. Tutorial : Defining Probability for Science . Neil A . Thacker

Preface For many years I have recommended the short reference on statistics [2] and similar introductory texts to my students and researchers. Barlow's book can be considered a fair reflection of the main stream view of the topic [14]. Yet despite this, I generally gave the caveat that I disagreed with some parts of the book and indeed the conventional view. On a recent reading of the book I concluded that many of my objections were confined to chapter 7, and in particular the discussion regarding definitions of probability. I therefore decided to write this document to provide a record of how I would have presented these sections, for distribution within our group. The document explains a physics based approach motivated by scientific considerations of uniqueness, falsifiability and quantitation. These considerations are intended to eliminate aspects of 'black magic' or arbitrariness, a view which seems to me to be important yet lacking from general texts. It summarises what I regard as the reasons I work as I do when designing and testing algorithms and systems for computer vision and image processing. Although this document is self contained, the interested reader might wish to look at the original version first, before reading mine. You would then be in a good position to decide if you want to continue to take the conventional view of the topic, or take the rather bold step of being more critical and forming some conclusions. Introduction The accepted method for all scientific data analysis is probability and statistics. Although all statistical techniques are related to probability the very definition of this word is not generally comprehended. In my view, the resulting lack of clarity on this issue leads to misunderstanding and inappropriate application of techniques. In subject areas where the analysis of data is the dominant activity, real progress is hampered by a lack of concensus regarding best scientific practice. This situation is not generally improved if we look in standard statistical reference texts for more clarity. The dominant attitude to statistical methods being that we can largely pick various measures out of thin air and worry about how they behave on data afterwards, rather than deriving techniques from principles based upon the characteristics of the data. There is in my view an over-tolerance of contradictory opinions and general failure to resolve fundamental issues. To do better we must start with a solid understanding of probability. …