# 统计代写|贝叶斯分析代写Bayesian Analysis代考|STAT4102

## 统计代写|贝叶斯分析代写Bayesian Analysis代考|Labeled Nodes and Comparative Expressions

A labeled node is one whose set of states is simply a set of labels. A number of examples of such labeled nodes are shown in Table 9.1. Irrespective of what the names of the labels are, they have no underlying semantic meaning. So, for example, in the node Injury there is no underlying assumption that, say, “broken bone” is better or worse than “damaged ligament” or that “broken bone” is better or worse than “other.” All that is assumed by the model is that the states are different. This makes sense for the nodes Student, Injury, Sport, Program language, Die roll, and Bank loss in the table. It makes less sense for the other nodes because implicitly in those cases we would like the states of the nodes to carry some other meaning. By declaring a node like Water level to be labeled (which, as we will see, is possible but not recommended), there is no implicit knowledge that the state “medium” represents a higher level than the state “low.” Any meaning has to be provided manually by the modeler in the way the NPT is defined. That was what we did in the way we specified the NPT in the example in Box 9.1. For example, in the NPT, if the water level at the start of the day was “medium,” then the probability the water level at the end of the day was “high,” given 2-5 mm of rainfall, is greater than the probability the water level is “high” if it started the day “low.”

In most cases when you create a labeled node there is little alternative but to define the NPT manually cell by cell.

## 统计代写|贝叶斯分析代写Bayesian Analysis代考|NoisyAND Function for Boolean Nodes

Just as NoisyOR provides a highly flexible “noisy” version of the OR function there is an analogous NoisyAND for the AND function (see Box $9.8$ for the formal definition). Again we assume there is a set of factors (represented as Boolean variables $X_1, \ldots, X_n$ ) that can be considered as “causes” independently of each other in terms of their effect on some Boolean variable $Y$. Consider the following example:

A soccer team generally only wins a match if all of the team “components”-the keeper, defence, midfield and attack-all play well. However, there is a “luck” factor which means that (rarely) they might win if some, or even all, components do not play well. Similarly because of “luck” there is a chance that they will not win even if all of them play well. In addition to luck some components are more critical than others. For example, although it is rare to win if even one component does not play well it is especially critical that attack plays well in order to win.

Assuming that each of the team components are independent of each other in terms of their effect on the match result (Figure 9.22), this type of problem is easily modelled as a noisyAND function. As with noisyOR we must specify a weight value (between 0 and 1 ) associated with each parent representing its “criticality” and a leak value (between 0 and 1) representing the “luck” factor.

For example, using the AgenaRisk syntax, we can define the NPT for “team wins” as:
noisyand (Keeper, 0.7, Defence, 0.9, Midfield, $0.8$, Attack, 1, 0.05)
If you run the model you will find that, when all of the components are true there is still a $0.05$ probability (equal to the leak value) that the team will not win. To see the impact of the weights, note that when all the components are true except for “Attack plays well” which is false, then the probability of winning is 0 because the “Attack” component has weight 1 (i.e. maximum criticality). However, because “Midfield” is not as critical there is still a small probability of winning when “Midfield plays well” is false and the other components are true.

## 统计代写|贝叶斯分析代写Bayesian Analysis代考|NoisyAND Function for Boolean Nodes

noisyand (Keeper, 0.7, Defence, 0.9, Midfield,0.8, Attack, 1, 0.05)

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