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.

The history of statistics is filled with many controversies, in which the prime focus has been the difference in the “interpretation of probability” between Frequentist and Bayesian theories. Many philosophical arguments have been elaborated to examine the problems of both theories based on this dichotomized view of statistics, including the well-known stopping-rule problem and the catch-all hypothesis problem. However, there are also several “hybrid” approaches in theory, practice, and philosophical analysis. This poses many fundamental questions. This paper reviews three cases and argues that the interpretation problem of probability is insufficient to begin a philosophical analysis of the current issues in the field of statistics. A novel viewpoint is proposed to examine the relationship between the stopping-rule problem and the catch-all hypothesis problem.

Good statistical practice is an integral part of modern science. Null hypothesis significance testing (NHST) is the most widely used statistical method. Nevertheless, misuse and misinterpretation of NHST are widespread, and severe criticisms have been levelled against NHST. In this study, I revisit the primary documents of Fisher, Neyman, and E. Pearson relating to statistical testing. I compare Fisher’s significance testing with Neyman-Pearson hypothesis testing and clarify their thoughts on statistical testing. I hope this study will guide researchers in stopping and thinking about p-value statistics before abandoning it.

Undoubtedly, whether to accept the likelihood principle or not has been, and still is, one of the most crucial issues for philosophical debates on statistics, though interests in it are waning from statistical debates due to general preferences for more practical issues of statistics. The principle says all you need in parameter analyses of a statistical model is found in likelihood for the data obtained. Bayesians and likelihoodists have traditionally regarded this principle as fundamental, declining any forms of statistics which violate it. Frequentism, on the other hand, try to reject this principle, upholding error probability as a more crucial factor for statistical analyses. But arguments made so far on the likelihood principle still seem to stay on those as to what principle we prefer to choose in statistical analyses. The validity of this principle seems to have never been explored fully enough through the arguments on either side. In this paper, I briefly review how these arguments have been made and show some difficulty in maintaining the principle. I think this has some impact upon statistical practices as well.

Bayesian models of human object perception have been widely studied. Helmholtz’s idea of perception as unconscious inference is formalized by Bayes’ theorem. Human object perception is now widely called Bayesian inference or statistical inference, while obtaining a Bayesian quantitative model of human perceptual learning has become a primary goal for the consciousness scientists who utilize Helmholtz’s idea.

Helmholtz’s model uses Bayesian inference (updating of degree of belief) as a scientific model. In this study, I perform a philosophical analysis of Helmholtz’s scientific model from the viewpoint of philosophical Bayesianism. I apply potential problems of philosophical Bayesianism concerning the updating rule to the Bayesian perceptual learning model. There are at least two problems concerning the updating rule in the philosophy literature: the so-called catch-all hypothesis problem and the old-evidence problem (Glymour 1980). I especially discuss the application of the old-evidence problem to Helmholtz’s model, and thereby claim that the model has a potential deficiency. Additionally, I offer a clue to the solution to the old-evidence problem in the Bayesian model.

Despite the fact that Bayesian inference has been widely used in science, it seems that inadequate attempts have been made to link scientific and philosophical Bayesian inference. This study aims to provide this link.