# Conditional Dependencies and Position Fixing
## 4 Random Data Evaluation  
In random data evaluation, the aim is at the discovery of certain patterns included within the available sets of their instances. Upgrading histograms is usually the first step of the analyses. A histogram consists of bins or cells that are represented as adjacent rectangles. The histogram displays the proportion of cases that fall into each bin. Although histograms are popular and widely used, attempts to judge or calculate their quality or value are rather scarce. Histograms should be subjected to either intuitive or objective evaluation. The MTE, with its probability assignments, stipulates their impartial evaluation. The differentiations refer to their bin heights and ranges, as well as to the structure expansion. The uncertainty refers to a certain feature within the discussed scope that is considered constant within a particular domain. The number of items with the same or almost the same value of the feature defines the uncertainty. In this view, the uncertainty is related to the distinguishability. There are more indistinguishable abscissa points presented in Histogram (b) of Figure 3 than in Histogram (a) (see depicted bins in the right part of the figure). Thus, Histogram (a) contains a less amount of uncertainty than Histogram (b). We can use the diversity in the bin heights as a factor to measure the distinguishability. The average number of cases that fall below and above the horizontal central line of a histogram is the objective measure of the bin diversity. The inserted numbers in Figure 3 are the respective metrics for the presented cases. The greater the figure, the \"better\" the histogram. The total of all the points that fall above and below the presented horizontal line may be zero when there is a uniform distribution of the feature, which is in line with the popular understanding of uncertainty. We can perceive of doubtfulness as the thinking that something might be  
Figure 2: (a) Instance of observation with its distribution set; (b) horizontal- and vertical-axis histograms; (c) horizontal- and vertical-axis converted histograms. somewhere within a given scope, but there is no hint as to where. A histogram with the same cell heights is extremely unreliable. The total of the instances below and above the central line is zero. Relative rather than absolute uncertainty is often of primary importance. Position fixing is an example of a problem in which the relativity of the uncertainties really matters. The idea is to establish the grades that affect the final solution by each piece of evidence compared with other ones. The relative weight of the contribution to the final solution is an important issue. Given a set of histograms and the range and bin height for each structure, we can calculate the adequate measures. We can obtain the relative deflection and result uncertainty attributed to the \(i\)-th structure with the following formula:  
\[ \begin{array}{c}\Delta_{Hi}=\frac{g_{Hmax}-g_{Hi}}{g_{Hmax}}\\ \Theta_{Hi}=\Theta_{H\text{s}}+\Delta_{Hi}*\Theta_{H\text{s}}\end{array} , \tag{1}\]  
where \(g_{Hmax}\) is the maximum bin height measure for the histograms involved, calculated as the average number of cases that fall below and above the medium value, and the following holds: \(g_{Hmax}>0\) (the greater the value, the more diversified the histogram) (see Figure 3 for illustration); \(g_{Hi}\) is the bin height measure for the \(i\)-th histogram; \(\Theta_{H\text{s}}\) is the subjectively valued minimal uncertainty regarding the bin height measure for the histograms involved. As mentioned above, the number of items with features of the same value defines the uncertainty. Thus, considering two histograms with the same numbers of bins and different bin widths, one can assume that the wider structure embeds greater uncertainty. Histogram (a) in Figure 4 contains a smaller amount of uncertainty than Histogram (b). Figure 4: Interpretation of histogram uncertainty with respect to bin widths: (**a**) better-quality histogram; (**b**) worse-quality histogram.