Towards a New Information-Dynamic Framework for Measuring Evidence in Biology

E.T. Jaynes, Ariel Caticha and others have suggested deep connections between statistical mechanics and certain aspects of statistical inference, tethering the two fields together via an information-based maximum entropy principle. In this talk I propose purely information-based interpretations of both the 1^st and 2^nd Laws of thermodynamics. This allows us to ask and answer a question that has gone begging until now: What is the analogue of temperature (T) on the information/inferential side? I argue that the physical quantity T has a familiar, but surprising, interpretation as statistical evidence. Moreover, this formulation provides a template for measuring evidence on an absolute (Kelvin) scale for the first time. The new “information dynamic” paradigm that emerges from this work also shows that our standard measures of evidence, including the p-value, patently lack calibration: A given change in any particular measure does not always correspond to the same amount of change in the strength of evidence; different measures are on fundamentally different scales; and any one of them may even indicate decreasing strength of evidence while the evidence strength is actually increasing. This almost certainly helps to explain why reliance on p-values often proves to be misleading.