Simulated Bayesian Updating

GoldSim provides an advanced feature for dynamically revising distributions during a simulation using "simulated Bayesian updating". This feature is most valuable when using GoldSim to simulate a project of some kind (e.g., developing a new product, building a new facility). It is often the case that as a project progresses, additional information about uncertain variables is acquired. From the project operator's point of view, their uncertainty is decreasing, and hence as time progresses, the probability distributions used in their model of the project are converging towards the true values of the variables. As their knowledge increases they are better able to make appropriate decisions for the project's path forward.

Basic Concepts

Every realization of the model produces a different sampled True_Ore_Grade. In the realization shown above, the True_Ore_Grade was sampled to be just less than 8. As can be seen, the initial mean and standard deviation of the Estimated_Ore_Grade are 10 and 3, respectively (the same as the statistics for the True_Ore_Grade distribution). However, starting at 10 days, more information is learned about the ore grade. This has two effects on the Estimated_Ore_Grade distribution: 1) the standard deviation is reduced; and 2) the mean approaches the true value. Whenever new information is obtained (in this example, every 10 days), the standard deviation is further reduced, and the mean moves closer to the true value. At 50 days (when it is assumed that "perfect information" is obtained), the standard deviation goes to zero, and the mean converges to the true value. 

Example Application: Decision Based on Ore Grade Quality

We assume that four studies regarding the ore grade are carried out (at 10, 20, 30 and 40 days), each reducing the Uncertainty Reduction Factor by 0.2, such that perfect information regarding the ore grade is never obtained.

Assume that the estimated ore grade must be greater than 12 for the project to proceed. Because the ore grade cannot be known with certainty, however, this decision must be based on probabilities. In particular, when simulating the project, it is assumed that the project will proceed if and only if we have at least 50% confidence that the ore grade is greater than 12 (i.e., we will proceed if the probability of the ore grade being at least 12 exceeds 50%).

To Open the Model File:

1. Start GoldSim
2. Click on the File and select Open Example...
3. Browse to General Examples --> Stochastic
4. Select the file called BayesianUpdating.gsm