parameter value. However, the first change has a log-odds change of .**811, while the second**
one has a log-odds change of .**981.**
Finally, the result can be used to obtain a better intuitive understanding of parameter changes that do or do not matter, a topic which we will discuss **in the next section.**

## 4. Changes That (Don'T) Matter

We now return to a central question: When do changes in network parameters matter and when do they not matter? As we mentioned earlier, there have been experimental studies investigating the robustness of belief networks against parameter changes (Pradhan et al.,
1996). But we have also shown very simple and intuitive examples where networks can be very sensitive to small parameter changes. This calls for **a better understanding of the** effect of parameter changes on queries, so one can intuitively **sort out situations in which**
such changes do or do not matter. Our goal in this section is to **further develop such** an understanding by looking more closely into some of the implications of Theorem 3.3. We start first by highlighting the difference between this theorem and previous results on sensitivity analysis.

## 4.1 Network-Specific Sensitivity Analysis

One of the main differences between our results and other sensitivity analysis approaches is that we do not need to know the belief network, and hence, do **not need to perform** inference. To clarify this difference, we compare it with the sensitivity function approach
(van der Gaag & Renooij, 2001), which computes the sensitivity function that relates a query, f(x), and a parameter, x, **in the form:**

$$f(x)={\frac{a\cdot x+b}{c\cdot x+d}},$$

where a, b, c, d **are constants that depend on the given network and are computed by** performing inference as suggested by van der Gaag and Renooij (2001).

Going back to Example 2.1, we can express the query Pr (fire | smoke, report**) as a**
function of the parameter x = Pr (smoke | fire**). The function is given by:**

$$f(x)={\frac{0.00}{0.9684\cdot x}}$$
0.9684 · x + 0.**003165**
,
and we plot this function in Figure 6. We can see that at the current parameter value .01, the query value is .25, but if we decrease it to .003, the query value increases to .**5, which**
is one of the suggested parameter changes by SamIam.

However, we can find a bound on the relations between the query and the parameter using Theorem 3.3, without doing inference on the network (and without knowing the network). For example, by changing the current parameter value from .01 to .**003, the new**
query value will be within the bounds of .09 and .**53. On the other hand, if we want the** query value to increase to .5, we have to at least decrease the parameter value from .**01 to**
.003, or increase it to .03.