Numerical Evidence

Context

Instead of a specific probability distribution, an observation or scenario may exist in the form of a single numerical value, which means that we need to set Numerical Evidence.
For instance, a stock market analyst may wish to examine how other stocks performed given a hypothetic period of time during which the average of the daily returns of JNJ was −1%. Naturally, this requires that we set evidence on JNJ that has an expected (mean) value of −0.01 (=−1%).
However, this task is not as straightforward as it may sound. The question will become apparent as we go through the steps to set this evidence.

Additionally, as was the case with Probabilistic Evidence, we have to choose the type of validation, but we now have three options under Observation Type:
- No Fixing, which is the same as the green button , i.e., validation with static likelihood.
- Fix Mean, which is the same as the purple button , except that the likelihood is dynamically computed to maintain the mean value, although the probability distribution can change as a result of setting additional evidence.
- Fix Probabilities, which is the same as the purple button , i.e., validation with dynamic likelihood.

Apart from setting the validation method, we also need to choose the Distribution Estimation Method as we need to come up with a distribution that produces the desired mean value.
Needless to say, there is a great number of distributions that could potentially produce a mean value of −0.01. However, which one is appropriate?
To make a prudent choice, we first need to understand what the evidence represents.
Only then can we choose from the three available algorithms for generating the Target Distribution that will produce the Target Mean/Value.

If the Numerical Evidence is equal to the current expected value, using MinXEnt (a) or Value Shift(b) will not change the distribution. Using the Binary algorithm (c), however, will return a different distribution (except in the context of a binary node).