Scientific and statistical inferences build heavily on explicit, parametric models, and often with good reasons. However, the limited scope of parametric models and the increasing complexity of the studied systems in modern science raise the risk of model misspecification. Therefore, I examine alternative, data-based inference techniques, such as bootstrap resampling. I argue that their neglect in the philosophical literature is unjustified: they suit some contexts of inquiry much better and use a more direct approach to scientific inference. Moreover, they make more parsimonious assumptions and often replace theoretical understanding and knowledge about mechanisms by careful experimental design. Thus, it is worthwhile to study in detail how nonparametric models serve as inferential engines in science.Keywords: models, data, inductive inference, nonparametric statistics, bootstrap resampling
Probabilistic ModelingModeling plays a key role in empirical science, especially when overarching theories cannot be applied. Many efforts in science focus on constructing, comparing and revising models of physical entities, phenomena and processes. Bohr's model of the atom, Volterra's model of predator-prey populations and the random walk model for the motion of molecules in a fluid are among the most popular ones. Models enable us to recognize fundamental relations between physical quantities, to understand the effects of causal interventions and to generalize observed effects to more complex and realistic cases. Often, their construction is triggered by concrete puzzles: For instance, Volterra (1926) developed his mathematical model of predator-prey population dynamics in response to the surprising shortage of adriatic fish after World War I. Volterra's model started from abstract considerations, but its predictions were found to be in stunning agreement with reality (see Weisberg's (2007) case study for more details). The way the Volterra model has been developed, refined and transferred to other scientific inquiries exemplifies a general strategy: to set up mathematically tractable models which capture fundamental mechanisms of the underlying system, and to gradually amend and refine them in order to account for the complexity of large-scale systems in the real world. In other words, models allow us to discover characteristic regularities (e.g. cycles in the population dynamics) as well as to explain concrete phenomena, such as "why does a disruption in fishing activity increase the predator/prey ratio?".Hence, it is not surprising that philosophers of science have been spending a lot of paper on the various features of model-building. In particular, they studied † Contact information: