Bayesian model averaging for river flow prediction

Abstract

This paper explores the practical benefits of Bayesian model averaging, for a problem with limited data, namely future flow of five intermittent rivers. This problem is a useful proxy for many others, as the limited amount of data only allows tuning of small, simple models. Bayesian model averaging is theoretically a good way to cope with these difficulties, but it has not been widely used on this and similar problems. This paper uses real-world data to illustrate why. Bayesian model averaging can indeed give a better prediction, but only if the amount of data is small — if the data is so limited that it agrees a wide range of different models (instead of consistent with only a few near-identical models), then the weighted votes of those diverse models in Bayesian model averaging will (on average) give a better prediction than the single best model. In contrast, plenty of data can fit only one or a few very similar models; since they’ll vote the same way, Bayesian model averaging will give no practical improvement. Even with limited data that agrees with a range of models, the improvement is not very big large, but it is the direction of the improvement that stands out as a help for forecasting. Working around these caveats lets us better predict river floods, and similar problems with limited data.