Conventional statistics and hierarchical Bayes: a discussion on the difference in philosophy

I will join and give a talk about my recent work on conservation genetics of spruce at Institute of Statistical Mathematics (ISM) on this Thursday. I have been preparing for the seminar for this weekend, and it will take for another couple of days.

To be honest, giving a talk at ISM is the kind of work that I'd like to avoid. Unlike to a meeting of ecologists, audiences come from various scientific backgrounds, although the title of the seminar is like "statistics and field ecology". How could I appeal to ecologists and mathematicians simultaneously?

For this time, I have one idea to establish my talk. It is about differences in philosophy between conventional statistical tests and statistical models, especially hierarchical Bayes (HB) models.

Thanks to good textbooks for ecologists and softwares such as WinBUGS, HB have widely spread among ecologists for last couple of years. On the other hand, as long as I know, the most of researchers who intended to use HB did not notice to differences in philosophy between conventional statistics and HB. They thought HB was just an improvement of conventional statistics. Mathematically, it may be true for some cases. But I'd like to emphasize the difference in the way to analyze the data.

Conventional statistics such as t-test summarlize the data to simple form, like "there was significant difference between two values". Then, researchers discuss about processes of interest from those significant differences among values. In this case, data can be analyzed without any prior hypothesis.

On the contrary, statistical models such as HB fits the prior hypothesis on the process of interest (or the model) to data. Then, researchers examine the shape of the fitted model. In this case, the model should be exist prior to analysis.

If I contrast those methods in their philosophy, I would say, conventional statistics is inductive, but HB is deductive.

This difference is not serious in the simple statistical models such as linear regression, ANOVA and GLM. Since the shape of the model is limited, researchers usually do not care about the process of interest, but only care about significances of coefficients in the model. Simple statistical models can be used like conventional statistical tests.

However, as the model become flexible, researchers must pay attention to the shape of the process of interest prior to analysis. HB can model complex processes very flexibly, and can integrate multiple processes which interact each others. In this case, the significance of individual parameter is no longer important, rather the behavior of entire process is important.

Unfortunately, some researchers did not noticed this difference, and still care about the "significance" of individual parameters in the large complex model without considering the entire behavior of the model. The reason they still care about the "significance" is probably because "significance" is easy to understand, and they do not have idea to discuss the result from HB.

In my talk, I'd like to show one example to discuss the result from HB. That is quantitative prediction of the process under multiple scenarios. Actually, the result is still insufficient, and it needs more suggestions. I would be happy if I discuss about above my idea and my results there.