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Negative and Likelihood Findings

Negative and likelihood findings are findings with some uncertainty attached.

Negative:  A positive finding is knowledge that some variable definitely has a particular value.  However, you may know that the value of a node is not some state without knowing what its value is.

This is called a negative finding.  For example, say the node “Temperature” can take on the values cold, medium, and hot.  You may obtain information that the temperature is not hot, although it doesn’t distinguish between medium and cold at all.  That is a single negative finding.

If you receive another negative finding that the temperature is not medium, then you can conclude that it is cold.  So several negative findings can be equivalent to one positive finding.

Likelihood:  A third type of finding is a likelihood finding (also known as “virtual evidence”).  In this case you receive uncertain information about the value of some discrete node.  It could be from an imperfect sensor, or from a friend who is not always right.

Say you have a thermo sensor to measure “Temperature”, which is designed so that when the temperature is hot it is supposed to turn on.  In actual practice you find that when the temperature is cold the sensor never goes on, when the temperature is medium it goes on 10% of time, and when it is hot it always goes on.  If at a certain time you observe the sensor on, and want to enter this finding into the Temperature node, then you do so as a likelihood finding.

A likelihood finding consists of one probability for each state of the node, which is the probability that the actual observation would be made if the node were in that state.  For our temperature example, the likelihood finding would be (0, 0.1, 1).  A common mistake is to think that the likelihood is the probability of the state given the observation made (in which case the numbers would have to add to one), but it is the other way around.

Entering:  You can enter a negative finding for a belief-bar node of a compiled net, by holding down the shift key while you click on the name of the finding you know its not.  You can enter a likelihood finding for a node by choosing “Likelihood” from its findings menu.  You will then be queried for the likelihood numbers.

You can enter a negative finding by entering a likelihood finding consisting of all 1s, except a single 0 for the state that you know it’s not.  By having more than a single 0 you can enter several negative findings at the same time.

Accumulating:  Whenever you enter a positive finding for a node, all the old findings for that node are automatically retracted first.  However, if you enter more than one likelihood finding for a node, you will be queried if you first want the previous finding(s) to be removed, or if you want them to accumulate.  By letting them accumulate you can enter several independent pieces of evidence (e.g. imperfect observations) for the same node.  If they are not conditionally independent given the observed node, and it is too inaccurate to approximate them as independent, then they should be entered by adding child nodes to the observed node (one for each observation), connecting them together to show the dependency, and then entering positive findings for the child nodes.

Locating:  To find all the nodes with negative or likelihood findings, use Edit Select Nodes Likelihood Findings.
 

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