Advances in Mathematical Biosciences

Dear Colleagues,

In recent decades, mathematical and statistical methods have increased greatly in importance in health and biomedical research. There are two main approaches to mathematically infer knowledge about unknown quantities from observed data. The most common approach in current biomedical research is frequentist statistics, in which observations are evaluated with respect to their compatibility with pre-specified hypotheses on the values of unknown quantities. The other approach, historically founded in the works of Bayes and Laplace in the 1700s but now rising to renewed prominence due to computational and methodological developments, is Bayesian statistics, in which observations are used to update a priori assumed distributions of probable values of unobserved quantities.

In many respects, these two approaches show a striking symmetry, answering similar questions by different probabilistic concepts. On the other hand the abstract philosophical interpretation of these two paradigms of probability theory can be seen as explicitly anti-symmetric in reversing the assumed causal role between unobserved quantities and observations. This apparent conflict is of great interest, not only from a purely mathematical standpoint, but also as it greatly influences the interpretation of biomedical research results, and hence it can directly impact decisions on both individual treatments as well as public health.

Hence, this Special Issue is soliciting contributions, including original research papers, reviews, and commentaries, on current mathematical developments of both Bayesian and frequentist inference, their interplay, and their impacts on applied health and biomedical research.

Dr. Sören Möller
Guest Editor

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