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• Soft Evidence - Mean Values (5.3)

# Context  # New Feature: Binary and Value Shift Distribution Estimation Three Distribution Estimation Methods are now available for generating probability distributions so that a Target Mean Value can be achieved.

Example

Let's use the following node Radio as an example. The marginal mean value this node's distribution is 0.498. For the purpose of this example, we now arbitrarily set a Target Mean Value of 0.598. Theoretically, a large number of distributions could be generated that all have the desired mean value of 0.598.

The following panels show how the three available estimation methods generate different distributions, which each achieve the same Target Mean Value of 0.598.

For MinXEnt, the target distribution is chosen such that the Cross-Entropy is minimized between the original probability distribution and the target distribution (which produce the Marginal Mean Value and the Target Mean Value respectively). In the context of optimization, you have to select the MinXEnt estimation when the Drivers do not correspond to Direct Driver nodes but rather to their effects (the Direct Drivers are hidden parents of the Drivers in the model). This is the case, for instance, when a node represents a consumer's satisfaction with regard to product attribute, rather than a measure of the product attribute itself, e.g. the satisfaction with fuel economy (5-very satisfied, 4-somewhat satisfied,..., 1-not at all satisfied) as opposed to the fuel economy itself (MPG, l/100km).

The MinXEnt estimation can also be interpreted as a "realistic" or "easy-to-achieve" distribution, as the "distance" from original distribution to the target distribution is minimized.

The Target Mean Value is generated by interpolating between two adjacent state values. In the context of optimization, you have to select the Binary estimation when the Drivers correspond to Direct Drivers nodes. Here, Soft Evidence does not represent uncertainty. Rather, it is used to generate continuous values by means of interpolation (compare to membership degrees in Fuzzy Logic). Casually speaking, Binary Evidence is a "mix" between Hard Evidence and Soft Evidence.

The Target Mean Value is generated by shifting the values of each particle by the exact same amount. Similarly to MinXEnt, Value Shift estimation can be used for optimization when the Drivers do not correspond to Direct Driver nodes but rather to their effects. With Value Shift estimation, the Target Mean Value is achieved by shifting the rating of each particle by the same amount. For instance, in a satisfaction survey analysis, this estimation simulates changes on Hidden Direct Drivers that have the exact same effect (e.g. +1) on each respondent, regardless of what the original satisfaction level of the respondent was. No Fixing is the option for setting static likelihood distributions. Once the probability distribution has been found by using one of the three Distribution Estimation Methods, the corresponding likelihood distribution is computed and associated to the node.

Fix Means and Fix Probabilities are the options for setting dynamic likelihood distributions, i.e. distributions that are dynamically updated after each new finding to prevent changes of the target mean values. Fix Mean is only based on the MinXEnt estimation. It allows updating the distribution after each new finding to minimize the cross-entropy between the final distribution and the posterior distribution (the one that takes into account the current pieces of evidence).