... chapter2.1
This chapter first appeared as a technical report [RY96a]. 
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... hierarchy.2.2
We must remark that it is important to realize that convergence to a limiting value for the FGM is not the same as convergence of its parameters. 
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... dictionary3.1
The work described in this chapter was first described in [RY96b] and will appear in [RY97a] 
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...Matlab4.1
Mathematica is a product of Wolfram Research, and Matlab is a product of the Math Works Inc. 
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...Purify4.2
Purify is a product of Pure Software Inc. 
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... Unix4.3
Unix is a registered trademark of AT&T 
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... probability4.4
Strictly we mean the value of a nonnegative functional, since FGMs need not be viewed as stochastic models. Nevertheless, since so many applications are probabalistic, we will use the term ``probability.'' 
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... chapter5.1
This chapter first appeared as a technical report [RY96c] 
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... point5.2
The inverse image is a unique point because $S(\delta)$is invertible. 
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... uniform-continuously5.3
and in fact nearly linearly for small $\delta$. 
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... radius.5.4
A maximum exists because entries in $S$ corresponding to covariance diagonal, are nonnegative, preventing many negative values from being representable. 
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... harm6.1
That is, for a given optimization problem, the global optimum over the enlarged parameter set, is at least as good as the global optimum for the original problem 
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... estimation6.2
Maximum-likelihood estimation is sometimes understood to include the assumption that the distribution from which the sample is drawn is a member of the parameterized family under consideration. We are modelers and assume that nature can be only approximately described by our densities. We therefore do not imagine that there is a true value $\Phi^*$which must be estimated. We simply seek the best fit of our model, to the observed data. 
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