(In this set of notes we will use boldface symbols to denote random variables, and non-boldface symbols for deterministic objects.) By itself, such an interpretation is little more than a change of notation. However, the power of this interpretation becomes more apparent when one then imports ...
And so on, until we reach the fourth element in the second row, which is represented by A24. Matrices. There are several ways to represent a matrix symbolically. The simplest is to use a boldface letter, such as A, B, or C. Thus, A might represent a 2 x 4 matrix, as illustrated...
Then one would expect a “randomly” selected arithmetic progression in (using the convention that random variables will be in boldface) to be contained in with probability about . This is not true in general, however it was shown by Ben and myself that for any , there was a set of ...
In summary: What is a tensor and what are some of its applications?A tensor is a geometric object which is linear function of its variables which maps into scalars. For example: Let g be the metric tensor. Its a function of two vectors. The boldface notation represents the tensor itself ...
U is a common cause of X and Y; Z affects the outcome Yonly through X; Z does not share common causes with Y; Z has a direct causal effect on X. In the above, we have marked syntactical terms relating to the graph itself (the “map”) in boldface and terms involving external con...
We find that out of the 30 possible tests, only one difference is significant at the five percent confidence level (the one that appears in boldface). Consequently, it is possible to pool the data. Table 7. Two-sided p-values of the Z-tests that compare the mean disapproval rates ...