On the existence of both more-model-structure and less-model-structure trends in statistical modeling:

There are two broad lines of development active at the moment arising out of mainstream statistical ideas. The first is the invention of models strongly tied to subject-matter considerations, representing underlying dependencies, and their analysis, perhaps by Markov chain Monte Carlo methods. In fields where subject-matter considerations are largely qualitative, we see a development based on Markov graphs and their generalizations. These methods in effect assume, subject in principle to empirical test, more and more about the phenomena under study. By contrast, there is an emphasis on assuming less and less via, for example, kernel estimates of regression functions, generalized additive models and so on. There is a need to be clearer about the circumstances favoring these two broad approaches, synthesizing them where possible.