I have started to think about what I want to say on *Statistical Engineering* at the RSS conference in Brighton next month. I have been thinking a lot about the iterative learning cycle involving the interchange between inductive and deductive logic; as statisticians, do we pay enough attention to this distinction? It seems to me that the scientific context of the problems we are involved in solving should play a central role in this iteration. I will say something about this with regard to engineering problems.... but what do statisticians working in other fields think about this? Your thoughts ahead of conference would be welcome...

Tim Davis

Empirical (inductive) models in the context of engineering statistics can be viewed as approximations to the respective deductive (albeit often unknown) models resulting from the fundamental laws of physics & math that govern the behavior of engineering systems. As such, relevant pieces of deductive knowledge can indeed be helpful in hypothesis formulation, predictor selection, etc. Other fields of applied statistics, such as, for example, in biological, agricultural or social sciences may not have a luxury of a well developed fundamental mathematical apparatus. (I'm unaware of any first principle equation describing, for instance, human's blood count or political party preference.) Hence, they have to rely almost exclusively on inductive reasoning and empirical models . All the above is, of course, IMHO. --Vasiliy Krivtsov

ReplyDeleteI would say that deductive logic should be the preferred first line of attack in problem solving, both in engineering and science. This is because thought experiments are often the easiest way to understand if your ideas make sense. I am not a statistician, but supervising PhD students I am often struck by their reluctance to sit down for a moment and contemplate the structure of their problem and the logical consequences of their ideas for solutions. They often prefer to start out by building complex models with all the little constants and parameters in place, to get 'the correct answer'. I suspect this is a general problem in engineering and science, due to how we, in the teaching system, teach students to attack every textbook problem with a mathematical equation. I keep repeating the words of Box, Hunter, and Hunter to my students: Statistics is not a substitute for subject matter knowledge. We should use our subject knowledge as much as possible, because it makes it easier to understand what the data are telling us. And, to be able to solve any real (unstructured) problem, we have to learn how to think about problems (find their structure). The deductive logic of thought experiments is the starting point here.

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