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The systematic use of trees for knowledge...
Bayesian model
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In a “binary” tree, all non-leaf nodes have...
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Algorithm TREE-CLASS: Begin at root node....
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Organizing the tree in the diagnostic...
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That is, the probability comparing the...
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Cue interactions go beyond the bivariate...
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The systematic use of trees for knowledge representation can be used for fast and frugal decisions. Tree-structured schemes are ubiquitous tools for organising and representing knowledge.

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Bayesian model

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In a “binary” tree, all non-leaf nodes have exactly two children; in general trees nodes may have any number of children. The leaf nodes of a classification tree represent a “partition” of the set of objects into classes defined by the answers to the questions. Each leaf node has an associated class label, to be assigned to all objects for which the appropriate answers are given to the questions associated with the leaf’s ancestor nodes.

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Algorithm TREE-CLASS: Begin at root node. Execute rule associated with current node to decide which arc to traverse. Proceed to child at end of chosen arc. If child is a leaf node, assign to object the class label associated with node and STOP. Otherwise, go to (2).

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Organizing the tree in the diagnostic direction produces a much more efficient classification strategy. This tree has two major advantages over the tree in Figure 1. for a diagnostic task. First, we can follow the TREE-CLASS algorithm for the first two steps before becoming stuck at the second-to-last level above the leaf nodes. For example, for the hypothetical woman with M+ and U+ described above, we would be able to place her among the 114 women at the leftmost node on the third level from the top.

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That is, the probability comparing the leaves of Figures 1 and 2 reveals that they are the same. That is, they contain the same numbers, although their ordering is different, as is the topology of their connection to the rest of the tree. One might question whether a natural sampler would partition the population in the causal or the diagnostic direction.

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Cue interactions go beyond the bivariate contingencies that are typically observed in the naive (unconditional) linear model framework. A straightforward demonstration of the interaction effect is given by what is now called “Meehl’s paradox” (after its initial description by the clinician-statistician Paul E. Meehl, one of the pioneers in the field of clinical decision making, 1950).