Philosophy of Statistical Sciences: The Roles of Mathematics and Statistical Models in Estimation and Other Inductive Inferences

Statistical models have been used to test scientific hypotheses in ecological studies.The use of statistical model is critical when crucial quantities of interest are not directly measurable but statistically estimable from the acquired data.Both mathematical models and statistical models belong to mathematics, nevertheless, their roles in scientific inferences differ.A mathematical model quantitatively expresses a qualitatively expressed scientific hypothesis from which a scientist can deductively derive quantitative predictions.On the other hand, a statistical model mathematically expresses a stochastic data-generating process which allows the analyst to connect a mathematical model with data through probability distributions.Compared with mathematical models, statistical models have been insufficiently examined by philosophers, and philosophical analyses of statistical issues have focused on classical statistical tests and Bayesian inferences that are distant from up-to-date Bayesian statistics.Further, some statistical terminologies are differently used between philosophers and statisticians.Interdisciplinary studies between philosophy and statistical sciences such as ecology should consider the implications of modern statistical approaches.