Loss-based Bayesian Prediction


This project proposes a new paradigm for prediction. Using state-of-the-art computational methods, the project aims to produce accurate, fit-for-purpose predictions which, by design, reduce the loss incurred when a prediction is inaccurate. The new paradigm will produce significant benefits for all fields in which the consequences of predictive inaccuracy are severe.


Project background and aims

Predicting the future value of any quantity of interest, be it economic, financial, or arising from the physical world, carries with it the risk of error: the predicted value is likely to differ from the value that eventuates. The impact of prediction error varies according to context. For example, under-predicting a large fall in the value of a financial portfolio may have severe consequences (including insolvency), whilst failing to predict demand for electricity that exceeds capacity is consequential, given the economic and societal impact of black-outs. This project proposes a completely new approach, in which predictions are expressly designed to reduce the problem-specific “loss’’ that can result from prediction error. We refer to this approach as “loss-based’’ prediction.

In particular, we use the Bayesian statistical paradigm to seamlessly produce predictive probability distributions that are expressly designed to minimize the loss incurred when predictions are inaccurate. By shifting the focus of forecast production away from the standard “model-based’’ approach to a “loss-based’’ approach, predictions produced under our loss-based paradigm display a higher degree of robustness and accuracy, in terms of the user-chosen “loss’’, than methods that are focused on a general measure of prediction accuracy. Consequently, by designing the predictions around a problem specific “loss’’, the resulting forecasts are purpose-built to reduce the prediction error associated with the specific problem at hand. Benefits are anticipated in all spheres in which the consequences of prediction error are significant.

The proposed shift in prediction paradigm will have significant practical benefits in all spheres where the consequences of prediction error are significant. In addition, this research yields new theoretical insights regarding the limiting behaviour of these new predictive distributions, including their ability to mimic the true, unknown predictive. Practical implementation of this approach relies on novel computational methods that allow users to easily access the predictive distributions constructed under this framework.

While there are a host of areas where the application of these methods would be particularly useful, we highlight two examples with clear practical benefits:

  1. Portfolio analysis: The goal of portfolio analysis is to determine an optimal allocation of weights across possible investment choices. The portfolio allocation problem exhibits different solutions depending on the chosen definition of “optimality”. Unlike existing approaches, this approach to forecasting allows us to target our predictions towards achieving the precise form of optimality that is sought, rather than just a general criteria that may or may not be related to the portfolio problem at hand.
  2. Energy demand: Point forecasts that minimize loss functions which, in turn, assign differential weights to under - and over - prediction of energy demand, has received significant attention, and represents the different societal and financial costs associated with energy demand. Our approach allows for the full production of distributional forecasts under these, sometimes involved, classes of loss functions, and allows us to more easily document the uncertainty associated with such forecasts relative to other methods.

Funding information

  • Australian Research Council DP200101414 (2020-2022)