Brien 2010. Crisis early warning and decision support: Contemporary approaches and thoughts on future research. International Studies Review 12: 87104.

S. P. O'Brien 2010. Crisis early warning and decision support: Contemporary approaches and thoughts on future research. International Studies Review 12: 87104.

S. E. Page 2008. Uncertainty, difficulty, and complexity. Journal of Theoretical Politics 20: 115–49.

S. E. Page 2008. Uncertainty, difficulty, and complexity. Journal of Theoretical Politics 20: 115–49.

S. E. Page , L. M. Sander , and C. M. Schneider-Mizell 2007. Conformity and dissonance in generalized voter models. Journal of Statistical Physics 128: 1279–87.

S. E. Page , L. M. Sander , and C. M. Schneider-Mizell 2007. Conformity and dissonance in generalized voter models. Journal of Statistical Physics 128: 1279–87.

J. C. Pevehouse , and J. S. Goldstein 1999. Serbian compliance or defiance in Kosovo? Statistical analysis and real-time predictions. Journal of Conflict Resolution 43: 538–46.

J. C. Pevehouse , and J. S. Goldstein 1999. Serbian compliance or defiance in Kosovo? Statistical analysis and real-time predictions. Journal of Conflict Resolution 43: 538–46.

A. E. Raftery 1995. Bayesian model selection in social research. Sociological Methodology 25: 111–63.

A. E. Raftery 1995. Bayesian model selection in social research. Sociological Methodology 25: 111–63.

A. E. Raftery , T. Gneiting , F. Balabdaoui , and M. Polakowski 2005. Using Bayesian model averaging to calibrate forecast ensembles. Monthly Weather Review 133: 1155–74.

A. E. Raftery , T. Gneiting , F. Balabdaoui , and M. Polakowski 2005. Using Bayesian model averaging to calibrate forecast ensembles. Monthly Weather Review 133: 1155–74.

A. E. Raftery , M. Kárný , and P. Ettler 2010. Online prediction under model uncertainty via dynamic model averaging: Application to a cold rolling mill. Technometrics 52: 5266.

A. E. Raftery , M. Kárný , and P. Ettler 2010. Online prediction under model uncertainty via dynamic model averaging: Application to a cold rolling mill. Technometrics 52: 5266.

A. E. Raftery , and Y. Zheng 2003. Long-run performance of Bayesian model averaging. Journal of the American Statistical Association 98: 931–8.

A. E. Raftery , and Y. Zheng 2003. Long-run performance of Bayesian model averaging. Journal of the American Statistical Association 98: 931–8.

M. J. Richards , and H. M. Kritzer 2002. Jurisprudential regimes in Supreme Court decision-making. American Political Science Review 96: 305–20.

M. J. Richards , and H. M. Kritzer 2002. Jurisprudential regimes in Supreme Court decision-making. American Political Science Review 96: 305–20.

T. W. Ruger , P. T. Kim , A. D. Martin , and K. M. Quinn 2004. The Supreme Court Forecasting Project: Legal and political science approaches to predicting Supreme Court decision-making. Columbia Law Review 104: 1150–210.

T. W. Ruger , P. T. Kim , A. D. Martin , and K. M. Quinn 2004. The Supreme Court Forecasting Project: Legal and political science approaches to predicting Supreme Court decision-making. Columbia Law Review 104: 1150–210.

G. Schneider , N. P. Gleditsch , and S. Carey 2011. Forecasting in international relations: One quest, three approaches. Conflict Management and Peace Science 28: 514.

G. Schneider , N. P. Gleditsch , and S. Carey 2011. Forecasting in international relations: One quest, three approaches. Conflict Management and Peace Science 28: 514.

J. A. Segal , and A. D. Cover 1989. Ideological values and the votes of U.S. Supreme Court Justices. American Political Science Review 83: 557–65.

J. A. Segal , and A. D. Cover 1989. Ideological values and the votes of U.S. Supreme Court Justices. American Political Science Review 83: 557–65.

J. M. Sloughter , T. Gneiting , and A. E. Raftery 2010. Probabilistic wind-speed forecasting using ensembles and Bayesian model averaging. Journal of the American Statistical Association 105: 2535.

J. M. Sloughter , T. Gneiting , and A. E. Raftery 2010. Probabilistic wind-speed forecasting using ensembles and Bayesian model averaging. Journal of the American Statistical Association 105: 2535.

J. M. Sloughter , A. E. Raftery , T. Gneiting , and C. Fraley 2007. Probabilistic quantitative precipitation forecasting using Bayesian model averaging. Monthly Weather Review 135: 3209–20.

J. M. Sloughter , A. E. Raftery , T. Gneiting , and C. Fraley 2007. Probabilistic quantitative precipitation forecasting using Bayesian model averaging. Monthly Weather Review 135: 3209–20.

R. L. Smith , C. Tebaldi , D. Nychka , and L. O. Mearns 2009. Bayesian modeling of uncertainty in ensembles of climate models. Journal of the American Statistical Association 104: 97116.

R. L. Smith , C. Tebaldi , D. Nychka , and L. O. Mearns 2009. Bayesian modeling of uncertainty in ensembles of climate models. Journal of the American Statistical Association 104: 97116.

D. R. Songer , J. A. Segal , and C. M. Cameron 1994. The hierarchy of justice: Testing a principal-agent model of Supreme Courtcircuit court interactions. American Journal of Political Science 38: 673–96.

D. R. Songer , J. A. Segal , and C. M. Cameron 1994. The hierarchy of justice: Testing a principal-agent model of Supreme Courtcircuit court interactions. American Journal of Political Science 38: 673–96.

J. E. Vincent 1980. Scientific prediction versus crystal ball gazing: Can the unknown be known? International Studies Quarterly 24: 450–4.

J. E. Vincent 1980. Scientific prediction versus crystal ball gazing: Can the unknown be known? International Studies Quarterly 24: 450–4.

J. A. Vrugt , M. P. Clark , C. G. Diks , Q. Duan , and B. A. Robinson 2006. Multi-objective calibration of forecast ensembles using Bayesian model averaging. Geophysical Research Letters 33: L19817.

J. A. Vrugt , M. P. Clark , C. G. Diks , Q. Duan , and B. A. Robinson 2006. Multi-objective calibration of forecast ensembles using Bayesian model averaging. Geophysical Research Letters 33: L19817.

J. A. Vrugt , C. G. Diks , and M. P. Clark 2008. Ensemble Bayesian model averaging using Markov chain Monte Carlo sampling. Environmental Fluid Mechanics 8: 579–95.

J. A. Vrugt , C. G. Diks , and M. P. Clark 2008. Ensemble Bayesian model averaging using Markov chain Monte Carlo sampling. Environmental Fluid Mechanics 8: 579–95.

M. D. Ward , B. D. Greenhill , and K. M. Bakke 2010. The perils of policy by p-value: Predicting civil conflict. Journal of Peace Research 47: 363–75.

M. D. Ward , B. D. Greenhill , and K. M. Bakke 2010. The perils of policy by p-value: Predicting civil conflict. Journal of Peace Research 47: 363–75.

M. D. Ward , R. M. Siverson , and X. Cao 2007. Disputes, democracies, and dependencies: A re-examination of the Kantian peace. American Journal of Political Science 51: 583601.

M. D. Ward , R. M. Siverson , and X. Cao 2007. Disputes, democracies, and dependencies: A re-examination of the Kantian peace. American Journal of Political Science 51: 583601.

P. F. Whiteley 2005. Forecasting seats from votes in British general elections. British Journal of Politics & International Relations 7: 165–73.

P. F. Whiteley 2005. Forecasting seats from votes in British general elections. British Journal of Politics & International Relations 7: 165–73.

J. H. Wright 2008. Bayesian model averaging and exchange rate forecasts. Journal of Econometrics 146: 329–41.

J. H. Wright 2008. Bayesian model averaging and exchange rate forecasts. Journal of Econometrics 146: 329–41.

J. H. Wright 2009. Forecasting U.S. inflation by Bayesian model averaging. Journal of Forecasting 28: 131–44.

J. H. Wright 2009. Forecasting U.S. inflation by Bayesian model averaging. Journal of Forecasting 28: 131–44.

X. Zhang , R. Srinivasan , and D. Bosch 2009. Calibration and uncertainty analysis of the SWAT model using genetic algorithms and Bayesian model averaging. Journal of Hydrology 374: 307–17.

X. Zhang , R. Srinivasan , and D. Bosch 2009. Calibration and uncertainty analysis of the SWAT model using genetic algorithms and Bayesian model averaging. Journal of Hydrology 374: 307–17.

Recommend this journal

Email your librarian or administrator to recommend adding this journal to your organisation's collection.

Political Analysis
  • ISSN: 1047-1987
  • EISSN: 1476-4989
  • URL: /core/journals/political-analysis
Please enter your name
Please enter a valid email address
Who would you like to send this to? *
×
MathJax

Metrics

Altmetric attention score

Full text views

Total number of HTML views: 0
Total number of PDF views: 27 *
Loading metrics...

Abstract views

Total abstract views: 106 *
Loading metrics...

* Views captured on Cambridge Core between 4th January 2017 - 23rd August 2017. This data will be updated every 24 hours.