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The Bayesian Approach to Forecasting


Demand Planning Supply Chain Management Forecasting

The Bayesian approach uses a combination of a priori and post priori knowledge to model time series data. That is, we know if we toss a coin we expect a probability of 0.5 for heads or for tails—this is a priori knowledge. Therefore, if we take a coin and toss it 10 times, we will expect five heads and five tails. But if the actual result is ten heads, we may lose confidence in our a priori knowledge. This may be explained by a change to the coin that was introduced to alter the probability—this is post priori knowledge. Another example of post priori knowledge is future price change or marketing promotion that is likely to alter the forecast.

The main principle of forecasting is to find the model that will produce the best forecasts, not the best fit to the historical data. The model that explains the historical data best may not be best predictive model for several reasons:
• The future may not be described by the same probability as the past. Perhaps neither the past nor the future is a sample from any probability distribution. The time series could be nothing more than a non-recurrent historical record.
• The model may involve too many parameters. Overfitted models could account for noise or other features in the data that are unlikely to extend into the future.
• The error involved in fitting a large number of parameters may be damaging to forecast accuracy, even when the model is correctly specified.

In any of these cases, the model may fit the historical data very well, yet still forecast poorly, illustrating that there is a vast difference between its internal and external validities.

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